Answer to Question #162784 in Microeconomics for ahmet namet

Question

1.      A consumer enjoys commodities x and y according to the utility function U(x,y) =10X Y

a.      Maximize consumer’s utility assuming that px= 6TL , py = 4TL and that the total income is 50 TL

Calculate the expenditure function

Answer 1

The slope of an indifference curve is called the Marginal Rate of Substitution. This is the rate at which good Y can be substituted for by good X, leaving the consumer at the same level of utility. The proposition is sometimes summed up as the diminishing marginal rate of substitution.

Let us consider a situation where the consumer has only two commodities, X and Y, and he can purchase. A reduction in Y acquisition must accompany the increased addition of commodity X if the consumer has to maintain a constant utility level by staying on the same indifference curve.

The quantity of commodity X is measured on the horizontal axis while the amount of commodity Y is calculated on the vertical axis. The fact that the indifference curve, Uo, is downward-sloping indicates that as more of one commodity is acquired, the consumer has to forego some quantity of the other thing to maintain a constant level of satisfaction (or stay on the same indifference curve, Uo). Suppose the consumer is initially at point A where he acquires XI units of commodity X and Y1 units of commodity Y. This combination of the two commodities yields him a level of satisfaction represented by the indifference curve, Uo. If the consumer increased his acquisition of commodity X by one unit from XI units to XI + I units, he would have to move to a higher level of satisfaction represented by an indifference curve further away from the origin than Uo. If he has to maintain a constant satisfaction level, he has to reduce his commodity Y purchase from Yl units to Y2 units. This will bring him to point B, where he again has the same level of satisfaction as he had at point A, but with more X and fewer Y... Δ y1 is the MRS XY at point A because it measures Y's quantity that the consumer must give up at point A to acquire one more commodity X.

In our case amount of commodity Y that the consumer has to give up to acquire one additional unit of commodity X is the Marginal Rate of Substitution of commodity X for commodity Y. Ite3 is sometimes abbreviated as U(x,y) =10X Y. And given that an indifference curve is convex to the origin, U(x,y) =10X Y is not constant but varies along the indifference curve.

Change in X / Change in y = U(x,y) =10X Y

6/4 (Change in x over the change in y) =50

6/4p =50

p=25/3

P = 8.33

P x U

83.33