A very good morning friends. I welcome you all to the Shankar summary 2024. Today we are going to see second part of our economics compilation video. Here are the list of articles which we are going to discuss today. Let us get started. Let us look at this quiz question. This quiz question is talking about fully accessible route mechanism for investment. Before answering, let us see in a brief about fully accessible route to get concepts clear. Reserve Bank of India RBI has introduced a separate channel of investment called fully accessible route in 2020. See, it enables the non-resident Indians, NRIs, to invest in specified government bonds. An important point to be noted here is that the eligible investors can invest in specified government securities without being subjected to any kind of investment ceilings. See, the scheme will operate along with the two existing routes of FBI like a medium term framework and voluntary retention route. See, this is the basic of our FAR. In our discussion, now let us see some facts about voluntary retention mechanism to have a clear picture of these things. See, VRR, our voluntary retention route is another scheme introduced by RBI to encourage the foreign portfolio investors for long term investments in the Indian debt markets. See, it provides operational flexibility and exemptions from certain regulatory requirements. Moreover, this route requires a retention period of over 3 years with the FBI maintaining a minimum of 75 percentage of allotted amount in India. See, the investment levels are available on tap and allotted by clearing corporation of India limited CCIL on a first come first serve basis. See, this is the base points about voluntary retention routes. So, with this basic idea, now let us go back and solve this question. See the first statement, eligible NRIs can invest in specified government securities without subjected to any kind of investment ceilings. See, this is correct as we have seen in our discussion about FAR. See the second statement, it operates alongside with two existing routes of MTF and VRR. See, this is also correct as we have seen in our discussion. So, both the statements are correct. So, the correct option is option C. Let us move on to solve the next MCQ. Look at this question. This question talks about a concept called safe harbor which was recently seen in the news. Before solving, let us see in a brief about what is safe harbor is. Firstly, safe harbor is a protection available under section 79 of the IT Act 2000. See, it is a legal immunity that online intermediaries like Insta, FB, X enjoy against the contents which are being posted on it by the users. Know that this protection is available as long as these platforms abide by the rules certain due diligence requirements such as censoring content when asked by the government or courts. See, this concept originally came from section 230 of the United States Communications Decency Act which has been termed as one of the foundational laws behind the modern internet. Okay, now we should know why this concept has flared up in the recent news. See, Digital India Act 2023 which was a policy to replace the IT Act 2000 reviews this safe harbor principle. See, as we have seen now, this is the principle which primarily shields the online platforms from the liability related to user generated content. With this removal, this can be counterproductive to the fundamental rights of expression. So, with this basics, let us go back and solve the question. See, the term safe harbor which was seen in the news is associated with, see out of four options, we know that the correct option is option A online content. See, with this basics, let us move on to the next MCQ. See, this MCQ is about the non-banking financial companies or NBFC. As we know that this is an important concept which can be asked again and again in the exam. So, in this context in our discussion today, let us see some important points about NBFC and we shall see the concepts and then we shall come again and solve this question. Okay, let us start our discussion. Non-banking financial companies or NBFCs are financial institutions that provides banking services but know that they do not hold a full banking license. In India, for example, they are registered under Companies Act 1956 whereas a commercial bank will obtain license for commercial banking business under section 22 of the Banking Regulation Act 1949. Moving on our discussion, NBFCs are regulated by variety of organizations like NBFCs like investments and credit companies, core investment companies, infrastructure finance companies are regulated by RBI. On the other hand, NBFCs like housing finance companies are regulated by National Housing Bank. Moreover, Merchant Banker Venture Capital Funds companies are regulated by SEBI. Fourthly, Insurance companies are regulated by IRDAI and fifthly, Chid fund companies are regulated by their respective state governments and finally, NIDI companies are regulated by Ministry of Corporate Affairs Government of India. See, this is why I mentioned that NBFCs are regulated by various types of organization depends upon the target group whom they work for. Okay, moving forward, let us see how NBFCs are different from banks. See, the first major difference is in relation to the demand deposits. See, while banks can accept demand deposits, NBFCs cannot accept it. Here, demand deposits are nothing but savings account. The second difference is NBFCs do not form part of the payment and settlement system while we know that banks are of course a part of the system. Thirdly, NBFCs cannot issue checkbooks. Then NBFCs cannot offer money transfer services like the traditional banks. The moving on, the next major difference is that NBFCs do not have to maintain any reserve ratio such as cash reserve ratio, statutory liquidity ratio while banks must mandatory maintain these reserve ratios. Also, NBFCs cannot provide deposit insurance facilities which are offered by the Deposit Insurance and Credit Guarantee Corporation. What does it means? It means deposit insurance is a protection mechanism provided by the government to safeguard depositors' money which is held in the banks. It assures the depositors that their funds up to a certain limit will be reimbursed even if the bank fails. In India, NBFCs cannot provide deposit insurance. So, if you deposit money in NBFC and if that NBFC becomes insolvent, then the money deposited with NBFC will be completely lost. See, there are some of the differences between the bank and NBFCs with this broad basics. Now, let us go back and solve the question. See the first statement. It says that NBFCs cannot engage in acquisition of the securities which are issued by the government. See, the statement is incorrect because NBFCs will be primarily engaged in the business of loans and advances, acquisitions of the shares, stock, bonds, debentures, etc. So, the statement one is incorrect. See, the second one. NBFCs cannot accept demand deposits like the savings account. See, of course, this is correct because we have seen in our discussion. So, the statement one alone is incorrect. So, the correct option is option B. See, the basic, let us move on to the next MCQ. Let us look at this MCQ. It talks about Financial Action Task Force or FATF. Before solving this question, we ought to know why this has appeared in the news. See, FATF or Financial Action Task Force has recently removed the Cayman Island from the gray list. See, this may lead to positive FTA flow from this region in the near future to India. See, this is the context on which the question appeared. See this question. Now, we shall discuss the basics about FATF before we are going to solve the question. So, firstly, what is Financial Action Task Force or FATF? See, FATF is an intergovernmental body established in 1989 during the G7 summit in Paris. The objective of the body is to set the standards and promote effective implementation of the legal, regulatory and operational measures for combating money laundering, terror financing and other related issues that will threat the integrity of the international financial system. See, its secretariat is located at the OECD headquarters in Paris. Note that FATF also added terror financing as the main area of focus. See, this was done after the 9-11 terror attack of the US. Then later, the focus was broadened to include restricting the funding of the weapons of mass destruction. Now, moving on a discussion, see, FATF includes 39 countries including US, India, China, Saudi Arabia, Britain, German, etc. Know an important point