Question

I. Chapter 3: Question 3.17 on page 104 from Besanko and Braeutigam 5th ed.

Answer all parts of Problem 3.15 for the utility function U(x, y) = xy + x. The marginal utilities are MUx = y + 1 and MUy = x. a) Is the assumption that more is better satisfied for both goods? b) What is MRSx, y? Is MRSx, y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? How do you now. Show your work. c) On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve (it need not be exactly to scale, but it needs to reflect accurately whether there is a diminishing MRSx, y . Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U1. d) On the same graph draw a second indifference curve U2, with U2 > U1. II. Janice consumes two goods. Janice has a utility function given by U = 4X 0. 5 Y 0. 5 Px = $25, Py = $50 , Income = $750. First find her MUx and MUy (If you can find the derivate show your work). MUx = 2Y 0. 5/ X 0. 5 MUy = 2X 0. 5/ Y 0. 5 a. Write Janice’s budget constraint. b. Calculate the optimal combination of X and Y and graph it. c. Suppose the government rations the purchase of X to 10 units per time period. Assuming Janice does not save any income, how much of Y will Janice choose to purchase? Is Janice satisfying the conditions of consumer equilibrium while the restriction is in effect? Show tour answer. d. Calculate the impact of ration on Janice’s total utility.

Answer 1