In continuation to our session and theory of production and cost, we are going to cover a few more concepts today in today's session. So if you remember in the last couple of sessions, we are just discussing about the different type of production analysis. We started with short run production analysis and we discussed through the law of diminishing return and then again we started the return to scale, that is the long run analysis of production and there we check that how the scale differ with respect to change in the input and proportionately the change in the output. Then we discussed the case of producer equilibrium or so called the least cost input combination with the help of the two concept that is isoquant and isocost and through which how they reach the or how the firms or how the producer they reach the equilibrium. Then we discussed about the expansion path and economic region of production which talks about basically which one is the feasible region where the two inputs can be substituted one to another and that is the efficient region because by producing or by using less of input the producer is producing the desirable output. So in today's session we will see what are the different kind of production function mainly and mainly we talk about the Cub Douglas production function which is used more in economic analysis. Then again we will continue our discussion optimal input combination through a graphical representation how the graphical representation in case of a maximization of output and minimization of cost and again we will see that when there is a change in the input price whether it is the input price of the capital or input price of the labor how it changes. Then we will talk about numerical examples related to the law of diminishing return and return to scale how generally this the firm uses this law of diminishing returns or return to scale empirically whether it is really works that marginal product gets decreases and then it reaches the negative and whether there is a evidence of increasing decreasing and constant return to scale. So to start this today's discussion we will see that all the production function they are based on the assumption it is not that we can just formulate a production function just taking a functional form which talks about the relationship between the input and output rather the production function they in order to formulate a production function we need to assume certain thing and what are the general assumption over here there is perfect divisibility of both inputs and outputs. So inputs are divisible and output also divisible two factor of production generally we use you do not use more than two factors like if you look at there are number of factor of production like labor, capital, time, raw materials, technology and entrepreneurship but for all this analysis whether it is short run whether it is long run we generally use only capital and labor as the input not any other inputs in the production process. Then we are assuming that both the factor inputs that is labor and capital they are substitute to each other but they are in a limiting sense there is no unlimited substitution or they are not close they are not perfectly substitute to each other like if you remember the if it is perfectly substitute then the output can be produced either with the help of capital or with the help of labor. But in this case we are assuming that certain amount of both the inputs are necessary in the production process the production cannot be run only on the basis of the input or only on the basis of the capital. Then technology is given technology cannot change maybe at least in the short run in the long run it can be changed and also we assume that there is a inelastic supply of fixed factor in the short run and that is the reason short run there are few factors those are considered as fixed and in specific sense when we are taking the case of two inputs here generally capital is fixed and there is inelastic supply and whenever there is a increase in the output or whenever there is a need to increase the production output generally the labor gets changed in order to increase the output because and there is an inelastic supply of fixed factor in the short run. So, in that context when we in the economics literature there are two main type of production function are used one cop dog less production function and second one is the cost and elasticity of substitution production function that is CES production function. We mainly use typically in economics literature either cop dog less production function or cost and elasticity of substitution popularly known as CES production function. Today we will focus more on the cop dog less production function because this is mostly used in case of the economic analysis cop dog less production function takes the form of q that is output which is a which is a k to the power a and l to the power b where a and b they are the positive fraction and k and l is the k is the capital and l is the level over here. So, q is the a k to the power a and alternately we can take this as l is to the power 1 minus a because a plus b has to be equal to 1. So, if a plus b is equal to 1 then alternately we can formulate this production function h q is equal to capital a k to the power a and l to the power 1 minus a. Now, what are the properties of cop dog less production function? Firstly, the multiplicative form of power function can be transformed into a log linear form like log q is equal to log a plus small a log k and b log b. So, in logarithmic form the function becomes simple to handle and can be empirical estimated using linear regression technique. So, the first property is cop dog less production function can be transformed into a log linear form and why it generally what is the benefit if it is getting transformed into a log linear form? It becomes simple to handle and when we are doing a empirical analysis using the cop dog less production function then this is easy to handle and using linear regression technique we can empirically estimate the cop dog less production function. Then secondly, the second property of cop dog less production function is that power function are homogeneous and the degree of homogeneity is given by the sum of exponent a plus b as in the cop dog less function. So, if a plus b is equal to 1 the production function is homogenous degree 1 and implies a constant return to scale. So, the power function are homogeneous and the degree of homogeneity is given by the sum of exponents of a and b as in the cop dog less function. So, if a plus b is equal to 1 then this the production function is homogenous of degree 1 and implies constant return to scale. If a plus b is greater than 1 then it implies a increasing return to scale and if a plus b is less than 1 again it is implies a decreasing return to scale. So, depends upon the value of the exponent in the cop dog less production function that is for a and b that determines that what kind of production function it is and what kind of scale it is bearing on. Thirdly, the a and b represent the elasticity coefficient of output for input k and l respectively. So, the output elasticity coefficient e in respect to capital can be defined as the proportional change in the output as a result of given change in k keeping l constant. So, if you are keeping l constant and if you are trying to find out what is the elasticity coefficient of output for input with respect to capital only then this is del q by q that is the change in the output with respect to change in the capital. So, del k by k and if you simplify this then this is del q by del k multiplied by k by q. So, this is nothing but the elasticity coefficient with respect to input k keeping l as the constant. So, partial elasticity of this production function which is a dependent on capital and labor keeping l as the fixed the elasticity coefficient with respect to capital is del q by del k multiplied by k by q. So, taking the specific production function that a q is equal to a k to the power a l to the power b with respect to k and substituting the result into the equation the elasticity of coefficient e k can be derived as del q by del k that is a then capital a k to the power a minus 1 and l b. So, substituting the value of q and del q by del k in the equation elasticity of coefficient with respect to capital says that a a k by a minus 1 l b and in a inverted bracket we have k divided by a k l by b and when we simplify this we get it equal to a. So, elasticity coefficient with respect to capital keeping labor as constant the value is equal to a. Similarly, when we find out for the b the same procedure we can follow and we can find out the output coefficient with respect to labor capital as constant and the value of output coefficient with respect to labor is coming out to be b. So, elasticity coefficient of capital elasticity coefficient for capital keeping labor as constant it is a the same procedure can be applied to find out the elasticity coefficient with respect to labor and the elasticity coefficient of output for labor is coming to the l and the value of it will come as the b. So, properties of Cub Devil's production function in continuation of this, we have the fourth property and here the constant a and b represent the relative distributive share of input k and l in the total output q. So, fourth property talk about the constant a and b and what it represent. So, basically constant a and b associated with input capital and labour represent the relative distributive share of input k and l in the total output q. So, the share of k in q is given by del q by del k multiplied by k and similarly the share of l in q is del q by del l multiplied by l. So, del q by del k multiplied by k is the share of k in q and share of l in q is the del q by del l multiplied by l. So, the if you look at this del q by del k multiplied by K, the first part is talks about the change in the Q with respect to change in the K multiplied by the the actual amount of K and the share of L in Q is the del Q by del L that is the that is the change in the output with respect to labour and multiplied by L. So, fourth property is talks about the constant of A B associated with labour and capital and they generally represent the relative distributed share of input K and L in the total output. So, in continuation with the fourth property the relative share of K in Q can be obtained as del Q by del K multiplied by K multiplied by 1 by Q which comes to A and the relative share of L in Q can be obtained as del Q by del L multiplied by L 1 by Q that comes to B. Finally, the Cobb-Douglas production function its general form that is Q is equal to K to the power A L to the power 1 minus A implies that at 0 cost there will be 0 production because the value of intercept is or the value of constant is missing here. So, if in the general form if it is Q is equal to K to the power A and L to the power 1 minus A it implies that at 0 cost there will be 0 production because the capital A value is missing over here. So, given this Cobb-Douglas production function if the production function is A K to the power A L to the power B the average product of L is A P L and K is A P K. So, A P L is A K by L 1 minus A and A P K is A L by K by 1 and similarly we can find out the marginal product for capital and marginal product for labour MPL is A Q by L and MPK is 1 minus A Q by K. So, considering this as a considering this as a Cobb-Douglas production function accordingly the value of the average product for labour average product for capital marginal product for labour and marginal product of capital will change. Similarly, when we are finding out the marginal rate of technical substitution of L for K then taking that specifically the Cobb-Douglas production function. So, as we know this marginal rate of technical substitution is the slope of the isoquant and how the slope of the isoquant can be represent this is the ratio of the marginal product of both the inputs. So, in this case the ratio of the marginal product of capital and labour. So, this is when we are finding out marginal rate of technical substitution specifically for the Cobb-Douglas production function then marginal rate of technical substitution of L for K is MPL by MPK that is A by 1 minus A K by L. Here we have to note that the marginal rate of technical substitution L by K is the rate at which marginal unit of labour L can be substituted for marginal unit of capital K along a given isoquant without affecting the total output. So, it is like rate of substitution between two inputs without and the even if the input level is changing or the amount of input getting used from labour and capital is changing still it has to be in the same isoquant. So, the level of output is not changing. Similarly, if you take a CS production function or any other form of production function we can in the similar