Pete and Dud Live in a Two-Commodity World

question 34

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.

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