Problem 1: Suppose that in an economy there are two goods, food, F, and clothing, C, and two consumers, Anne and Bob. Anne and Bob both have the same utility function U(F,C) = FC. The marginal rate of substitution of food for clothing associated with this utility function is MRSFC = Firms in this economy have produced 10 units of food and 10 units of clothing. %3! Explain why an allocation where Anne gets all the food and Bob gets all the clothing does not satisfy exchange efficiency. Explain why this allocation would never happen if Anne and Bob both have to pay the market prices for food and clothing and both make optimal choices. Hints: 1: Use the definition of exchange efficiency from the class slides or textbook. 2: Optimal choices must solve MRS=price ratio.
Problem 1: Suppose that in an economy there are two goods, food, F, and clothing, C, and two consumers, Anne and Bob. Anne and Bob both have the same utility function U(F,C) = FC. The marginal rate of substitution of food for clothing associated with this utility function is MRSFC = Firms in this economy have produced 10 units of food and 10 units of clothing. %3! Explain why an allocation where Anne gets all the food and Bob gets all the clothing does not satisfy exchange efficiency. Explain why this allocation would never happen if Anne and Bob both have to pay the market prices for food and clothing and both make optimal choices. Hints: 1: Use the definition of exchange efficiency from the class slides or textbook. 2: Optimal choices must solve MRS=price ratio.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Problem 1:** Suppose that in an economy there are two goods, food, \( F \), and clothing, \( C \), and two consumers, Anne and Bob. Anne and Bob both have the same utility function \( U(F, C) = FC \). The marginal rate of substitution of food for clothing associated with this utility function is \( MRS_{F,C} = \frac{C}{F} \). Firms in this economy have produced 10 units of food and 10 units of clothing. Explain why an allocation where Anne gets all the food and Bob gets all the clothing does not satisfy *exchange efficiency*. Explain why this allocation would never happen if Anne and Bob both have to pay the market prices for food and clothing and both make optimal choices.
**Hints:**
1. Use the definition of exchange efficiency from the class slides or textbook.
2. Optimal choices must solve \( MRS = \text{price ratio} \).
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