way we can derive the basic concept used in the production analysis like average product, marginal product and the marginal rate of technical substitution both for L for K and K for L. Now, if you remember in the last class we talk about the least cost input combination and least cost input combination is one where the slope of the isocost is equal to the slope of the isoquant and this is the point at which the producer or the firm maximizes the output looking at the given constant. So, today we are going to spend may be another spending detail that how the equilibrium conditions are derived, how we can say that the slope of isocost has to be equal to the slope of isoquant. We will see then we look at the graphical representation and then we will come to the point where the input prices changes and how it generally affects the least cost input combination and how the effects are being captured. So, we will first see that how the equilibrium conditions are derived or may be how the precondition for the least cost inputs are derived and then we look at into the graphical representation both for the maximization case and for the minimization case. So, let us look at into the equilibrium condition how the equilibrium conditions are derived. So, this is so if this is the production function that is where x is the function of labour and capital in this case how we can find out what is the equilibrium condition. Now, here there is a constant that is subject to C bar that is W L plus R k. So, if you remember this is your isocost. Now, this if you can change this constant into this then this is C bar minus W L minus R k which has to be equal to 0. Now, whenever we need to maximize something minimize something with a with respect to a constant in this case we need to use a Lagrangian multiplier. Generally known this as a Lagrangian multiplier method and here what is the Lagrangian multiplier the Lagrangian multiplier here is x C bar minus W L R k which is equal to 0. Now, what is this Lagrangian multiplier generally this is the undefined constant or undefined constant which generally used to maximize or minimize a function because if there is a constant associated with this if there is a constant associated with this we cannot directly maximize the production function and that is the reason we need to take the help of the Lagrangian multiplier method and these are the and the Lagrangian multiplier is the undefined constant which generally used to maximize or minimize a point. So, once we get the Lagrangian multiplier method then we will get the composite function composite function is x plus lambda C bar minus W L minus R k which has to be equal to 0. So, this is the composite function using the Lagrangian multiplier method. Now, what is the next job next job we need to maximize it and we will see what should be the first order condition and what should be the second order condition in order to maximize or in order to minimize. So, given this as the composite function what should be the first order condition if you if you remember all the first order condition if it is a maximization or may be it is a minimization the partial derivative has to be equal to 0. So, here we will take the partial derivative with respect to the undefined constant and we will set them equal to 0 in order to find out the first order condition. So, del Q by del L which is equal to has to be equal to 0 del Q by del k which has to be equal to 0 and del Q by del lambda which has equal to be 0. So, this implies del x by del L plus lambda minus W equal to 0 then this implies del x by del k plus lambda minus R is equal to 0 and this implies C minus W L minus R k which has to be equal to 0. So, from equation first to if you solve for lambda then this comes to del x by del L is equal to del W or then this equal to del x by del L by W and this leads to lambda is equal to this is our marginal product for labor by W. Similarly, from equation two if you find solve for the value of lambda then this is del x by del k is lambda R or x is equal to del x by del k by R and this is since this is m p k by R. After solving for both this lambda from then this comes to m p k by R which is equal to m p l by W leads to m p l by m p k equal to W by R. This is the first order condition for the least input combination because this represents the slope of isocond this represents the slope of isocost. Since the cost and is given in the form of isocost and the output is given in this case we can say that the first order condition has to be the point at which the slope of the isocost has to be equal to the slope of the isocond. So, the ratio of marginal product of labor and capital gives us the slope of the isocond and the ratio of input prices that is W and R that gives us the slope of the slope of the isocost. So, first order condition for least cost input combination says that at the point of equilibrium or at the point of least cost input combination the slope of the isocost has to be equal to the slope of the isocond. Next we will see what should be the secondary condition for this maxima or minima with respect to the least input combination. This requires the marginal product curve for both the factors has to be negative. So, del square x del L square and del square x del k square. So, this is what this in order to find out the slope we need to take the second order derivative with respect to labor and secondary derivative with respect to capital. So, this has to be 0 that is del square x by del L square has to be less than 0 and del square x and del k square has to be less than 0. So, second order condition for the least input combination requires the marginal product for both the factors that is capital and labor. The marginal product curve for both the factor has to be negative and how we will find out the marginal product curve for both the factors is to negative. We need to take the second order derivative of the with respect to capital and with respect to labor of the composite function and that gives us del square x by del L square for the second derivative for the labor del square x by del k square the second order derivative for the capital. And second order condition says that it has to be negative and that is the reason the second order derivative that del square x del L square has to be less than 0 del square x del k square has to be less than 0. First we will see how graphically we look at both the input and the maximization case and the minimization case in case of the least cost input. So, what is the essential difference between the maximization and minimization case? In case of maximization case the cost is given and if taking cost is the constant the isocost line is the constant the producer has to maximize the output whereas, in case of minimization case the output is fixed and looking at the fixed output what is the challenge for the producer or the challenge for the firm is to minimize the cost. So, let us look at the maximization case first. So, maximize with maximization of x which is a function of labor and capital with respect to the input prices that is W and R. So, if we look at there are two graphs, graph one is where there are three isoquant and the isocost is given and graph two is where the isoquant is there in a different shape and there are two isocost line. So, in case of maximization case what happens this isocost is given and with this isocort the challenge of the producer is to get the maximum level of output and looking at this the consumer will always pick up a combination in Q 2 level of output because the Q 2 level of output can be achieved with the isocost K and L which is given. But in case of second case if you look at the isoquant is taking a shape of concave and which is not possible because in case of concave it is not following the basic rule of the production analysis like if you look at basic rule of a isoquant because even if with the same isoquant they are able to achieve the combination it is not giving the same level of same level of output across all these stages or may be the input combination are different because they are when they are moving from one point to another point they are using more of the inputs of both but they are producing the same level of output which is not the cost efficient or which is not the input efficient. That is the reason in case of maximization case the output level is can be achieved with the the maximum output level can be achieved with the isocost line given or in term of the cost is given. Next we will see the minimization case where the output is given the challenge for the producer is to minimize the cost of production or minimize the input prices with respect to the given level of output. So, these are all isocost these are the point which talk about the cost of production if you are taking any of this combination of input prices and looking at this if you look at if the x bar is the output level that is given then in this case the producer will always look for this that to produce this level of output which one and can be the minimum cost and so in this case to achieve this level of output K 3 L 3 is the minimum isocost or the minimum cost of production that is the reason they will choose this point as the least cost input combination because to produce the given level of output this is the minimum possible cost. So, in case of minimization case the challenge of the producer the challenge of the firm is to minimize or they will always look for the combination which gives us the least cost to the producer least cost to the firm for a given level of output. Let us look at the case where if there is a change in the input prices how it affects the least cost input combination. So, change in input price if you look at it affect the optimal combination of inputs at different magnitude depending on the nature of the input price change. So, if all input price change in the same proportion. So, it bound to happen the optimal combination of inputs has to change if there is a change in the input price either in the different magnitude or in the same magnitude depends on the nature of the input price change. So, if all input price changes in the same proportion the relative prices of input that is the slope of the budget constant or they may remain unaffected. So, if all input prices changes in the same proportion the relative prices of inputs also if you look at the moves in the same proportion and those are remain unaffected, but when the input prices changes at a different rate in the same direction or the opposite direction or the price of only one input changes while the price of other input remain constant the relative price of input will change. Input price when it change in the different rate in the same direction different rate in the opposite direction input price of one changes other remaining constant the relative price of input will change. This change in the relative input out price change in both in the input combination and the level of output as a result of substitution effect of change in the relative prices of input. So, this change in the relative input prices changes both the input combination and the level of output. So, whenever there is a change in the input prices it affects the input combination and the level of output as a result of substitution effect of change in the relative price. So, a change in the relative price of inputs either in the same or the opposite would imply that some input have become cheaper in relation to the others. So, cost minimization firm attempts to substitute relatively cheaper inputs for more expenses one refers to the substitution effect of relative input price change. Because whenever the price of one input changes it becomes cheaper with respect to the other inputs and what the cost minimizing producer or cost minimization firms they do it over here. They generally try to replace the expensive input with respect to the cheaper inputs and this is generally known as the substitution effect of relative input price change. So, this numericals we will just look at later that how the quantity of labor and capital changes before that we will look at the graphical representation that when there is a change in the input prices how it affects the least cost input, how it affects the level of output or how it affects the level of input combination. So, initially this is the ISO cost K L is the ISO cost Q is the output Q 1 is the isoquant and this is the level of output. Now, price of labor input decreases with the help of that now the quantity of the or if you look at the ISO cost will change from K L to K L dash. So, once it changes from K L to K L dash then in this case now what is the new input combination the new input combination is if you look at this becomes L 3 that is L 1 and this is K 2 this is K 1. So, with the change in the input price now the firm will use more of labor and less of capital that is the