Question

3. Suppose a consumer's utility function is given by U(A,B) In(A)+In(B). Suppose the price of each apple A) is є2, and the price of a loaf of bread (B) is є2 and the consumer's income was €40. (i) Find the marginal utility of apples and the marginal utility of bread and use these to determine if the ii) Write down the Lagrangian for this problem and solve for the optimal consumption of apples and iii) Report and interpret your solution for the Lagrange multiplier marginal utility of bread is increasing or decreasing in the amount of bread consumed bread. Does your solution seem reasonable?

Answer 1

This shows that there is an inverse relationship between amount of bread consumed and marginal utility received from it .

So, As amount of bread consumed increases marginal utility decreases.

ii).

(iii). Solution from Lagrangian multiplier shows that Bread and apples are consumed in equal quantity. Optimal consumption bundle is (10,10). That is the consumer must to buy 10 units of apple and 10 units of bread to obtain maximum utility.