that India became a member of FATF in 2010. Note that the FATF plenary is the decision-making body of the FATF. It meets three times per year. Now, let us see the two types of lists of FATF. Firstly, grey list. See, officially it is termed as jurisdiction under increased monitoring. See, the countries that are considered safe haven for supporting the terror financing and money laundering are put in the FATF grey list. See, this inclusion serves as a warning to the country that it may enter blacklist. Secondly, blacklist. See, it is called a high-risk jurisdiction subject to call for action. See, these blacklist countries are often termed as non-cooperative countries or territories or NCCT. Know that these countries support terror funding and money laundering activities. FATF revives the blacklist regularly adding or deleting the entities. Know that currently North Korea, Iran, Myanmar are in the blacklist. Now, let us see what are the consequences of being put in the blacklist? See, firstly, no financial aid will be given to them by the IMF, World Bank, ADB or EU. Secondly, they also face a number of international economic and financial restrictions and sanctions. See, this is the basic about the FATF. Now, let us solve the question. See the first one. India is a member of the tax force. See, this is correct. As you have seen that, India became a member in 2010. So, the statement one is correct. See the second one. The mandate of the group is to deal with the money laundering only. See, this is wrong because we saw that the mandate of the group varies from money laundering to terror financing to weapons of mass destruction etc. So, the statement is wrong. Third one is, non-cooperative territories are placed under a great list of FATF. See, this is wrong because the technical name of blacklist is called non-cooperative territories. So, the third statement is also wrong. So, the correct option is option A. With these basics, now let us move on to the next MCQ. Look at the MCQ. It talks about an economic concept called evergreening. Okay, before solving the MCQ, we shall see about the concept of evergreening. See, the term evergreening of loan refers to a banking practice in which the bank attempts to sustain a loan which is on the brink of default by providing further loans to the same default borrower. See, it is a temporary fix that generally obscures the true condition of stressed loans and delays the recognition of the losses by the banks. See, the objective is to prevent the loans from being classified as non-performing asserts and to minimize the impact on the profitability of the banks and provisioning requirements. Simple. See, it refers to a specific types of loan where the principal payment is deferred and typically only the interest is expected to pay until the end of loan term. See, the setup allows for the indefinite postponement of the principal and operates similar to the revolving credit. Okay, now let us see the reasons for adopting this practice. Firstly, impact on the profitability. See, banks need to make higher provisions if an account turns to an NPA. As we know that NPA will significantly impact their profitability. Secondly, avoiding NPA classification. See, banks resort to evergreening to avoid classifying them as the NPA thereby delaying the recognition of losses. Thirdly, liquidity and provisioning. See, evergreening allows the banks to avoid provisioning to cover loan losses and help them to maintain liquidity. Okay. With this, let us see what are the methods of evergreening. Firstly, inter-bank arrangements. See, banks collaborate to evergreen each other's loan through sale and buyback of the loans or debt instruments. Secondly, structured deals. See, it will encourage sound borrowers to engage in the structured deal with the stressed borrowers to conceal the stress. Thirdly, internal adjustments. It involves the use of internal or office account to adjust the borrowers' repayments obligation. Fourthly, renewable loans. See, renewing the loan or dispersing the newer additional loans to the stressed borrowers are related entities which are closer to the repayment date of the earlier loans. See, with this basics about evergreening, now let us solve the question. The term evergreening makes news repeatedly in the recent past, which are the following, but I defends it. See, out of the four options, option B, a banking practice to deal with a bad loan fits the correct definition of evergreening. So, the correct option is option B. So, with this basics, let us move on to the next MCQ of the day. Look at this MCQ. It lists four types of funds and it asks us how many of them will fit into the definition of Alternative Investment Fund. Before answering this, we have to be aware about the basics of Alternate Investment Fund, AIF. Let us start our discussion. See, AIF or Alternative Investment Funds or the Special Investment category funds which are very different from the conventional investment instruments know that any AIF has two characteristics. They are the funds which are established in India and secondly, they are the privately pulled instrument vehicle which collects funds from the sophisticated investors who are both from foreign or Indian for investing. See, it pulls funds from the investors and invest them under different category of investments as specified by SEBI for the benefit of borrowers. Know that this investment vehicle must adhere to the regulations of the SEBI under SEBI Alternative Investment Fund regulations 2012. We should know that the various forms of AIF are venture capitalists, infra funds, limited liability partnership, trust, etc. Now, moving on our discussion, we shall see about three categories of the AIFs. Category 1, see, this kind of investments can invest in startups, yearly stage ventures, social ventures, SMEs and sectors in which the government or regulators consider us socially or economically desirable. See, it includes the venture capital funds like angel funds, SME funds, social venture funds, etc. Secondly, category 2, Alternative Investment Funds. Here, these are the funds which are not classified either under category 1 or under category 3. See, they do not undertake leverages or borrowing other than to meet the day-to-day operational requirements and as permitted in the regulations. Thirdly, we should know that the various types of funds are real estate fund, debt fund, private equity fund, funds for the distrust assets, etc. And finally, category 3 AIFs. See, these are the funds which employ complex or diversive traditional diverse trading strategies and may employ leverages including the investments in the listed or unlisted hedge funds, pipe funds, etc. We should know the basics that category 1 and 2 are closed ended funds and having a minimum tenure of 3 years whereas the category 3 can be either open ended or closed ended funds. Here, we should know the basic about them, right? Open ended funds can be brought or sold anytime whereas the closed ended funds can be brought only during the launch and can be redeemed only when the investment tenure is over. See, with this broad basics, let us go back and solve the MCQ related to AIF. See, out of these four funds which are listed, all four of them will fit into the definition of alternative investment funds. So, the correct option is option D. With this basics, now let us move on to the next MCQ of the day. Look at this MCQ. This MCQ is about the statements regarding credit information companies. See, the news about credit information companies often appeared in the newspaper. So, it is very important from our example's perspective. See, here two statements are given. First, we are going to see about the basics of CIC before answering this. Let us start our discussion. Firstly, credit rating agencies or CRA is a company that assigns credit ratings which rate debtor's ability to pay back the debt by making the timely principal and interest. See, they collect public data, credit transaction, payment history of the individuals and companies regarding the loan credit card etc. Note that the primary function is to gather the data from the various sources like bank, lenders, financial institutions and other rating agencies etc. See, then the CICs will compile this data and make a credit report. Okay, now with this basics, let us see the benefits of CIC. Firstly, banks, NBFCs refers to the CIC reports and scores to decides the credit worthiness of the borrowers before granting a loan or issuing a credit card. Secondly, an important point to be noted is that CICs in India are licensed by RBI and governed