reason the combination now earlier it is K 1 L 1 now it is K 3, K 2 and L 3. Now, to get to keep it in the same level what the producer will do the may be at least at the same level of output still want to change the input combination now what they will do they will try to draw a parallel line which also tangent at a point which is at this level. So, suppose this is your point E this is your point E 1 this is your point E 2. So, at this case if you look at still at U j say higher level of labor as compared to the previous level, but it is U j also a higher level of capital. So, the movement from this E 2 E 1 is the price effect that is in the form of L 1 to L 3 the movement from may be E 1 to E 2 is budget effect because the producer is trying to keep the income level the real income level of the producer at the same level that is the reason we got a compensated budget line which is may be K dash and L dash which compensate or which may be the reduce the real income of the producer in term of change in the input prices and that leads to a different combination that is E 2. So, E 1 to E 2 E 1 the movement from E 2 E 1 is the price effect which is in term of the labor input because use we can say L 1 and L 3 movement from E 1 to E 2 is that is L 2 to L 3 is because of the income effect because the real income is changing and movement from may be E 2 E 2 is the substitution effect because of the change in the real income. So, if you look at the price effect is the combination of the substitution effect and the income effect. So, if you remember your price effect substitution effect and income effect in case of the consumer theory this is nothing but the counter part of the counter part of the counter part of that in the production theory which talks about the change in the input prices if there is a change in the input prices generally the producer try to substitute that with a cheaper input as compared to expensive input that is the reason they go on using more of that input. So, in this case also the same thing has happened the producer is once the price of labor has gone down the producer has try to optimize it and use more of the labor as compared to the capital and that leads to the combination of the change in the input combination or also the change in the level of output. Now, next we will see the input combination or may be the input combination how it changes or how to find out numerically when the production function is given price of inputs is given like W and R and if the production function is given and to produce a specific level of output how to optimize the cost of production and what should be the minimum cost of production. For that we will just take a example of a we will take a numerical example like Q is equal to 100 K that is to the power 0.5 and L to the power 0.5 this production function is in the form of a cup dog less production function where W is 30 and R is 40. So, W is the price of labor that is 30 rupees R is the price of capital that is 40 rupees and what we need to do here we need to find the quantity of labor and capital that the firm should use in order to minimize the cost of producing of 144 units of output. So, if we look at this is the minimization of case like the second case where the unit of output is given we need to minimize the cost and what is the minimum cost we need to find out that. Then how we will go for this we will use the we will take the help of the Lagrangian multiplier to solve this. So, Q is equal to 100 K 0.5 and L 0.5 and here if you look at then we have W is equal to 30 and R is equal to 40. So, first we will try to find out the composite function. Now, composite function is rupees 30 L plus rupees 40 K plus lambda dash that is Q 0 minus 100 L to the power 0.5 K to the power 0.5. Now, the what we need to do we need to find out the first order condition the first order condition we need to find del z by del L that is 30 minus lambda dash 50 L that is L minus 0.5 K 0.5 has to be equal to 0 or 50 lambda dash L minus 0.5 K 0.5 has to be equal to 30. Suppose this is our equation 1. Now, we need to look at the first order partial derivative or the first order derivative or the partial derivative with respect to the other input. In the first case we have checked it for L. Now, we will check it for K. So, here we need to find out del partial derivative with respect to K that gives us 40 minus lambda dash 50 L 0.5 K minus 0.5 which has to be equal to 0.5. Or 50 lambda dash L 0 to the power 0.5 K to the power minus 0.5 which is equal to 40 let us call it equation 2. Now, to find out the partial derivative with respect to lambda that is Q 0 minus 100 L 0.5 K 0.5 which is equal to 0. So, you can call it 100 L to the power 0.5 K to the power 0.5 which is equal to Q 0 that is equation 3. So, now, if you divide equation 1 by equation 2 suppose equation 1 by equation 2 then this is 30 by 40 equal to lambda dash that is 50 L minus 0.5 K 0.5 K 0.5 which is equal to 0.5 K 0.5 K 0.5 then lambda dash 50 L 0.5 K minus 0.5 simplifying this again. So, if you simplify this then this is 3 by 4 equal to K 0.5 K 0.5 L 0.5 and L 0.5 that comes to 0.5. Comes to 3 by 4 by K by L. So, K is equal to we can say 3 by 4 L or 0.75 L. So, in order to take the first order partial derivative once we get the partial derivative out of the first order derivative with respect to L then the first order derivative with respect to K and then the first order derivative with respect to lambda and then we solve for the value K in term of L. Now, what we have got from all this calculation that is K is equal to 3 by 4 L. Now, we will see how we can substitute the value of K into value of this into the equation and find out the value of K and L because ultimately what we need to find out we need to find out ultimately to produce 144 units of output what is the minimum cost because the minimum cost the firm has to incur or what should be the minimum cost on which ISO cost they have to learn. So, if you substitute the value of K into the given production function for 144 units of output that is 144 that is 100 L 0.5 and 0.75 L because K is equal to 0.75 L. So, that comes to 100 L 0.75 which comes to 144 100 0.75 then it comes to 14486.6 that comes to 16.6767. So, 16.67 is the value of L. Now, we to find out K is equal to 3 by 4 L. So, that comes to 12.5. So, 12.5 is the capital and capital is 16.67 is the labour. So, capital and labour we need we got the value of capital and labour. Next we need to find out what is the cost when the capital is labour is 16.67 and capital is 12.5 because ultimately again let me remind it ultimately we need to find out what is the minimum cost of producing this given level of output. So, C is equal to W L plus R K. So, W is 30 L is 16.67 plus R is 40 and K is 12.5. So, that comes to rupees 100 1000.50. So, in order to produce 144 output this is the minimum cost. So, this is the given level of output and this is the minimum cost. So, whether it is a minimization case or maximization case how generally we solve it numerically, we solve it numerically with the help of this last case. So, it is a minimum cost. So, this is the minimum cost. So, it is a minimum cost. So, that is the minimum cost. So, whether it is a minimization case help of this Lagrangian multiplier method, where we take the constant in the form of a Lagrangian multiplier. We formulate a composite function, then we take the first order partial derivative with respect to 0. Simplifying this, that gives us the value of capital and labor. We put the value of capital and labor in the production function equation. We get the exact value of capital and labor. Use this in the cost function and that gives us the minimum cost of producing the given level of output. Now, let us see if you remember in the last class, we talk about the short run production function that is in term of the law of diminishing return. Next, we will see that numerically how we get the value of the three stages, the different stages of production and how we find out the value of average product, marginal product and at what level generally the diminishing marginal return set in and what level labor is the average product of labor is the highest. So, the form produces the output according to the production function that is Q is equal to 100 K L minus L Q. So, the production function is 100 K L minus L to the power Q. Capital is fixed at 10 because this is a short run production function. Now, what we need to do? We need to find out the value of average product. We need to find out the value of marginal product and then maybe we can find out what is the different stages or what is the different level of output or level of labor where the where the producer is achieving the different level of output. So, first we will find out the marginal product of labor. Now, marginal product of labor is del Q by del L. So, that comes to 20, that comes to the case of 20 K L minus 3 L square. So, that comes to 200 L minus 3 L square. Now, to so this is the marginal product of labor. Now, we will find out the average product of labor. Average product of labor is Q by L. So, that comes to 10 K L minus L square which is equal to since K is equal to 10. So, this is 100 L minus L square. So, average product for average product is 100 L minus L square. Marginal product for labor is 200 L minus 3 L square. Now, second one is we need to find out when MPL is maximum. Where the first order partial derivative with respect to L is equal to 0. So, that comes to 200 minus 6 L which is equal to 0. L is equal to 33.33. Now, what is the significance of this level of labor? The significance of this level of labor is that at this level since marginal product of labor is maximum beyond this generally the law of diminishing returns at in if you remember your three stages of production function like how the total product curve. So, initially it is convex, then it is convex and then it is decreasing. So, this corresponding to this our marginal product of labor is maximum because after this the total product of labor is increasing at a decreasing rate and beyond this MPL is maximum and beyond this if you look at then the total product is increasing at the decreasing rate and marginal product is decreasing. So, we can say corresponding to this point MPL is maximum and this is the point where the law of diminishing return set in. And the second point we will look at is when MPL is equal to 0, MPL is equal to 0 when this 200 L minus 3 L square is equal to 0. So, in this case maybe L is equal to if you find out this comes to 66.66 and where this value of L comes the value of L comes at this point because corresponding to this MPL is 0 and TPL is maximum. So, if you remember from till this point this is your point beyond which there is the law of diminishing return set in. Then when a average product of labor is highest average productive labor is highest when DAPL with respect to DL is 0 that comes to L is equal to 50. So, this comes somehow here the average product of labor is maximum when it intersecting the marginal product of labor. So, corresponding to this L is equal to 50. So now, we can say that from 0 to 50 the first stage of production from 50 to 66 unit of labor, second stage of production and beyond 66 unit of labor we have third stage of production. And how we have identified this first stage, second stage and third stage? First stage ends till the point the marginal product is equal to the average product and average product is maximum at that point where marginal product is equal to the average product. Where the second stage ends, second stage ends when the total product level is maximum or the marginal product is 0. So, that achieve at the unit of labor unit at 66 beyond 66 we have the third stages of production. So, depends upon the labor unit we can find out at which level generally the stages of production are decided whether at the first stage, whether at the second stage and third stage. So, first stage is up to a point where the marginal product of a labor is equal to the average product of labor. Second stage is the point where total product of labor is maximum marginal product of labor is 0 and third point is beyond this. So, once we find out the value of labor where marginal product of labor is equal to 0 that is the definition of the second stage. Once we find out the maximum value of APL that gives us the may be the beginning of the second stage and when we find the marginal product of labor is maximum that gives us the point beyond which the law of diminishing return setting. So, in the next session we will talk about the cost of production different types of cost, how the cost function is formulated and what is the logic of different shape of the cost function in the short term and in the long run. So, these are the session references generally these are the references that is being used for the preparation of this particular session.


