# 3. Let us say that in a two-person society, person 1 has a utility function...

 

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# 3. Let us say that in a two-person society, person 1 has a utility function of U₁ = 4X₁ + 2X₂ and person 2 has a utility function of U₂ = X₁ + X₂ both defined over the two goods, X₁ and X₂. The marginal cost of producing good 1 is fixed at 4 and the marginal cost of producing good 2 is fixed at 2. In a perfectly competitive economy, the ratio of the prices of goods 1 and 2 is therefore 4 to 2. (a) An egalitarian free-market politician suggests that prices be set by the market, but income be distributed equally. If each person receives an income of $100, what would the distribution of goods be at the competitive equilibrium? (b) A libertarian politician wants the market to set both prices of goods and the incomes of people. If person 1 consumes 50 units of good 1 and 25 units of good 2 and person 2 consumes 25 units of good 1 and 50 units of good 2 at the libertarian outcome, how much income will each have? (c) Why are the competitive prices in parts (a) and (b) of this problem independent of the distribution of income? # 3. Let us say that in a two-person society, person 1 has a utility function of U₁ = 4X₁ + 2X₂ and person 2 has a utility function of U₂ = X₁ + X₂ both defined over the two goods, X₁ and X₂. The marginal cost of producing good 1 is fixed at 4 and the marginal cost of producing good 2 is fixed at 2. In a perfectly competitive economy, the ratio of the prices of goods 1 and 2 is therefore 4 to 2. (a) An egalitarian free-market politician suggests that prices be set by the market, but income be distributed equally. If each person receives an income of $100, what would the distribution of goods be at the competitive equilibrium? (b) A libertarian politician wants the market to set both prices of goods and the incomes of people. If person 1 consumes 50 units of good 1 and 25 units of good 2 and person 2 consumes 25 units of good 1 and 50 units of good 2 at the libertarian outcome, how much income will each have? (c) Why are the competitive prices in parts (a) and (b) of this problem independent of the distribution of income?

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Person 1 U 471 2X2 Person 2 U X X2 Two good X X good 1 4 222 good good 1 good 2 X ... View the full answer