Question

Ana gets utility from Pepperoni sticks and Tea. Ana enjoys variety across the two goods. Her dog, Lexie, gets utility only from Pepperoni sticks.

(a) [5 points] With P on the x-axis and T on the y-axis, draw some representative indifference curves for Ana. In a separate but identically labeled diagram, draw some representative indifference curves for Lexie. Identify the direction of increasing utility.

(b) [15 points] Assume Ana is endowed with 10 P and 5 T and Lexie is endowed with 5 P and 10 T. Draw an appropriately labeled Edgeworth Box and identify the endowment point.

(c) [5 points] On the same Edgeworth Box, or a new one if you prefer, highlight all points in the Edgeworth Box that make up the contract curve.

(d) [15 points] Are there gains from trade between Ana and Lexie? Suppose Ana wants to re-allocate P and T between her and Lexie in such a way that maximizes her own utility but makes Lexie no worse off. What would the new allocation be? Highlight it on your diagram.

Answer 1

(a)Ana gets utility by consuming both P and T which means her utility is increasing in consumption of both the goods. Cobb – Douglas utility function represents such preferences.

Her dog prefers only P which means her dog is neutral towards T. So, the IC will be drawn with P being a normal good and T being a neutral good.

(c)The contract curve is the horizontal axis of Lexie.

This is because consider point a on this HA, if we move to point b then we make Lexie better off but at the same time we make Ana worse off by moving her to a lower IC. So, it is a contract curve (i.e. set of all pareto efficient points) because over this line we can make someone better off only by making someone else worse off.

Any point inside the edgeworth box cannot be PE because as we move from c to d Ana’s utility increases but Lexie’s utility remains same. This shows we can make someone better off without making someone else worse off so not PE.

(d)Yes, there are gains from trade between Ana and Lexie.

If Ana reallocates in this manner then new allocation will be Anna will have (10,15) and Lexie will have (5,0). It is so because in this way Lexie’s utility remains 5 whether she has allocation (5,0) or (5,10) because her utility is independent of availability of T. Her utility only depends on T so her utility will be affected only by changing the amount of P.

But Ana’s utility increases in consumption of both T and P so when she takes 10 units of T from Lexie her utility maximizes without making Lexie worse off.