by credit information companies Regulation Act 2005 or CICRA and they will be often regulated by the various rules and regulations issued by the RBI. See, as per section 15 of this CICRA Act, every credit institutions like banks should be a member of at least one CIC. Moreover, CICRA acts to place that a CIC may seek and apply information from its members only. Okay, now at present, four CICs are given third week of registration by the RBI. They are Credit Information Bureau India Limited, SIBL, Equifax Credit Information Services Private Limited, Xperian Credit Information Company of India Private Limited and CRI of High Market Credit Information Services Private Limited. So, with this basics, let us now see the question. First thing, they collect the credit history of both the individuals and companies to create credit report. See, this statement is correct because as we have seen in our discussion. Secondly, know that CICs are regulated by the Reserve Bank of India. See, this is also correct and guys, I am giving an extra data that credit rating agencies which is very different from CIC, credit rating agencies are regulated by SEBI. Okay, so here both the statements are correct. So, with this basics, let us move on to the next MCQ of the day. Look at this question. It is about the concept called base erosion and profit sharing. It says that which of the following better describes the BEPS. Okay, now before answering this question, let us look at a concept which is very much related to BEPS which is called double taxation avoidance agreement or DTA. Okay, let us start our discussion. See, DTA is a treaty signed between two or more countries. The key objective of DTA is that the taxpayers in these countries can avoid being taxed twice for the same income which is generated by them. Know that it is applicable in the cases where a taxpayer residing in one country A and earn his income from other country B. Now moving on in our discussion, know that India establishes DTA with other countries through section 90 of the IT Act 1961. Presently, India has DTA with more than 80 countries. See, it is legislated on a reciprocal basis and covers residents of India as well as residents of the negotiating country. Here, you should know about an important point that an individual or a corporation, not a resident of India or the country with which India signed DTA cannot climb benefits under the DTA. Moving on our discussion, DTA can either cover all types of income or it can also target a specific type of income depending upon the types of businesses or holdings etc. Okay, now the following categories are generally covered under a double taxation avoidance agreement. They are services, salary, property, capital gains, savings or fixed deposit accounts. So, with this basics, now let us see the question. Here, DPS is very much related to the tax avoidance strategy. Let us option B. So, this basic points, let us move on to the next MCQ. Look at this MCQ. This MCQ is about the statements with reference to minimum support price or MSP. See, questions about MSP will often ask in the UPSC preliminary examinations. So, it is in our best interest to know inside out about MSP. Okay, now let us start our discussion. See, in the slides I have attached it to recent previous question based on MSP for your understanding. Please have a look at them. Now, let us see about MSP from exam perspective. Firstly, what is minimum support price or MSP? See, MSP is a form of market intervention by the government of India. It is the price at which the government purchases the crop from the farmers. Know that by doing so, it will protect the farmers against any sharp fall in the prices. Moreover, MSP is announced by the central government at the beginning of every sowing season. To be more precise, MSP is approved by Cabinet Committee of Economic Affairs, chaired by the Prime Minister on the basis of the recommendation by Commission for the Agricultural Cost and Price or CACP. Now, I am displaying the determinants of MSP for your reference. Please have a look at them. Now, let us see the objectives of MSP. See, in simple words, it is the price fixed by the government of India to protect the farmers against excessive fall in prices during the bumper production years. On the other hand, during any drought season, it will provide a guarantee price for the produce. Thirdly, it will ensure food security in the country as the crops procured under MSP is used for PDS system. See, this is all about the objectives. Now, let us see the crops which are covered under MSP. See, government announces MSP for 20 to mandated crops and FRP for sugarcane. See, among the 22 crops, 14 belong to cariff season, 6 belong to robby season and 2 belong to commercial crops. Here, I am displaying a list of crops for your reference. So, please memorize them often, as it is directly asked in the preliminary. So, with these basic points, let us move on to solving the question. Here, the first statement states that MSP is fixed by the government on the basis of the recommendations of the CACP. See, we know that it is correct. See, the second statement, the Rangarajan committee recommended that the MSP should be at least 50% more than the varied average. See, this statement is wrong because this recommendation is given by Swaminathan commission, not Rangarajan commission. See, the third statement, in India, MSP is applicable to 20 to cariff, robby and commercial crops including sugarcane. See, this is wrong because we know that sugarcane is given a separate price called FRP, which is very different from MSP. So, eliminating 2 and 3, the correct option is option A. So, this basics, let us move on to the next MCQ. Look at this MCQ. It talks about the lending instruments of the IMF. Like other questions, before answering, let us get into the basics of the various lending instruments of the International Monetary Fund. See, the first one is standby agreement. See, the standby agreement provides short-term financial assistance to the countries who are facing the balance of payment problems. Historically, it has been the IMF lending instrument most used by the advanced and emerging market countries. See, when a country receives funds via SBA, then that country must take measures to address the problems that led the country to seek funding in the first place. Moreover, SBA is provided in tranks and before each tranche is provided, the IMF reviews the country's policies. Recently, IMF provided bailout packages for the Pakistan is also provided under SBA facility. Now, the second one is standby credit facility or SCF. See, the SCF provides financial assistance to the low-income countries with short-term balance of payment needs. Note that it is one of the facilities provided under poverty reduction and growth trust PRGT of IMF. Note that both SBA and SCF are provided to avoid present prospective or potential balance of payment crisis. See, when the BOP crisis or balance of payment crisis extends for a protracted period, then the IMF provides support through extended fund facility or extended credit facility. See, both these facilities provide financial assistance to the countries which are facing serious medium-term BOP problems because of the structural weaknesses that requires time to address. To help countries implement the medium-term frameworks, these facilities offer longer program engagement, longer repayment period. See, the advanced and emerging economies are offered extended fund facility and the low-income countries are provided extended credit facility. Note that in 2019 Pakistan used the extended fund facility to get financial support from the IMF. I am moving on to our discussion. For urgent BOP needs, the IMF has rapid financing instrument facility and rapid credit facility. Here, note that this RCF or rapid credit facility appeared in 2022 preliminary question. Okay, now back to our discussion. See, both are designed to provide finding to the countries that are experiencing a sudden and unexpected BOP crisis. Here, the RFI is mainly used by the advanced and the emerging economies and RCF is mostly used by the low-income countries. The next one is short-term liquidity line or SLL. Here, the SLL is provided for IMF countries with very strong policy frameworks and fundamentals who face potential moderate short-term liquidity needs. See, these countries with strong policy frameworks fall into the BOP shocks due to external shocks. The SLL aims to minimize the risk of these shocks thereby avoiding the crisis to go into a deeper crisis and eventually spread into other