The most common a priori form taken by these functions involve some constant, times capitalÂ­toÂ­theÂ­alpha, times laborÂ­toÂ­theÂ­beta; that is their CobbÂ–Douglas form.
These functions are generally assumed to satisfy the Inada conditions. At the point of profit maximization, the partial derivative of this function with respect to each of its arguments is equal to the price of that argument. In the Solow model, this function is reÂ­engineered to contain a function "AÂ­ofÂ­t," which is an exogenously imposed rate of technological progress that multiplies L. A common one of them is given by the minimum between linear functions of each of its arguments; that Leontief one of these functions has zero substitutability. If these functions are homogenous in their arguments, they exhibit constant (*) returns to scale. The most common a priori form taken by these functions involve some constant, times capitalÂ­toÂ­theÂ­alpha, times laborÂ­toÂ­theÂ­beta; that is their CobbÂ–Douglas form. For 10 points, name these functions that relate inputted "factors" like materials and labor to the number of goods that are outputted.
These functions are generally assumed to satisfy the Inada conditions.
production functions [accept "utility functions" until the second line; accept any specific production function, e.g. CobbÂ–Douglas functions]