It might be tempting to believe you can understand an organization's culture simply by using your senses. But the items you perceive on the surface are only one level of the culture puzzle. Organizational culture expert Edgar Schein says that there are really three levels of culture, artifacts or the tangible surface level products, espoused beliefs and values or an organization's ideologies, goals and rationalizations and basic underlying assumptions, things so ingrained that they're taken for granted by the group. Schein believes to understand a group's culture, you must attempt to get at its shared basic assumptions and understand the learning process by which such basic assumptions evolve. So when you're trying to understand an organization's culture, its artifacts may be a good place to start. But keep digging, it isn't until you reach the underlying assumptions that you'll have a more complete picture. Lead well this week.


TEFL Brittany Take our TEFL training course in Brittany and learn to teach English as a foreign language in a picturesque village in the northwest of France. Plelloff is a charming village situated in the Coates d'Armor region of Brittany, close to many age-old villages that date back centuries. Although the TEFL course takes place in a beautiful small village, the location and surrounding areas have all the required facilities and amenities that you will require during your stay. The Brittany region is a wonderland of typical French hamlets for you to explore in your free time. With varied landscapes, amazing cuisine and some of the best wines in the world, this part of France continues to astound both first-time visitors and those who return year after year. Summer activities are numerous with the local Lake Guerlain being popular for jet skiing, water skiing and more. Plelloff is not too far from the beach either, so you can spend some time soaking up the sun or taking a leisurely stroll along the coast. Cycling is also popular in the region and you may like to explore the local on two wheels under your own steam. There are few real hills here so cycling is a pleasant option. Weekend visits to Paris are also a popular option and our TEFL Training Center will be happy to provide you with any assistance they can. TEFL course in Brittany. Our center is set in a tranquil location free from noise pollution and other annoying distractions. We have excellent teaching resources, modern teaching aids and a professionally-minded training staff that are dedicated to supporting you throughout the duration of the course. Your accommodation options in Brittany include a cozy country house in nearby Sylphiac, a luxury cottage or more simple rooms within our training complex. We have single and shared room options of varying prices available. However, bookings do fill up quickly, so it's best to reserve your seat on the course as soon as possible. The course fees listed on our website are inclusive of course-related lessons, materials, teaching practice, assessments, certificates, references, lifetime job assistance and more. We have no hidden costs or extra charges, so the prices you see on the site are the prices you will pay. Getting started. If you are at least 18 years of age and speak English fluently, you are eligible to apply for the course. The application is brief and we will send you a prompt reply. Once approved, you will receive additional information about the course content and schedule your accommodation options, travel arrangements, as well as payment options and more. If you choose to take our training course in Brittany it doesn't mean that you have to stay and work here. If you would prefer to move on after the course, just tell us where you would like to work and we will provide you with our lifetime job assistance. Try to take our TEFL course in Brittany now and soon you could become a certified EFL teacher in the beautiful countryside of northern France.


This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information, and to find out how you can volunteer, please visit LibriVox.org. Recording by Tom Yates. TomInBKK.com Leaves of Grass by Walt Whitman Book 34. Sands at 70. Manahata My city's fit and noble name resumed. Choice, aboriginal name, with marvelous beauty. Meaning, a rocky, founded island. Shores wherever gaily dash the coming, going, hurrying sea waves. Palmanok Sea beauty, stretched and basking. One side, thy inland ocean, laving, broad, with copious commerce, steamers, sails. And one, the Atlantic's wind caressing, fierce or gentle, mighty holes, dark gliding in the distance. Isle of sweet brooks of drinking water, healthy air and soil, isle of the salty shore and breeze and brine. From Matuk Point I stand as on some mighty eagle's beak, eastward the sea absorbing, viewing nothing but sea and sky, the tossing waves, the foam, the ships in the distance, the wild unrest, the snowy, curling caps that inbound urge and urge of waves, seeking the shores forever. To those who have failed, to those who have failed in aspiration vast, to unnamed soldiers fallen in front on the lead, to calm devoted engineers, to over ardent travelers, to pilots on their ships, to many a lofty song and picture without recognition, I'd rear laurel covered monument, high, high above the rest, to all cut off before their time, possessed by some strange spirit of fire, quenched by an early death. A carol closing sixty-nine, a carol closing sixty-nine, a resume, a repetition, my lines and joy and hope continuing on the same, of ye, oh God, life, nature, freedom, poetry, of you, my land, your rivers, prairies, states, you, modeled flag I love, your aggregate retained entire, of north, south, east and west, your items all, of me, myself, the jokin' heart yet beating in my breast, the body wrecked, old, poor and paralyzed, the strange inertia falling, Paul, like round me, the burning fires down in my sluggish blood, not yet extinct, the undiminished faith, the groups of loving friends, the bravest soldiers, brave, brave were the soldiers, high named today, who lived through the fight, but the bravest pressed to the front and fell, unnamed, unknown, a font of type, this latent mine, these unlaunched voices, passionate powers, wrath, argument or praise, or comic leer, or prayer devout, non-pareil, brevier, bourgeois, long primer merely, these ocean waves arousable to fury and to death, or soothed to ease and sheenie sun and sleep, within the pallid slivers slumbering. As I sit writing here, sick and grown old, not my least burden is that dullness of the years, querilities, ungracious glooms, aches, lethargy, constipation, whimpering and we, may filter in my dally songs. My canary bird, did we count great oh soul to penetrate the themes of mighty books, absorbing deep and full from thoughts, plays speculations? But now from thee to me, caged bird, to feel thy joyous warble, filling the air, the lonesome room, belong for noon, is it not just as great oh soul? Queries to my 70th year, approaching, nearing, curious, thou dim uncertain specter, bringest thou life or death, strength, weakness, blindness, more paralysis and heavier, or placid skies and sun, wilt stir the waters yet, or happily cut me short for good, or leave me here as now, dull, parrot-like and old, with cracked voice harping, screeching, the wall about martyrs, greater than memory of Achilles or Ulysses, more, more by far to thee than tomb of Alexander, those cartloads of old charnel ashes, scales and splints of moldy bones, once living men, once resolute courage, aspiration, strength, the stepping stones to thee, today, and here, America. The First Dandelion Simple and fresh and fair, from winter's clothes emerging, as if no artifice of fashion, business, politics had ever been, forth from its sunny nook of sheltered grass, innocent, golden, calm as the dawn, the spring's first dandelion shows its trustful face. America. Center of equal daughters, equal sons, all, all alike endeared, grown, ungrown, young or old, strong, ample, fair, endearing, capable, rich, perennial with the earth, with freedom, law, and love, a grand, sane, towering, seated mother, chaired in the adamant of time. Memories. How sweet the silent backward tracings, the wanderings as in dreams, the meditation of old times resumed, their loves, joys, persons, voyages. Today and thee, the appointed winners in a long-stretched game, the course of time and nations, Egypt, India, Greece, and Rome, the past entire, with all its heroes, histories, arts, experiments, its store of songs, inventions, voyages, teachers, books, garnered for now and thee, to think of it, the erudem all converged in thee. After the dazzle of day, after the dazzle of day is gone, only the dark, dark night shows to my eyes the stars. After the clanger of organ majestic, or chorus or perfect band, silent a thwart my soul, moves the symphony true. Abraham Lincoln, born February 12th, 1809. Today, from each and all, a breath of prayer, a pulse of thought, to memory of him, to birth of him, out of maize shows selected. Apple orchards, the trees all covered with blossoms, wheat fields carpeted far and near in vital emerald green, the eternal exhaustless freshness of each early morning, the yellow golden transparent haze of the warm afternoon sun, the aspiring lilac bushes with profuse purple or white flowers. Halcyon days, not from successful love alone, nor wealth, nor honored middle age, nor victories of politics or war, but as life wanes and all the turbulent passions calm, as gorgeous vapory silent hues cover the evening sky, as softness, fullness, rest infuse the frame like fresher balmy air, as the days take on a mellower light, and the apple at last hangs really finished an indolent ripe on the tree, then for the teeming quietest, happiest days of all, the brooding and blissful Halcyon days. Fancies at Navesink, one, the pilot in the mist, steaming the northern rapids, an old St. Lawrence reminisce, a sudden memory flash comes back, I know not why, here waiting for the sunrise, gazing from the hill, again tis just at morning, a heavy haze contends with daybreak, again the trembling, laboring vessel veers me, I press through foam-dashed rocks that almost touch me, again I mark where aft the small, thin Indian helmsman looms in the mist with brow elate and governing hand. Two, had I the choice, had I the choice to tally greatest bards, to limb their portraits stately, beautiful and emulate at will, Homer with all his wars and warriors, Hector, Achilles, Ajax, or Shakespeare's woe entangled, Hamlet, Lear, Othello, Tennyson's fair ladies, meter or width the best, or choice conceit to wield in perfect rhyme, the light of singers, these, these O.C., all these, I'd gladly barter, would you the undulation of one wave, its trick to me transfer, or breathe one breath of yours upon my verse, and leave its odor there.  