 Module 98, chapter consumer behavior and the properties of expenditure function that we are going to study. Here now the one property that we have to study that means that expenditure function is non-decreasing in the prices. Actually this phenomena it has been derived again from the shepherd lemma, mean that expenditure function either it is dealing with the price P1, either it is dealing with price P2 whatever but it will not be the non-decreasing. The main concept behind this function is that at least at least the consumer has to purchase one item must. If consumer is not going to purchase any item then he will not be able to incur certain expenditure. So whatever there will be the prices, consumer's expenditure function it depends upon the spending of the consumer. So the main essence here is that a consumer, whether he buys one item or two or more, but at least one item must not be purchased so that when he buys it the market's prices will affect him and his expenditure which is his income will only be in the form of expenditure. And that is why when we want to prove it then we use properties of shepherd lemma and then we can compare it because if he does not buy any item, whose price can be less or more, then we cannot prove this property. So if we look here then it means that whenever there will be the increase in the prices, expenditure function it will increase and when it will decrease in the prices, expenditure function it will decrease but related to the prices if we look at it then we cannot count it till the time the consumer is buying any item. If we look at it now regarding the different utilisation of commodities, then if we look at our example then if we look at the consumer, he buys a different item but if we say that he has a different item and we say that this is related to his utility that is equal to if we say on Hickson then this is P into which we say with respect to U and if we look at the second point on the second Hickson then that will be equal to P prime when the utility is kept constant. Now if we look at these two points then we look at their respective expenditure first point if we say that there is one E expenditure function we have P and if we look at it then that is related to its first utility and that is equal to P into X and the second expenditure we have P prime and with the given utility and with this is the P prime into X. Now if we look at the aspects between these two then because this price which we said that P prime dot X if P is which we said that P prime is greater than P then definitely its product will be higher so its product will be either equal or we can say if it is minimum or higher equal to the previous point. Now looking at this aspect if we look at it then it follows that it is related to it because our expenditure is related to it so expenditure will be increasing. Likewise if we say that P prime if less than P then this is our condition then we say that P prime X is greater than P dot X. So either it is increasing or decreasing in the form it asserts that the consumer has to purchase certain things at least either one commodity and with the change in the prices the expenditure it will be if it will be price increasing expenditure will be increasing and if price will be decreasing respective expenditure function will be decreasing. Thank you.