 Under the chapter of consumer behavior, we are going to continue the concept of expenditure function. In the previous module, we have discussed that why we are going to prefer the expenditure function and what is its significance. And in this module, we are going to study that how this expenditure function can help the consumer in deciding the required minimum level of the expenditure to attain the desired level of the utility. As in the previous setups, we have studied that when the consumer was having one budget line and he was facing one, two, three or the many utility functions. So then there was a one mathematical setup that the consumer can attain any of utility function but keeping in view that particular budget line, we have to decide that any utility function within the budget line that will be insufficient, any utility function outside the budget line it will be inaccessible. So we were going to decide that where the slope of the budget line and the slope of the utility line they both will intersect that tangency point will give us the optimal level. And here again we are utilizing the same concept but with the very simple twist. Here now we are having one fixed utility function but we are having various options of the expenditure. So we can say that the consumer has to attain a utility function say in the given chapter of the book we are having the example and that says that the consumer has to attain the utility function U2. So how he will be able to attain that utility level but when he is facing various expenditure functions and those expenditure functions or the budget lines we are going to express to E1, E2 and E3. So if we see these budget lines or the budget constraints we can express that the budget line E1 is some having small number of the budget then the other budget line E2 it is having more budget and then the E3 definitely it is having one higher level of the budget. But consumer wants to attain that particular level of the utility level U2 and hence even it is possible for him that he might be able to get that utility function either he is on E2 mean expenditure bundle 2 or at the same time expenditure or the budget constraint E3. Now he has to decide that whether he will spend more money to attain the same level of the utility or he will spend only and only that threshold level or the minimum level of the budget to attain the same desired level of the utility. So here now the consumer has to decide that he will attain the same utility level but he will not spend the more amount of the budget or excess amount of the budget. So now we are having this diagram and in this diagram we can see that this line it shows that this is that I have marked with this pen that it is the expenditure function E1 and then this expenditure function E2 and this is the expenditure function E3. So these three expenditure functions or the budget constraints that are provided to the consumer and consumer has to attain this utility function of U2. Now the consumer can attain this if he is on this highest level of the expenditure function here we can see that the point B and the point C both are tangent to this not tangent but they are going to intersect this so we can say that this expenditure function also provides the utility function to the consumer equal to the U2 utility level but that is not that minimum expenditure function when in contrast we see that this point A here the consumer is particularly tangent to this and here we can say that his utility function and his budget line they both are tangent so slope of the both curves they are equal to each other and consumer is going to attain the same utility level of U2 but at the less amount of expenditure and this less amount or I can say the minimum is of E2 so either he can spend E2 or either he can spend E3 so preference of the consumer will be to spend that minimum amount for the attainment of the desired level of the utility. Thank you.