Four, last of ebb, and daylight waning, last of ebb, and daylight waning, scented sea, cool, landward marking, smells of sedge and salt incoming, with many a half-caught voice sent up from the eddies, many a muffled confession, many a sob and whispered word, as of speakers far or hid. How they sweep down and out, how they mutter, poets unnamed, artists greatest of any, with cherished lost designs, love's unresponse, a chorus of ages complaints, hopes last words, some suicides despairing cry, away to the boundless waste and never again return.  Six, proudly the flood comes in. Proudly the flood comes in, shouting, foaming, advancing, long it holds at the high, with bosom broad out swelling, all throbs dilates, the farms, woods, streets of cities, workmen at work, mansales, top sales, jibs, appear in the offing, steamers, penance of smoke, and under the forenoon sun, with human lives gaily the outward bound, gaily the inward bound, flaunting from many a spar the flag I love. Seven, by that long scan of waves, by that long scan of waves, myself called back, resumed upon myself, in every crest some undulating light or shade, some retrospect, joys, travels, studies, silent panoramas, scenes ephemeral, the long past war, the battles, hospital sights, the wounded and the dead, myself through every bygone phase, my idle youth, old age at hand, my three-score years of life summed up, and more, and past, by any grand ideal tried, intentionless, the whole a nothing, and happily yet some drop within God's schemes ensemble, some wave, or part of a wave, like one of yours, ye multitudinous ocean.  Election Day, November 1884.  These seething hemispheres humanity, as now I'd name, the still small voice vibrating, America's choosing day. The heart of it not in the chosen, the act itself the main, the quadrinial choosing, the stretch of north and south aroused, seaboard and inland, Texas to Maine, the prairie states, Vermont, Virginia, California, the final ballot shower from east to west, the paradox and conflict, the countless snowflakes falling, a swordless conflict, yet more than all Rome's wars of old, or modern Napoleon's, the peaceful choice of all. Our good or ill humanity, welcoming the darker odds, the dross, foams and ferments the wine, it serves to purify while the heart, pants, life glows. These stormy gusts and winds, waft precious ships, swelled Washington's, Jefferson's, Lincoln's sails. With husky, haughty lips, O.C. With husky, haughty lips, O.C., where day and night I went, thy surf beat shore, imaging to my sense, thy varied strange suggestions, I see and plainly list thy talk and conference here. The troops of white-maned racers racing to the goal, thy ample smiling face dashed with the sparkling dimples of the sun, thy brooding scowl and murk, thy unloosed hurricanes, thy unsubduedness, caprice's wilfulness. Great as thou art above the rest, thy many tears, a lack from all eternity in thy content, not but the greatest struggles, wrongs, defeats, could make thee greatest, no less could make thee. Thy lonely state, something thou ever seekest and seekest, yet never gainest, surely some right withheld, some voice in huge monotonous rage, a freedom-lover pent, some vast heart, like a planets chained and chaffing in those breakers, by a lingon's swell and spasm and panting breath, and rhythmic rasping of thy sands and waves, and serpent hiss, and savage peels of laughter, and undertones of distant lion roar, sounding, appealing to the sky's deaf ear, but now, rapport for once, a phantom in the night, thy confident for once. The first and last confession of the globe, out surging, muttering from thy soul's abisms, the tale of cosmic elemental passion, thou tellest to a kindred soul death of general grant. As one by one withdraw the lofty actors from that great play on history's stage etern, that lurid partial act of war and peace of old and new contending, fought out through wrath, fears, darkness maze, and many a long suspense, all past and since in countless graves receding, mellowing, victors invanquished, linkens and lees, now thou with them, man of the mighty days, and equal to the days. Thou from the prairies, tangled, and many veined and hard has been thy part, to admiration has it been enacted. Red jacket from a loft. Upon this scene, this show, yielded today by fashion, learning, wealth, nor in caprice alone, some grains of deepest meaning. Happily, a loft, who knows, from distant sky clouds blended shapes, as some old tree or rock or cliff thrilled with its soul, product of nature's sun, stars, earth direct, a towering human form in hunting shirt of film, armed with the rifle, a half-ironical smile covering its phantom lips like one of Ossian's ghosts looks down. Washington's Monument, February 1885. Ah, not this marble, dead and cold, far from its base and shaft expanding, the round zone circling, comprehending. Thou, Washington, art all the world's continents entire, not yours alone, America, Europe's as well, in every part, castle of lord or laborer's caught, or frozen north or sultry south, the Africans, the Arabs in his tent, old Asia's there with venerable smile seated amid her ruins, greets the antique the hero knew, tis but the same, the heir legitimate continued ever, the indomitable heart and arm force of the never broken line, courage, alertness, patience, faith, the same, even in defeat, defeated not, the same. Wherever sails a ship, or houses built on land, or day or night, through teeming city's streets, indoors or out, factories or farms, now or to come or past, where patriot wills existed or exist, wherever freedom poised by toleration, swayed by law, stands or is rising, thy true monument, of that blive throat of thine, of that blive throat of thine, from arctic bleak and blank, I'll mine the lesson, solitary bird, let me too welcome chilling drifts, even the profoundest chill as now, a torpid pulse, a brain unnerved, old age land locked within its winter bay, cold, cold, oh, cold, these snowy hairs, my feeble arm, my frozen feet, for them thy faith, thy rule I take and grave it to the last, not summer zones alone, not chance of youth, or self's warm tides alone, but held by sluggish flows, packed in the northern ice, the cumulus of years, these gay heart I also sing, Broadway, what hurrying human tides or day or night, what passions, winnings, losses, arders, swim thy waters, what worlds of evil, bliss and sorrow stem thee, what curious questioning glances, glints of love, leer, envy, scorn, contempt, hope, aspiration, thou portal, thou arena, thou the myriad long drawn lines and groups, could but thy flagstones, curbs, facades, tell their inimitable tales, thy windows rich and huge hotels, thy sidewalks wide, thou of the endless sliding, mincing, shuffling feet, thou like the party-colored world itself, like infinite teeming, mocking life, thou visor'd vast, unspeakable show and lesson, to get the final lilt of songs, to get the final lilt of songs, to penetrate the inmost lore of poets, to know the mighty ones, Job, Homer, Eskilus, Dante, Shakespeare, Tennyson, Emerson, to diagnose the shifting, delicate tints of love and pride and doubt, to truly understand, to encompass these, the last keen faculty and entrance price, old age, and what it brings from all its past experiences. Old Salt Cossabone Far back, related on my mother's side, Old Salt Cossabone, I'll tell you how he died, had been a sailor all his life, was nearly nighty, lived with his married grandchild, Jenny, house on a hill with view of bay at hand and distant cape and stretch to open sea, the last of afternoons, the evening hours for many a year his regular custom, in his great arm chair by the window seated, sometimes indeed through half the day, watching the coming, going of the vessels, he mutters to himself and now the close of all. One struggling, outbound brig one day, baffled for long, cross-tides and much wrong going, at last at nightfall strikes the breezer right, her whole luck veering, and swiftly bending round the cape, the darkness proudly entering, cleaving as he watches, she's free, she's on her destination, these the last words, when Jenny came, he sat there dead, Dutch Cossabone, Old Salt, related on my mother's side, far back, the dead tenor. As down the stage again, with Spanish hat and plumes and gate inimitable, back from the fading lessons of the past, I'd call, I'd tell and own, how much from thee the revelation of the singing voice from thee, so firm, so liquid soft, again that tremulous manly timber, the perfect singing voice, deepest of all to me the lesson, trial and test of all. How through these strains distilled, how the wrapped ears, the soul of me absorbing, Fernando's heart, Manrico's passion call, Erani's sweet generos, I fold thenceforth or seek to fold, within my chance transmuting, freedoms and loves and faiths, unloose, cantible, as perfumes, colors, sunlight's correlation. From these, for these, with these, a hurried line dead tenor, a wafted autumn leaf, dropped in the closing grave, the shoveled earth, to memory of thee, continuities, nothing is ever really lost or can be lost, no birth, identity, form, no object of the world, nor life, nor force, nor any visible thing, appearance must not foil, nor shifted sphere confuse thy brain, ample our time and space, ample the fields of nature, the body sluggish, aged cold, the embers left from earlier fires, the light in the eye grown dim, shall duly flame again, the sun now low in the west rises for mornings and for noons continual, to frozen clods of the spring's invisible law returns, with grass and flowers and summer fruits and corn. Yanondio a song, a poem of itself, the word itself a dirge, amid the wilds, the rocks, the storm and wintery night, to me such misty strange tableau the syllables calling up. Yanondio, I see far in the western north, a limitless ravine with plains and mountains dark. I see swarms of stalwart chieftains, medicine men and warriors as flitting by like clouds of ghosts they pass and are gone in the twilight, race of the woods, the landscapes free and the falls, no picture, poem statement passing them to the future. Yanondio Yanondio unlime they disappear. Today gives place and fades, the cities, farms, factories fade, a