Pete and Dud Live in a Two-Commodity World

Multiple Choice

Pete and Dud live in a two-commodity world.Pete's utility function is U ^P(x ^P₁, x ^P₂) = x ^P₁x ^P₂.Dud's utility function is U ^D(x ^D₁, x ^D₂) = min{x ^D₁, x ^D₂}.Pete is initially endowed with 3 units of commodity 1 and 4 units of commodity 2.Dud is initially endowed with 7 units of commodity 1 and 6 units of commodity 2.

A) Both consume 5 units of each good in competitive equilibrium.
B) At competitive equilibrium, Dud consumes 6 units of each, since the 7th unit of his endowment of commodity 1 gives him no added utility.
C) At a competitive equilibrium, Dud must consume equal amounts of both goods, so the price of good 1 must equal the price of good 2.
D) The prices of the two goods cannot be equal in equilibrium since Pete and Dud do not have equal endowments.
E) None of the above.