Question

Peta and Dudley live in a two-person, two-commodity world. Quantities of the first good are denoted by x while quantities of the second commodity are denoted by y. Peta’s preferences can be represented by the utility function uP(x,y) = x y and Dudley’s are represented by the utility function uD(x,y) = min{x,y}. Peta is initially endowed with 3 units of commodity 1 and 4 units of commodity 2 while Dudley is initially endowed with 7 units of commodity 1 and 6 units of commodity 2.

Select one:

a. None of the other four answers are correct

b. At a competitive equilibrium, Dudley must consume equal amounts of both goods, so the price of good 1 must equal the price of good 2.

c. At the competitive equilibrium, Dudley consumes 6 units of each, since the 7th unit of his endowment of commodity 1 gives him no added utility.

d. The prices of the two goods cannot be equal in equilibrium since Peta and Dudley do not have equal endowments.

e. Both consume 5 units of each good in the competitive equilibrium.

Answer 1

(e) is not correct as you may find that they are not consuming 5 units of each goods at the equilibrium (see details). Hence, this option is not true.

(d) The prices of both goods are same as derived. Hence, this option is not true.

(c) This option is also not true as Dudley does not consume 6 units of each goods at the equilibrium.

(b) At a competitive equilibrium, Dudley must consume equal amounts of both goods, so the price of good 1 must equal the price of good 2. This statement seems to be true.

Find the detailed derivation below.