muffled sonorous sound, a wailing word is born through the air for a moment, then blank and gone and still and utterly lost. Life, ever the undiscaraged, resolute struggling soul of man have former armies failed, then we send fresh armies and fresh again. Ever the grappled mystery of all Earth's ages, old or new ever the eager eyes, hurrahs, the welcome clapping hands the loud applause, ever the soul dissatisfied, curious, unconvinced at last, struggling today the same, battling the same, going somewhere. My science friend, my noblest woman friend, now buried in an English grave and this a memory leaf for her dear's sake ended our talk. The sum, concluding all we know of old or modern learning, intuitions deep, of all geologies, histories, of all astronomy, of evolution, metaphysics all, is that we all are onward, onward, speeding slowly, surely bettering, life, life an endless march, an endless army, no halt but it is duly over. The world, the race, the soul, in space and time, the universes all bound as, is befitting each, all surely going somewhere. Small the theme of my chant. Small the theme of my chant, yet the greatest, namely oneself, a simple, separate person. That, for the use of the new world I sing. Man's physiology complete from top to toe, I sing. Not physiogamy alone nor brain alone is worthy for the muse. I say the form complete is worthy or far. The female equally with the male I sing nor cease at the theme of oneself. I speak the word of the modern, the word in mass. My days I sing and the lands with interstice I knew of hapless war. Oh friend, whoever you are at last arriving hither to commence. I feel through every leaf the pressure of your hand which I return and thus upon our journey footing the road and more than once and linked together let us go. True conquerors old farmers travelers, workmen no matter how crippled or bent, old sailors out of many a perilous voyage, storm and wreck old soldiers from campaigns with all their wounds, defeats and scars enough that they've survived at all, long life's unflinching ones forth from their struggles trials, fights to have emerged at all in that alone true conquerors over all the rest the United States to old world critics here first the duties of today, the lessons of concrete, wealth, order travel, shelter products, plenty as of the building of some varied vast perpetual edifice whence to arise inevitable in time the towering roofs, the lamps the solid planted spires tall shooting to the stars the calming thought of all that coursing on whatever man's speculations amid the changing schools theologies, philosophies amid the balling presentations new and old the round earth's silent vital laws, facts modes continue thanks in old age thanks in old age thanks Iraigo for health, the midday sun the impalpable air for life, mere life for precious ever lingering memories of you my mother dear you father you brothers, sisters friends for all my days, not those of peace alone the days of war the same for gentle words caresses gifts from foreign lands for shelter, wine and meat for sweet appreciation you distant, dim, unknown or young or old countless unspecified readers beloved, we never met and never shall meet and yet our souls embrace long, close and long for beings, groups, love deeds, words, books for colors forms for all the brave, strong men devoted, hearty men who have forward sprung in freedom's help all years, all lands for braver, stronger more devoted men special laurel Iraigo to life's wars chosen ones the canineers of song and thought the great artillerist the foremost leaders, captains of the soul as soldier from an ended war returned as traveler out of myriads to the long procession retrospective thanks, joyful thanks a soldier's traveler's thanks life and death the two old, simple problems ever intertwined close home elusive, present baffled, grappled by each successive age insoluble passed on two hours today and we pass on the same the voice of the rain and who art thou said I to the soft falling shower which, strange to tell, gave me an answer as here translated I am the poem of earth said the voice of the rain eternal I rise in palpable out of the land in the bottomless sea upward to heaven, whence vaguely formed, altogether changed and yet the same I descend to lave the droughts atomies, dust layers of the globe and all that in them without me were seeds only, latent unborn and forever by day and night I give back life to my own origin and make pure and beautify it for song issuing from its birthplace after fulfillment, wandering wrecked or unrecked duly with love returns soon shall the winter's foil be here soon shall the winter's foil be here soon shall these icy ligatures unbind and melt a little while and air, soil, waves effused shall be in softness bloom and growth a thousand forms shall rise from these dead clods and chills as from low burial graves thine eyes, ears all thy best attributes all that takes cognizance of natural beauty to perceive the simple shows the delicate miracles of earth dandelions, clover the emerald grass the early scents and flowers the arbitus underfoot the willows yellow-green the blossoming plum and cherry with these the robin lark and thrush singing their songs the flitting bluebird for such the scenes the annual play brings on the past forgetting while not the past forgetting today at least contention sunk entire peace brotherhood up risen foresign reciprocal our northern southern hands lay on the graves of all dead soldiers north or south nor for the past alone for meanings to the future Reeves of roses and branches of palm the dying veteran amid these days of order ease, prosperity amid the current songs of beauty, peace, decorum I, Castor Romanis likely to will offend you I heard it in my boyhood more than a generation since a queer old savage man a fighter under Washington himself large, brave, cleanly hot-blooded, no-talker rather spiritualistic had fought in the ranks fought well had been all through the revolutionary war lay dying sons, daughters church deacons lovingly tending him sharpening their sense their ears towards his murmuring half-caught words let me return again to my war days to the sights and scenes to forming the line of battle to the scouts ahead reconaturing to the cannons, the grim artillery to the galloping aids carrying orders to the wounded the fallen the heat, the suspense the perfume strong the smoke, the deafening noise away with your life of peace your joys of peace give me my old wild battle life again stronger lessons have you learned lessons only of those who admired you and were tender with you have you not learned great lessons from those who reject you and brace themselves against you or who treat you with contempt or dispute the passage with you a prairie sunset shot gold maroon and violet dazzling silver emerald fawn the earth's whole amplitude and nature's multi-form power consigned for once to colors the light the general air possessed by them colors till now unknown no limit confine not the western sky alone the high meridian north, south, all pure, luminous color fighting the silent shadows to the last twenty years down on the ancient wharf the sand I sit with a new corner chatting he shipped as greenhand boy and sailed away took some sudden vehement notion since twenty years and more have circled round and round while he the globe was circling round and round and now returns how changed the place all the old landmarks gone the parents dead yes he comes back to lay in port for good to settle as a well-filled purse no spot will do but this I see him from this loop now held in leash I see I hear the slapping waves the restless keel the rocking in the sand I see the sailor kit the canvas bag the great box bound with brass I scan the face all berry brown and bearded the stout strong frame dressed in its russet suit of good scotch cloth then what the told out story orange buds by mail from Florida a lesser proof than old Voltaire's yet greater proof of this present time and the thy broad expanse America to my plain northern hut in outside clouds and snow brought safely for a thousand miles over land and tide some three days since on their own soil live sprouting now hear their sweetness through my room unfolding a bunch of orange buds by mail from Florida twilight the soft voluptuous opiate shades the sun just gone the eager light dispelled I too will soon be gone dispelled a haze nirvana rest in night oblivion you lingering sparse leaves of me on winter nearing boughs and I some well shorn tree of field or orchard row you tokens diminute and lorn not now the flush of May or July clover bloom no grain of August now you pallid banner staves you pennants valueless you over state of time yet my soul dearest leaves confirming all the rest the thundering leaves confirming all the rest the faithfulist hardiest last not meager latent boughs alone not meager latent boughs alone oh songs scaly and bare like eagles talons but happily for some sunny day who knows some future spring some summer bursting forth to verdant leaves or sheltering shade to nourishing fruit apples and grapes the stalwart limbs of trees emerging the fresh free open air and love and faith like scented roses blooming the dead emperor today with bending head and eyes thou too columbia less for the mighty crown laid low in sorrow less for the emperor solace breathest send this out over many assault sea mile morning a good old man a faithful shepherd patriot as the greeks signal flame as the greeks signal flame by antique records told rose from the hilltop like applause and glory welcoming in fame some special veteran hero with rosy tinge served so I aloft from manahata's ship friend shore lift a high kindled brand for thee old poet the dismantled ship in some unused lagoon some nameless bay on sluggish lonesome waters anchored near the shore an old dismantled gray and battered ship disabled done after free voyages to all the seas of earth hauled up at last and howzer tight lies rusting moldering now precedent songs farewell now precedent songs farewell by every name farewell trains of a staggering line in many a strange procession wagons from ups and downs with intervals from elder years mid-age or youth in cabin ships or the old cause or poets to come or palmonoke song of myself calamus or atom or beat beat drums or to the leaven soil they trod or captain my captain cosmos quicksand years or thoughts thou mother with thy equal brood and many many more unspecified from fiber heart of mine from throat and tongue my life's