countries. See, the next one is flexible credit line. See, the FCL is provided to the countries with very strong policy frameworks and track records in economic performance. Note that the financial support received under FCL is used to prevent the crisis from happening. Then comes the precautionary and liquidity line PLL. See, it is designed to meet the liquidity needs of the member countries with sound economic fundamentals but with some remaining vulnerabilities that preclude them from using the FCL facilities. To put it simply, basically countries with good economic fundamentals but not good enough to receiving funding via FCL will receive PLL facility. Finally, there is resilience and sustainability facility or RSF. See, it provides affordable long-term financing to the countries which are undertaking reforms to reduce the risks to prospective balance of payment stability including those related to climate change, pandemic preparedness, etc. See, these are all the various lending instruments of the IMF. So, to back to our discussion, see here out of these three statements, see the first one and second one, these two are correct because just now we have seen it in our discussion. Now, regarding the third statement, see India has received packages from IMF via both SBA and EAF and EFF. See, in 1981, India received EFF fund and between 1957 to 1991, India received SBA fund. Here, the correct option is option C. With this basic understanding, let us move on to the next MCQ of the day. Look at this MCQ. It talks about the institution called National Company Lord Tribunal. See, it often appeared in the news. So, the various composition and functioning of the NCLT is very important for the examination perspective.  See, firstly, NCLT, National Company Lord Tribunal was constituted in 2016 under the Companies Act 2013. See, it is a statutory body which means created by the parliamentary law. Know that it was formed to deal with the corporate disputes that are of civil nature. This means NCLT works on the line of normal civil court in the country. But the difference is, they are constituted specifically to deal with the civil corporate disputes which are arising out of Companies Act 2013. Note that NCLT decides the matters in accordance with the principles of natural justice. Since it is performing judicial functions, it is also called a quasi-judicial authority. Now, let us see the benches of NCLT. See, it has a principle bench at New Delhi. Apart from this, it also has benches at Ahmedabad, Allahabad, Bengaluru, Chandigarh, Chennai, Gauhati, Hyderabad, Kolkatta and Mumbai. See, with this basics, now let us see the composition of the body. See, it consists of a president and some other judicial and technical members. The president of the tribunal will be appointed by the central government after consultation with Chief Justice of India. Note that the president of the NCLT must be a judge of high court or he has been a judge of the high court for five years. Now, coming to the members, the members of the tribunal are appointed by the central government based on the recommendation of the selection committee. See, this is all about the composition. Now, finally, let us see the functions of NCLT. Firstly, NCLT adjudicates the cases related to insolvency and liquidation of the corporate companies. See, this role to NCLT is mandatory under insolvency and bankruptcy code 2016. Here, note that the NCLT deals with the insolvency of only corporates under the code. But in the case of the insolvency of the individuals and partnerships, it will be dealt by debt recovery tribunal. Secondly, NCLT deals with the cases pending under Sick Industries Company Special Provisions Act 1985. See, it was enacted to detect the unbearable companies or sick companies that has potential systematic financial risk. So, if any cases are filed under such an act, it will be subsequently dealt by NCLT. Finally, NCLT plays a crucial role in facilitating the mergers and acquisitions. When two or more companies wish to merge, they must seek the approval of the NCLT. See, the tribunal examines the proposal and ensures that it is complied with the relevant law and regulations. If the merger is approved, the NCLT oversees the process of integration and ensures that the interests of all stakeholders are being protected. Note that if anyone is aggrieved by the decisions of the NCLT, then they can make an appeal before NCLAT, that is National Company Law Appliate Tribunal. And all the decisions of the National Company Law Appliate Tribunal can be challenged to Supreme Court. See, this is all regarding the discussion. So, with these basics, now let us go back and solve the MCQ. Here, let us see the first statement. It says that NCLT deals with the corporate disputes that are of both civil and criminal nature. See, this statement is incorrect because we have known from our discussion that NCLT deals with the corporate civil disputes. Secondly, the decisions of the NCLT can be directly appealed before the Supreme Court. See, this is incorrect because for such appeals, NCLT has been created. The third one is, it deals with the insolvency cases of the corporate bodies under IBC. See, this statement is correct actually because as we have seen in our discussion. So, the correct option is option A. So, with these basics, let us move on to discuss next MCQ. Look at this MCQ. What is the purpose of setting up of small finance bank in India? See, we know that small finance banks, payment banks and the nuances between them are often asked in the preliminary. So, before answering, let us go and have a basic about them. Now, let us start our discussion. Firstly, let us see about payment banks. See, there are two kinds of banking license that are granted by the Reserve Bank of India, that is, universal banking license and differentiated banking license. Payment bank comes under differentiated banking license, since it cannot offer all the services that a commercial bank offers. Note that a payment bank cannot lend. It can take deposits up to 1 lakh per account. It can issue debit cards but not credit cards. Now, what is the main aim of payment banks? See, the major objective of the payment bank is to further the financial inclusion by providing small saving accounts and payment or remittance services to the migrant laborers, low income households, small businesses and other unorganized sectors. The other functions are the payment bank can work as a BC or banking correspondent of another bank. By doing so, they can distribute the simple financial products like mutual funds, insurance products, etc. Okay. Now, with this, let us see about small finance bank. See, small finance banks are a category of banks that are established to provide basic banking services and credit facilities to the underserved sections of the population. See, it includes small business owners, MSMEs, farmers and unorganized sector. The various examples of small finance banks are Ujjivan, Capital Small Finance Bank, Uttkars, etc. Now, let us see what are the aims of small finance banks. See, the objective is to provide financial inclusion to the segments which are often excluded from the traditional banking system. See, it helps them to have access to financial products like small loans, savings, insurance, etc. Now, let us see the regulation of small finance banks. Note that they are regulated by RBI. All norms and regulations of the RBI that are applicable to the commercial banks including the requirement of CRR, SLR maintenance are generally applicable to the small finance banks. Also, according to the RBI, if any small finance bank want to become a universal bank, it has to complete satisfactory track record of performance for a minimum period of five years. See, this is regarding the discussion. With this basic, now let us go and solve the MSQ. See, here it asked about the purpose of setting up of small finance bank. See, the first statement, to supply credit to the small business units. See, it is correct since we have seen in our discussion. Secondly, credit to small and marginal farmers also correct because just know we have seen. See, the third one, it increase the young entrepreneurs to set up business particularly in the rural areas. See, this may look correct but it is not the main aim of setting up of this SFB. So, the correct option is option A. See, this is all regarding the discussion. With this, we have come to the end of the video. If you like today's video, like, comment and share with your friends. For more updates regarding UPSC preparation, subscribe to Shankar IS Academy. Thank you.


