 Under the chapter of consumer behavior, we are going to study the indirect utility function. Indirect utility function is defined as the maximum level of the utility that can be attained by the consumer keeping the amount of the money income and the price constant. So, you will be amazed that it is similar type of the definition that we were having for the utility, but the main difference is here that here we are going to utilize the word of money income. Mean this is the utility maximization of a consumer when we keep his nominal income constant. It means we are not concerned with the constant level of the utility rather maximization of utility keeping his nominal income constant. Similarly when we have to deal with the utility maximizing approach, we utilize the approach either through the substitution method or we utilize the Lagrange method and then we keep the utility level might be constant, but in the indirect utility function we are not going to assess the utility maximization through the utility approach rather we take the expenditure approach. So, for the Marshallian demand function, we substitute the part of the debt function where income lies that income is replaced or the substitute by the budget or the income or the expenditure constraint because we know that whatever we are going to spend mean any consumer who is going to spend through his income that will be equal to his expenditure and this part of expenditure is being substituted in the Marshallian demand function. So, when we say the demand of the consumer it is the function of price of that commodity price of the other commodities and the expenditure that the consumer is going to incur. So, we maximize the utility through the price of commodity X through the price of commodity Y and then we change that what will be the change in the commodities demand through the change in his expenditure function. So, indirect utility function will take that what the consumer is going to spend for the purchase of that commodity and if the price has changed how the consumer will change his expenditure related to that commodity. So, consumer is going to maximize his utility and for this decision he is going to check through the change in his consumption incurred in the form of the expenditure. So, when we utilize this example we see that the utility is the function of price of the two commodities and here is the consumer's income and this is the budget line or the budget constraint and if we have to maximize the utility through the Lagrange possibility we take that this will be the optimal amount of X1 this is the X2 and this is the X3 but here we all having subject to the income. If this amount of the income here we just replace income is equal to expenditure and here we say that this expenditure will be just equal to the budget incurred on the consumer purchase of the various commodities. So, when we include this part this utility will take the form of not U rather it will become in the form of the V where we see that this V we give the notation to indirect utility function that now it is the function of the price that is the vector of all the prices and then M or the expenditure presented in the same units as the prices. So, the optimal level of utility will not be directly attained rather indirectly through the expenditure incurred on the various commodities in response to the price change. Thank you.