hot pulsing blood the personal urge and form for me not merely paper automatic type and ink each song of mine each utterance in the past having its long long history of life or death or a soldier's wound of country's loss or safety oh heaven what flash and startled endless train of all compared indeed to that what wretched shred even at the best of all an evening lull after a week of physical anguish unrest and pain and feverish heat toward the ending day a calm and lull comes on three hours of peace and soothing rest of brain old ages lambend peaks the touch of flame the illuminating fire the loftiest look at all or a city passion see or a prairie mountain would the earth itself the airy different changing hues of all in failing twilight objects and groups bearings faces reminisces the calmer sight the golden setting clear and broad so much in the atmosphere the points of view the situations whence we scan brought out by them alone so much perhaps the best unwrecked before the lights indeed from them old ages lambend peaks after the supper and talk after the supper and talk after the day is done as a friend from friends his final withdrawal prolonging goodbye and goodbye with emotional lips repeating so hard for his hand to release those hands no more will they meet no more for communion of sorrow and joy of old and young a far stretching journey awaits him to return no more shunning postponing severance seeking the word off the last word ever so little even at the exit door turning charges superfluous calling back even as he descends the steps something to eke out a minute additional shadows of nightfall deepening farewells messages lessening dimmer the forthgoers visage and form soon to be lost for eye in the darkness loft oh so loft to depart gargulous to be the very last end of Leaves of Grass chapter 34 this is a LibriVox recording all LibriVox recordings are in the public domain for more information auto-volunteer please visit LibriVox.org this reading by Chris Orange Leaves of Grass by Walt Whitman book 35 goodbye my fancy sail out for good idle on yacht heave the anchor short raise the mainsail and jibe steer forth oh little white-hulled sloop now speed on really deep waters I will not call it our concluding voyage but outset and shore entrance to the truest, best maturist depart depart from solid earth no more returning to these shores now on for eye our infinite free venture wending spurning all yet tried ports seas, horses, densities, gravitation sail out for good idle on yacht of me lingering last drops and whence and why came you we know not whence was the answer we only know that we drift here with the rest that we lingered and lagged but were wafted at last and are now here to make the passing showers concluding drops goodbye my fancy goodbye my fancy I had a word to say but it is not quite the time the best of any man's word or say is when its proper place arrives and for its meaning I keep mine till the last on on the same ye jock and twain on on the same ye jock and twain my life and recitative containing birth, youth, mid-age years fitful as motley tongues of flame in separate twine and merged in one combining all my single soul aims, confirmations, failures, joys nor single soul alone I chart my nation's crucial stage America's happily humanities the trial great the victory great a strange enclarishment of all the masses past the eastern world the ancient medieval here, here from the wanderings straying, lessons, wars defeats here at the west a voiced triumphant justifying all a glad-some-peeling cry a song for once of utmost pride and satisfaction I chant from it the common bulk the general average horde the best sooner than the worst and now I chant old age my verses written first for four new life and for the summers, autumn's spread I pass to snow-white hairs the same and give to pulses winter-cooled the same as here in careless trill I and my recitatives with faith and love wafting to other work to unknown songs, conditions on, on ye jock and twain continue on the same my 71st year after surmounting three score and ten with all their chances, changes losses, sorrows my parent's death the vagaries of my life the many tearing passions of me the war of 63 and 4 as some old broken soldier after a long, hot, wearying march or happily after battle today at twilight hobbling, answering company roll call here with vital voice, reporting yet saluting yet the officer overall apparitions a vague mist hanging round half the pages sometimes how strange and clear to the soul that all of these solid things are indeed but apparitions, concepts non-realities the pallid wreath somehow I cannot let it go yet, funeral though it is let it remain back there on its nail suspended with pink, blue, yellow all blanched and the white now grey and ashy one withered rose put years ago for thee, dear friend but I do not forget thee has thou then faded is the odor exhaled are the colours vitalities dead? no while memories subtly play the part vivid as ever for but last night I woke and in that spectral ring saw thee thy smile eyes, face, calm, silent loving as ever so let the wreath hang still a while within my eye-reach it is not yet dead to me not even pallid an ended day the soothing sanity and blithe-ness of completion the pomp and hurried contest glare and rush are done now triumph transformation, jubilati old age's ship and crafty deaths from east and west across the horizon's edge two mighty mastful vessels sail as steel upon us but we'll make race a time upon the seas a battle contest yet bare lively there our joys of strife and derring do to the last put on the old ship all her power today crowd top sail top gallant and royal studding sails out challenge and defiance flags and flaunting penance added as we take to the open take to the deepest freest waters to the pending year have I no weapon word for thee some message brief and fierce have I fought out and done indeed the battle is there no shock left for all thy affections lisps scorns manifold silliness nor for myself in rebellious self in thee down, down, proud gorge though choking of thee thy bearded throat and high-born forehead to the gutter crouched low thy neck to ailum sinary gifts Shakespeare Bacon's cipher I doubt it's not then more, far more in each old song bequeathed in every noble page or text different something unrect before different author in every object, mountain, tree and star in every birth and life as part of each evolved from each meaning behind the ostent a mystic cipher waits unfolded long, long hints after a long, long course hundreds of years denials, accumulations roused love and joy and thought wishes, aspirations ponderings, victories millions of readers coating, compassing, covering after ages and ages in crustaceans then only made these songs reach fruition Bravo Paris Exposition Add to your show before you close it France with all the rest visible concrete temples, towers goods, machines and oars a sentiment wafted from many million heart throbs ethereal but solid weak grandsons and great grandsons do not forget your grandsires from 50 nations and nebulous nations compacted sent overseas today America's applause love, memories and goodwill interpolation sounds over and through the burial chant organ and solemn service sermon, bending priests to me come interpolation sounds not in the show plainly to me crowding up the aisle and from the window of sudden battles, hurry and harsh noises war's grim game to sight and air in earnest the scout called up and forward the general mounted and his aides around him the new brought word, the instantaneous order issued, the rifle crack the thud, the rushing forth of men from their tents the clank of cavalry the strange celebrity of forming ranks the slender bugle's note the sound of horses hooves departing, saddles arms, a gutter more to the sunset breeze are whispering something again unseen where late this heated day thou entrest at my window laving, temping wall cool threshing, gently vitalising me, old, alone sick, weak down, melted worn with sweat, thou nestling, folding close and firm, yet soft companion better than talk book, art thou hast own nature, elements utterance to my heart beyond the rest and this is of them so sweet thy primitive taste to breathe within, thy soothing fingers, my face and hands thou messenger magical, strange bringer to body and spirit of me distanced as balked or called medicines penetrating me from head to foot I feel the sky, the prairies vast I feel the mighty northern lakes I feel the ocean and the forest somehow I feel the globe itself swift swimming in space thou blown from the lips so loved, now gone happily from endless store God sent for thou art spiritual, godly most of all known to my sense minister to speak to me here and now what word was never told and cannot tell art thou not universal concrete distillation laws, all astronomies last refinement, has to thou no soul? can I not know, identify thee old chance an ancient song reciting ending, once gazing towards thee mother of all musing, seeking a themes fitted for thee accept me thou saidst the elder ballads and a name for me before thou ghost each ancient poet of many deaths incalculable, happily our new world's chiefest debt little old poems even so far back preluding thee America old chance Egyptian priests and those of Ethiopia the Hindu epics, the Grecian Chinese Persian, the Biblical books and prophets and deep idles of the Nazarene, the Iliad Odyssey, plots, doings wanderings of Aeneas, Hesiod Ezekles Sophocles, Merlin, Arthur the Seed, Roland at Ronskival, the Nibelugan the Troubadour, Minstrels Minnisingers, Sculls Chaucer, Dante, flocks of singing birds the Borda Minstallary the bygone ballads, feudal tales essays, plays Shakespeare, Shiller Walter Scott, Tennyson at some vast, wondrous, weird dream presences, the great shadowy groups gathering around darting their mighty masterful eyes forward at thee thou with as now thy bending neck and head with courteous hand and word ascending, thou pausing a moment drooping thine eyes upon them blent with their music well pleased, accepting all curiously prepared for by them, thou interest at thy entrance porch A Christmas greeting Welcome Brazilian brother, thy ample place is ready a loving hand a smile from the north a sunny instant hall let the future care for itself where it reveals its troubles impedimenters, ours the present at the row the democratic aim, the acceptance and the faith to thee today our reaching arm our turning neck, to thee from us