Question

Suppose both julien and mohsen see burgers and bowls of pasta to be imperfect substitutes characterized by convex indifference curves. Julien currently has 1 pancake and 4 bowls of pasta and mohsen has 7 burgers and 6 bowls of pasta. At this allocation, Julien's marginal utility is 20 for burgers and 5 for pasta, and Mohsen's marginal utility is 6 for burgers and 18 for pasta.

True or False: Julien and Mohsen would both be better off if Julien gave Mohsen 2 bowls of pasta in exchange for 1 pancake. With the use of a diagram, explain your answer.

Answer 1

Solution:

The two goods in the economy are: burgers and pasta (I think pancake is an error, where buyers should have come; please verify!). Given the endowments of Julien and Mohsen, total endowment of

Burgers = 1 + 7 = 8 burgers

Pasta bowls = 4 + 6 = 10 pasta bowls

Marginal rate of substitution (MRS) is the slope of indifference curves. Here, MRSbp is the rate at which a pprson is willing to substitute a pasta bowl for a burger. Also

MRSbp = Marginal utility of burgers (MUb)/Marginal utility of pasta bowls (MUp).

Thus, note that at present allocation,

MRSbp for Julien = 20/5 = 4

MRSbp for Mohsen = 6/18 = 1/3

At both person's utility maximization, in order to reach the best allocation possible, MRS for both persons equate. Accordingly, notice the discrepancy is MRS of 2 consumers above. Clearly, this isn't the best allocation.

We know that as we increase consumption of 1 good, the marginal utility derived from it decreases. In order to reach a better allocation (such that both are better off) we can see that MRSbp of Julien needs to decrease while that of Mohsen should increase. Now, if pattern of exchange goes like this that pasta bowls are transferred from Julien to Mohsen in exchange for a burger, following will happen:

Marginal utility of pasta bowl will increase for Julie (as pasta bowl consumption reduces by her) and decrease for Mohsen

Marginal utility of burgers will decrease for Julien and increase for Mohsen.

This further means that MRSbp will decrease for Julien and increase for Mohsen, so we are moving towards equality. Further, this exchange rate must lie within the two MRS for such trade to be feasible, and making individuals involved better off. Since exchange rate of 1 burger for 2 pasta bowls (so, market exchange rate = 1/2) lies within 2 MRS (1/3 < 1/2 < 4), such trade will happen and ultimately (as already seen), Julien and Mohsen will be better off.

So, given statement is TRUE.