Water is now a scarce commodity, so at Mekuni, I ask my guests if they want water served at their table. I'm a Californian. I don't waste water.


The Bemidji Community Theatre has been working on their production of The Elves and The Shoemakers since January and this weekend the show will finally make its debut. There are 39 people in the cast and most of them are kids under 18. All of the actors also helped design the hand-painted set. There'll be performances this weekend from Friday to Saturday as well as next weekend with a few special matinee shows for schools. Tickets can be purchased at the box office or at Ken K. Thompson Jewelry. I hope that the energy builds up into the audience that they can put themselves into it and I guess relate as the show is going. I also hope it influences them a little bit. Just the story of how the shoemaker and his wife gave up their last little bit to help someone in need and showing how when you bless someone else, blessings come around. The theatre is also giving a special treat to the children who attend the show. Every child in the audience will walk away with a free book.


Last time we derived Adams-Bashforth method. Today we are going to consider the local discretization error in this method. Then we are going to consider new class of methods, which are known as predictor-corrector methods. So, we will see what are the advantages in this new method. After that I am going to derive what is known as midpoint method and compare it with Euler's method and the stability consideration of the midpoint method. So, Adams-Bashforth method we derived by using numerical quadrature. So, our right hand side function is f x y x. So, that is the function of x. For this function we fitted a cubic polynomial. So, we are integrating over the interval x n to x n plus 1. The cubic polynomial which we fit that is going to interpolate our given function g at x n x n minus 1 x n minus 2 x n minus 3. So, out of the 4 interpolation points only one belongs to the interval over which we are integrating and that gives us a formula. So, that is Adams-Bashforth formula. Now, we know how to derive the error in the numerical quadrature. So, using that we will show that the local discretization error is of the order of h raise to 5. So, that is our Adams-Bashforth method. So, this is our initial value problem y dash x is equal to f of x y x is equal to g x x belonging to a b. Initial value is y at a is equal to y 0 that is given. We look at uniform partition of interval a b. So, we divide it into n equal parts. H is length of the sub interval b minus a by n p 3 is the polynomial of degree less than or equal to 3 interpolating our function g at x n x n minus 1 x n minus 2 x n minus 3. This is the exact equation. So, y is our unknown solution y x n plus 1 minus y at x n is equal to integral x n to x n plus 1 g x d x. Then this g we are going to replace by our cubic polynomial interpolation. So, here it should be y n plus 1 is equal to y n plus 1 minus y n is equal to integral x n to x n plus 1. Instead of g it should be p 3 x d x. Now, this formula we derived yesterday.  So, thus we have got a formula for y n plus 1 in terms of y n y n minus 1 y n minus 2 and y n minus 3. So, thus we need to be given y 0 y 1 y 2 and y 3 in case of the single step formulae such as the Euler's method or Runge-Cutta methods y 0 is our initial condition. So, once you know y 0 you calculate y 1 you calculate y 2 and so on. On the other hand in this method we need to know y 0 y 1 y 2 and y 3. Once we know that then our procedure can continue then you calculate y 4. Now, for the y 4 you are once you calculate y 4 then y 5 will be in terms of y 1 y 2 y 3 y 4 and so on. So, these formulae these are not self starting. So, y 0 is given to us y 1 y 2 y 3 we need to calculate by some other method. Now, we are going to show that local discretization error in the Adams-Bashford formulae is of the order of h raise to 5. So, then y 1 y 2 y 3 also should be found with the same local discretization error h raise to 5 because if these are calculated less accurately then overall order of convergence is going to suffer. So, then in the case of Runge-Cutta method of order 4 we have the local discretization error to be h raise to 5. So, using this formula calculate y 1 y 2 y 3 and now use this formula now why cannot I just continue with the Runge-Cutta method the reason is here our y n plus 1 we have seen that the formula is in terms of y n y n minus 1 y n minus 2 y n minus 3. Then when you go to y n plus 2 then it will have y n plus 1 y n y n minus 1 y n minus 2 let me write. So, in order to calculate y n plus 1 what comes into picture is y n y n minus 1 y n minus 2 y n minus 3 when you look at y n plus 2 it will be y n plus 1 y n y n minus 1 and y n minus 2. So, these 3 values they are common to both y n plus 1 and y n plus 2. So, thus in the case of Adams-Bashworth method except for the first step afterwards you are going to have only one function evaluation per step in case of Runge-Cutta method of order 4 you have 4 function evaluations per step. So, that 4 you are reducing it to 1 while retaining the local discretization error to be h raise to 5. So, that is the advantage of Adams-Bashworth method as compared to the Runge-Cutta method of order 4. So, now let us look at the error in the Adams-Bashworth formula. So, we have the this is the error term integral x n to x n plus 1 divided difference of g based on x n x n minus 1 x n minus 2 x n minus 3 these were the interpolation points x multiplied by x minus x n x minus x n minus 1 x minus x n minus 2 x minus x n minus 3 d x. Now, you know that you can assuming g to be sufficiently differentiable then one can show that this is equal to also look at this your integration is over x n to x n plus 1. So, when I look at x minus x n x minus x n minus 1 x minus x n minus 2 x minus x n minus 3 this function is going to be bigger than or equal to 0. So, you can use mean value theorem for integral using the mean value theorem for integrals the divided difference will come out as the divided difference evaluated at some point c this is a polynomial. So, you can integrate and then when does the calculations it comes out to be 251 by 720 h raise to 5 fourth derivative of g at some point d n our y dash is equal to f which is equal to g. So, that is why g 4 is going to be y 5. So, this is going to be the error in the Adams-Bashforth formula and it is of the order of h raise to 5 and in order to calculate y 1 y 2 y 3 use Runge-Kutta method of order 4 which has local discretization error of the order of h raise to 5. So, now we are going to consider predictor-corrector formulae we started with numerical integration then when you use rectangle rule then what you get is Euler's method. After the rectangle rule suppose I want to consider the trapezoidal rule then on the left hand side I will have y n plus 1 on the right hand side also there will be y n plus 1. So, y n plus 1 will be defined only implicitly that is why even in the Adams-Bashforth method you will know that we did not include x n plus 1 as a interpolation points, but we took the earlier interpolation point. So, we are going to look at trapezoidal