the expectant eye thou cluster free, thou brilliant lustrous one, thou learning well the true lesson of a nation's light in the sky more shining than the cross, more than the crown the height to be superb humanity sounds of the winter sounds of the winter too sunshine upon the mountains many a distance terrain from cheery railroad train from nearer field barn house, the whispering air even the mute crops garnered apples, corn children's and women's tones rhythm of many a farmer and a flail an old man's gavel a slips among the rest think not we give out yet forth from these snowy hairs we keep up yet the lilt a twilight song as I sit in twilight late alone by the flickering oak flame musing on long past war scenes of the countless buried unknown soldiers of the vacant names as unindended airs and seas the unreturned the brief truce after battle with grim burial squads and the deep filled trenches of gathered from dead all America north, south, east, west whence they came up from wooded main New England's farms from fertile Pennsylvania Illinois, Ohio Mezhalos west, Virginia, the south the Carolinas, Texas even here in my room shadows and half lights in the noiseless flickering flames again I see the stalwart ranks on filling rising I hear the rhythmic tramp of the armies you million of its names all, all, you dark bequest from all your war a special verse for you a flash of duty long neglected your mystic roles strangely gathered here each name recalled by me from out the darkness and death's ashes hence forth to be deep deep within my heart recording for many future year your mystic role in tire of unknown names or north or south in barmed with love in this twilight song when the full grown poet came when the full grown poet came out spake pleased nature the round impassive globe with all its shows of day and night saying he is mine but out spake too the soul of man, proud, jealous and unreconciled, nay he is mine alone then the full grown poet stood between the two and took each by the hand and today and ever so stands as blender, uniter tightly holding hands which he will never release until he reconciles the two and wholly and joyously blends them osceola when his hour for death had come he slowly raised himself from the bed on the floor drew on his wardress shirt, leggings and girded the belt around his waist called for vermilion paint his looking glass was held before him painted half his face and neck his wrists and back hands put the scalp knife carefully in his belt then lying down resting moment rose again half sitting smiled gave in silence his extended hand to each and all sank faintly low to the floor tightly grasping the tomahawk handle fixed his look on wife and little children the last and hear a line in memory of his name and death a voice from death a voice from death solemn and strange in all his sweep and power with sudden indescribable blow towns drowned humanity by thousand slain the vaunted work of thrift goods, dwellings forged, street, iron bridge dashed, pel mel by the blow yet ushered life continuing on amid the rushing whirling wild debris a suffering woman saved safely born although I come unannounced in horror and in pang in pouring flood and fire and wholesale elemental crash this voice so solemn strange I too a minister of deity yea death we bow our faces veil our eyes to thee we mourn the old the young untimely drawn to thee the fair, the strong the capable, the household wrecked the husband and the wife the engulfed forger in his forge the corpses in the welling waters and the mud the gathered thousands to their funeral mounds and thousands never found or gathered then after burying mourning the dead faithful to them found or unfound forgetting not, burying the past he a new musing a day, a passing moment or an hour America itself bends low silent, resigned submissive war death, cataclysm like this America take deep to thy proud, prosperous heart in thy chart low, out of death and out of ooze and slime the blossoms rapidly blooming sympathy, help, love distant east from south and north and over sea its hot spurred hearts and hands humanity to human aid moves on and from within a thought and lesson yet thou ever darting globe through space and air thou waters that encompass us thou that in all the life and death of us, in action or in sleep thou laws invisible that permeate them and all thou that in all and over all through and under all incessant thou, thou the vital universal giant force resistless sleepless, calm holding humanity as in thy open hand as some ephemeral toy how ill to air forget thee for I too have forgotten wrapped in these little potencies of progress, politics culture, wealth, invention civilization have lost my recognition of your silent ever swaying power ye mightle elemental throes in which and upon which we float and every one of us is buoyed a Persian lesson for his overarching and last lesson the grey beard Sufi in the flesh scent of the morning in the open air on the slope of a teeming Persian rose garden under an ancient chestnuts tree widespreading its branches spoke to the young priests and students finally my children to envelop each word each part of the rest Allah is all, all, all imminent in every life and object may be at many and many a more moves yet Allah Allah, Allah is there has this stray wondered far is the reason why strangely hidden would you sound below the restless ocean of the entire world would you know the dissatisfaction the urgent spur of every life the something never stilled never entirely gone the invisible need of every seed it is the central urge in every atom often unconscious often evil downfallen to return to its divine source and origin however distant latent to the same in subject and in object without one exception the commonplace the commonplace I sing how cheap is health how cheap nobility abstinence no falsehood no gluttony lust the open air I sing freedom toleration take here the mainest lesson less from books less from the scrolls the common day and night the common earth and waters your work trade occupation the democratic wisdom underneath like solid ground for all the rounded catalogue divine complete the devilish and the dark the dying and diseased the countless 1920s low and evil crude and savage the crazed prisoners in jail the horrible rank malignant venom and filth the weapons the ravenous sharks liars the dissolute what is the part the wicked and the loathsome bear within earth's orbit scheme newts crawling things in slime and mud poisons the barren soil the evil men the slag and hideous rot mirages more experiences and sights stranger than you'd think for times again now mostly just after sunrise or before sunset sometimes in spring often in autumn perfectly clear weather in plain sight camps far or near the crowded streets of cities and the shop fronts account for it or not credit or not it is all true and my mate there could tell you the like we have often confabbed about it people and scenes animals trees colors and lines plain as could be farms and door yards of home paths bordered with box lilacs in corners weddings in churches thanksgiving dinners returns on long absent sons glum funerals the crepe veiled mother and daughters trialled in court jury and judge the accused in the box contestants battles crowds bridges warfs now and then marked faces of sorrow or joy I could pick them out this moment if I saw them again showed to me just to the right in the sky edge or plainly there to the left on the hilltops L of G's purport not to exclude or demarcate or pick out evils from their formidable masses even to expose them but add fuse complete extend and celebrate the immortal and the good haughty this song its words and scope to span vast realms of space and time evolution of the cumulative growths and generations begun in ripened youth and steadily pursued wandering, peering, dallying with all war peace day and night absorbing never even for one brief hour abandoning my task I ended here in sickness, poverty and old age I sing of life yet mind me well of death today's shadowy death dogs my steps my seated shape and has for years draws sometimes close to me as face to face the unexpressed how dare one say it after the cycles poems, singers plays vaunted Ioners Indias, Homer, Shakespeare the long long times thick dotted roads, areas the shining clusters and the milky ways of stars nature's pulses reaped all retrospective passions heroes, war, love, adoration all ages plummets dropped to their utmost depths all human lives throats, wishes, brains all experiences utterance after the countless songs all long or short all tongues, all lands something not yet told in posies voice or print something lacking who knows the best yet unexpressed and lacking grand is the scene grand is the scene, the light to me grand are the sky and stars grand is the earth and grand are lasting time and space and grand are their laws so multi-form puzzling evolutionary but grand are far the unseen soul of me comprehending, endowing all these lighting the light the sky and stars delving the earth sailing the sea what were all those indeed without the unseen soul of what amount without the more evolutionary vast puzzling oh my soul more multi-form far more lasting thou than they unseen buds unseen buds infinite hidden well under the snow and ice under the darkness in every square or cubic inch germinal exquisite in delicate lace microscopic unborn like babes in wombs latent folded compact sleeping billions of billions and trillions of trillions of them waiting on earth and in the sea the universe the stars there in the heavens urging slowly surely forward forming endless and waiting ever more forever more behind goodbye my fancy goodbye my fancy farewell dear mate dear love I'm going away I know not where or to what fortune or whether I may ever see you again so goodbye my fancy now for my last let me look back a moment the slower fainter ticking of the clock is in me exit nightfall and sooner the heart thud stopping long have we lived joyed caressed together delightful now separation goodbye my fancy yet let me not be too hasty long indeed have we lived slept filtered become really blended into one then if we die we die together yes we'll remain one if we go anywhere we'll go together to meet what happens maybe we'll be better off and blither and learn something maybe it is yourself now really ushering me to the true songs who knows maybe it is you little morbid really undoing turning so now finally goodbye and hail my fancy end of leaves of grass