rule and then we will apply iteration method and that gives rise to what are known as predictor-corrector formulae. So, we have this is the exact equation the trapezoidal rule and the trapezoidal rule will be the right hand side will be approximated by h by 2 h is the length of the interval x n plus 1 minus x n. So, h by 2 f of x n y n plus f of x n plus 1 y n plus 1. So, you have got y n plus 1 here you have got y n plus 1 here the function f it may be something we are not saying that f should be some simple function or f is any general function. So, that is why you have got only implicit definition of y n plus 1. When we look at the Euler's method you had y n plus 1 is equal to y n plus h times f of x n y n. So, you have a formula now here is only implicit and then the error this is the error in the trapezoidal rule. So, that is minus h cube by 12 y triple dash d n. So, the idea is look at the Euler's method here the error is of the order of h square this is your trapezoidal rule here y n plus 1 is defined only implicitly. So, calculate y n plus 1 using this Euler's method. So, let us call it y n plus 1 superscript 0 substitute in this formula and then you will get y n plus 1 1 then whatever value you get you substitute again. So, you are going to calculate y n plus 1 iteratively. So, here the formula which is given by Euler's method that is known as predictor formula or the open formula. The formula which is given by trapezoidal rule that is known as corrector formula. In general the corrector formula is more accurate than the predictor here you have local discretization error to be h square here you have got h cube. So, we are going to define the iteration scheme and that is known as predictor corrector formula. So, let me describe that. So, we have fix x n this is I am using the Euler's formula then y n plus 1 1 is equal to y n plus. So, this is the trapezoidal rule. So, I substitute here y n plus 1 0 in general y n plus 1 k is equal to y n plus h times f of x n y n plus f of x n plus 1 y n plus 1 k minus 1 divided by 2. So, now, we are doing iteration. So, we have to tell. So, in this algorithm what one needs to tell is what is your h the length of the sub interval then how many iterates I should have some stopping criteria for this iteration scheme. So, suppose I say that the maximum number should be capital K. Now, at each stage what one will do is check the relative error in the successive iterates. If that relative error is less than a prescribed epsilon then you stop otherwise you give some maximum number of iterates. If even after doing the maximum number of iterates if your relative error is not less than epsilon then what one can do is replace h by h by 2 reduce your step size in practice. If you have chosen the step size correctly then you need to evaluate only one or two steps or two iterates. So, you calculate one or two iterates and then you are going to get a formula. Now, the advantage is our predictor formula has local discretization error only h square whereas, our corrector formula has local discretization error h cube. So, we are trying to obtain a better approximation. Of course, it increases your work because you will be calculating the iterates one or two iterates. So, that will involve the function evaluation, but then you are getting a better solution. So, we have epsilon is prescribed stop the iteration when the relative error. So, these are our successive iterates then you divide by modulus of y n plus 1 k. So, that it becomes a relative error this should be less than epsilon. So, that tells us how many iterates we should calculate. So, as I said Euler's formula is open or predictor formula trapezoidal rule is closed or corrector formula and generally corrector formula is more accurate than predictor formula. And this for the algorithms we need to specify h maximum number of iterations and what to do if k exceeds capital K. So, in general you will need only one or two iterations otherwise you reduce h and then you continue. So, we have considered one predictor corrector formula. Now, we can use this idea and define other corrector predictor corrector formula. So, when we derived Adams-Bashforth method we had considered cubic interpolation polynomial which interpolates our function g at x n x n minus 1 x n minus 2 x n minus 3. If instead of choosing these interpolation points if I choose the interpolation points to be x n plus 1 x n x n minus 1 x n minus 2 then I will get a formula that formula will define y n plus 1 implicitly like in case of the trapezoidal rule. Then use Adams-Bashforth method as your predictor formula. So, we had considered pair of formulas it was Euler's method and trapezoidal rule. Now, instead of that instead of Euler's method we are going to consider Adams-Bashforth method and the corrector formula is going to be the one which is obtained by replacing function g by a cubic polynomial interpolation with interpolation points as x n plus 1 x n x n minus 1 x n minus 2. Now, here we have the order of convergence or the error is going to be h raise to 5 in both the methods. For Euler's method we had h square trapezoidal it was h cube, but now the formula which I am going to define it will have both to be h raise to 5, but in the corrector formula the coefficient is going to be smaller and the advantage in this method is going to be we will have some idea about the error like what we are trying to do in these methods is y is our unknown solution. So, we try to approximate value of y at points x n and then our approximations are we are denoting by y n. So, when I consider the error y at x n minus y n I know that their local discretization error in various methods I know, but I have no idea how much the error is going to be. So, in this method which we are going to define now we will have an idea about the exact error how much it is going to be. So, let us look at this method this method is known as Adam's Moulton method this is the equation satisfied by the exact solution y p 3 is a polynomial of degree less than or equal to 3 interpolating the given function at x n plus 1 x n x n minus 1 x n minus 2. So, now the interpolation points are x n plus 1 and x n these are going to be in our interval over which we are integrating and these are to the exterior in case of Adam's Moulton method. So, once by 4 only x n was in the interval of integration whereas, x n minus 1 x n minus 2 x n minus 3 they were outside the interval of integration then y n plus 1 minus y n is integral x n to x n plus 1 p 3 x d x I skip the details.   So, once again the y n plus 1 is going to be defined implicitly you have here as well as here and the error as I said that it is it is of the order of h raise to 5, but the coefficient now is smaller than in case of Adam's Moulton method. So, the error is minus 19 by 720 h raise to 5 y 5 and then some point d this is the Adam's Moulton predictor corrector method y 0, y 1, y 2, y 3 they are given calculate y n plus 1 0 using Adam's Bashforth formula. So, what we had used earlier Euler's formula now we are using Adam's Bashforth formula once you calculate y n plus 1 0 then you use Adam's Moulton formula.   So, starting iterate y n plus 1 0 is obtained by using Adam's Bashforth method then use Adam's Moulton formula for calculating y n plus 1 k and iterate till the relative error is less than a prescribed epsilon. So, here you have got error in the Adam's Bashforth method it is h raise to 5, but the coefficient is 251 by 77. So, this is the error in Adam's Moulton method. So, here you have got minus 19 by 720 y 5 d n h raise to 5. So, this y n plus 1 0 it was obtained by using Adam's Bashforth formula. So, when I look at the error y x n plus 1 y n plus 1 0 this will be 251 by 751 by 751 by 751 by 7720 y 5 evaluated at c n h raise to 5, the first iterate when you calculate it involves Adam's Moulton method. So, you have got y x n plus 1 minus y n plus 1 1 to be minus 19 by 720 y 5 d n h raise to 5. Now, in general your c n and d n they are in general your c n and d n they are going to be different, but let us assume that our interval is small, the interval x n to x n plus 1 is small and the fifth derivative of y it does not change too much. So, if that is the case then I can assume that y 5 the fifth derivative of y whether I evaluate at c n or whether I evaluate at d n they are going to be about the same. Then using that fact you will have, so suppose this y 5 c n and y 5 d n they are about the same. Now, let me subtract these two equations, so y x n plus 1 will get cancelled and I will have y n plus 1 1 minus y n plus 1 0 to be equal to I am subtracting, so it is 270 by 720 y 5 d n h raise to 5. So, what we are going to do is this is the exact error, in the exact error you have got fifth derivative of y evaluated at d n we do not know what the fifth derivative is. Now, for y 5 d n h raise to 5 I am going to substitute from here. So, y 5 d n h raise to 5 will be 720 by 270 and then this what is the advantage this y n plus 1 1 we have calculated y n plus 1 0 we have calculated. So, this is something like I know how to calculate, so let us see how to do that. Let me substitute for y 5 d n h raise to 5 from this equation and then I will get, so we have we have seen that y n plus 1 1 minus y n plus 1 0 is approximately equal to 270 by 720 y 5 d n h raise to 5 substitute from here in this equation. So, you will get minus 19 by 270 y n plus 1 minus y n plus 1 0 which is minus 1 upon 14 into this. So, thus the error in the first iterate in the Adams-Moulton predictor character formula that is going to be approximately equal to look at the error or the difference between y n plus 1 1 the iterate minus y n plus 1 0. So, we have obtained by using Adams-Bashforth method we have calculated y n plus 1 1 take their difference. So, we know what that divide by 14. So, this whatever is that number that is going to be the error in the y x n plus 1 minus y n plus 1 1. So, that is the error in the Adams-Moulton method. So, this is the advantage of Adams-Moulton method that it tells us you can calculate the exact error. Now, if I can calculate the exact error then I can do step control like so far what we have been doing is start with interval a b sub divide it into equal parts our h is b minus a by n. Now, what we can do is at each stage we can look at the error. So, this error we like we want our error to be less than some number say I want it to be less than 10 raise to minus 6 and then also I will have some lower that I wanted 10 raise to minus 6, but I also wanted to be say bigger than or means I will have some two bounds. Now, if your error satisfies these two bounds then you continue with the same h otherwise you change the step length. So, see we have got say interval a b we are sub dividing into n equal parts h is the step length. Now, what one can do is throughout now replace h by h by 2, but then that increases your work. So, what we want is a more flexible control over our step size h. So, d n plus 1 is going to be our minus 1 by 14 y n plus 1 1 minus y n plus 1 0. So, modulus of d n plus 1 by h that is going to be local error per unit step. Suppose, we want our local error per unit step to lie between even and e 2 if for a particular n if it is between even and e 2 then you continue with the same step. If it is say modulus of d n plus 1 by h is bigger than e 2 then you should reduce h to h by 2 and if it is less than e 1 here increase h to 2 h. So, here as an example we can look at say 10 raise to minus 6 is less than modulus of d n plus 1 by h less than 10 raise to minus 4. So, suppose this is these are my bounds. So, if modulus of d n plus 1 by h if it is becoming bigger than 10 raise to minus 4 then we need to reduce h to h by 2. If modulus of d n plus 1 by h is less than 10 raise to minus 6 then I am getting more accuracy. So, may be I do not need this much of accuracy. So, then I will increase my h to 2 h. So, that is how we have a control over the step length h. So, here is a comparison. So, we have got three methods. The first method of order 4 Adams Bashforth and Adams Moulton. In all the four methods the local discretization error is of the order of h raise to 5 advantage of Runge Kutta method is that it is self starting. Whereas, Adams Bashforth and Adams Moulton they are not self starting we need to calculate y 1, y 2, y 3 by using some other method. So, in the function evaluations Runge Kutta method it has got the maximum number of function evaluations and that is going to be 4. In Adams Bashforth method you have got only one function evaluation and in case of Adams Moulton you will have two function evaluation. Let us assume that you are doing only one iterate. So, you have got two function evaluations. So, when you compare Adams Bashforth and Adams Moulton for Adams Moulton the number of function evaluation is twice as compared to Adams Bashforth method, but then we have got the error control and also the coefficient in the error of Adams Moulton method it is smaller as compared to Adams Bashforth method. So, Adams Moulton is going to give us better result. So, as I said many times there is a tradeoff and the methods which survive they have got some merit like if one particular method is better than some other method in all the respect like here what we do is we consider the computational effort, order of convergence and now we are going to look at what is known as stability. So, if one particular method is better than the other method in all respects then the other method will not survive, because as you know one can write the number of function evaluations and the number of function evaluations will not survive, because as you know one can write several methods we have got a variety of methods. You have got numerical quadrature. So, now the numerical quadrature is obtained by considering interpolating polynomials. So, your numerical quadrature depends on your choice of interpolation points what degree of polynomial you are able to write. So, you can write many methods, but what we are studying are the representative methods and which are better in some respect than other methods. So, Runge-Kutta method is a single step method whereas, Adams Bashforth and Adams Moulton method they are multi-step methods. All have local discretization error and error to be h raise to 5. Runge-Kutta method is a classical method whereas, Adams Bashforth and Adams Moulton method they are of relatively recent origin. Now, what I want to do is I want to consider midpoint rule. So, we have we started with rectangle rule, the rectangle rule gives us Euler's method. Then the trapezoidal method we considered in the predictor character formula. Now, I want to look at midpoint method. So, if I integrate over x n to x n plus 1 and use midpoint formula that introduces a new node which I do not want. So, what we are going to do is instead of integrating over x n to x n plus 1, we will integrate over x n minus 1 to x n plus 1. So, we have got our interval of length 2 h. If you consider interval x n minus 1 to x n plus 1, its midpoint is going to be equal to x n. So, you are not introducing a new node. So, let us look at what midpoint method looks like and let us see what are the merits of it. So, as usual this is our initial value problem, this is the equation satisfied by the unknown solution y. Now, instead of taking integration over x n to x n plus 1, we are taking over x n minus 1 to x n plus 1. So, you will have y n plus 1 is equal to minus y n minus 1 is equal to length of the interval is 2 h value of g at the midpoint. So, that is g x n. So, it is 2 h f of x n y. So, thus the midpoint rule is y n plus 1 is equal to y n minus 1 plus 2 h f of x n y n Euler's method was y n plus 1 is equal to y n plus h f of x n y. The error in the midpoint rule is of the order of h cube and error in the Euler's method is of the order of h square. So, when we consider the midpoint rule and Euler's method, they are very much similar. In Euler's method, you add f of h times f of x n y n to y n. In midpoint rule, you add 2 h times f of x n y n to y n minus 1. So, when you consider the complexity, the number of function evaluations, it is going to be exactly the same, but in the midpoint method you are obtaining the local discretization error to be h cube whereas, in the Euler's method it is only h square. So, now, this method midpoint method should be even better than Range-Cutta method of order 2. In the case of Range-Cutta method of order 2, we had two function evaluations.  So, we had two function evaluations. So, now, here you have got only one function evaluation. Local error is h cube. So, in fact, this method it should make the Euler's method and Range-Cutta method redundant because as I said that what we compare is the local discretization error and function evaluations. So, when you compare Euler's method and the midpoint method, the function evaluations is the same and the local discretization error is 1 degree more in the midpoint method. So, midpoint method is superior to Euler's method. If you compare the midpoint method with Range-Cutta method, both have the same discretization error of the order of h cube, but the number of function evaluations is double in case of Range-Cutta method. So, then again the midpoint method is superior to Range-Cutta method, but still these two methods they have survived and that is because this midpoint method it has stability problems. So, what the stability problems are that we are going to see. Now, before we do that I just want to remark one more thing that in case of the midpoint method we have got y n plus 1 is equal to y n minus 1 plus 2 h times f of x n y n. That means this formula I cannot use for y 1 because for y 1 I will have to go to y of minus 1 which we do not know. So, here you need to be given what is y 0 and what is y 1, y 0 comes with the problem y 1 you will have to find from some other formula. So, this midpoint method again it will not be a self starting method look at this example. So, this example it is from Conte de Bourg's book here the exact solution is y x is equal to 1 by 2 e raise to minus 2 x plus half. He has given the result for interval 0 to 4 and h was chosen to be 1 by 32 you can yourself do the computations. So, what we want to do is we want to compare the midpoint method and the Euler's method. So, here are some of the results. So, x n's I am giving the selected values 0, 0.1, 1, 1.5 etcetera at 0 Euler and midpoint the error is 0. Now, look at the error in Euler's method. So, it is 0.00590 then 427, 232 then 1 0 has increased and then 1 more 0 has increased. So, the error in Euler's method it is monotonically decreasing. On the other hand if you consider the midpoint method when you have 0.5 here you have 142 and 0.000. So, for 0.5 the midpoint method gives you better results then at 1.0 still the midpoint method it is better for 1.5 now it is becoming worse here 3.0 it is worse and then still worse. So, compared to Euler's method in the midpoint method the error it is increasing whereas, in case of Euler's method we had a monotonically decreasing error. So, there is some problem in Euler's method. So, Euler's method is the same with the midpoint method. So, we have y dash is equal to lambda y. Let us look at this initial value problem y 0 is equal to 1. The exact solution of this differential equation is y x is equal to e raise to lambda x x belonging to say interval 0 to b. H is b by n x n is n h then y n plus 1 will be equal to y n plus h lambda y n. So, you have got 1 plus h lambda into y n then use again the same relation to obtain y n plus 1 is equal to h lambda raise to n plus 1. So, we have got look at e raise to x e raise to x can be written as 1 plus x plus x square by 2 e raise to c. So, the term x square by 2 e raise to c I write as term of the order of x square. So, e raise to n x will be 1 plus x raise to n plus term of the order of x square use binomial series expansion. That means, e raise to n h lambda is equal to 1 plus h lambda raise to n plus terms of the order of h square lambda square. So, we have the exact solution is e raise to lambda x n n h is our x n. So, you have y x n minus y n is of equal to order of h square lambda square. So, as h tends to 0 the error is going to tend to 0. So, this is for the Euler's method. Now, let us look at Runge-Kutta method. So, if I look at Runge-Kutta method of order 2 in that case again we can calculate.  So, it is h lambda y k 2 is h f of x n plus h y n plus k 1. So, this will be h lambda into 1 plus h lambda y n. So, that will give you y n plus 1 to be equal to y n plus h lambda y n plus h square lambda square by 2 y n. So, it is 1 plus h lambda plus h square lambda square by 2 raise to n plus 1. So, in case of Euler's method we had e raise to x to be approximately equal to 1 plus x. Now, here you have got one more term. So, your e raise to x is approximately equal to 1 plus x plus x square by 2. So, for these two methods there will not be any problem as h tends to 0 you are going to have the error will decrease. Now, next time what we are going to see is when you consider the midpoint method your differential equation is of order 1 it will be replaced by difference equation of order 2. So, that gives rise to extraneous solution and for some values of lambda this extraneous solution or the superfluous solution that is going to dominate the true solution and that creates the problem. So, this is the stability. So, we will consider this in more detail in the next lecture and then we are going to consider the approximate solution of boundary value problems. So, thank you.