Consider a consumer with preferences for two goods, food (F) and clothing (C). His preferences take the following form: U(F,C) = F1/2C. Let I denote consumer income, let PF denote the price of food and let PC denote the price of clothing. a. Is the “more is better” assumption satisfied for both goods? Explain. b. Derive an expression for the marginal rate of substitution of food for clothing (MRSF,C). c. Write and explain the two conditions that result in an interior optimum.
Consider a consumer with preferences for two goods, food (F) and clothing (C). His preferences take the following form: U(F,C) = F1/2C. Let I denote consumer income, let PF denote the price of food and let PC denote the price of clothing. a. Is the “more is better” assumption satisfied for both goods? Explain. b. Derive an expression for the marginal rate of substitution of food for clothing (MRSF,C). c. Write and explain the two conditions that result in an interior optimum. d. Derive this consumer’s demand functions for food and clothing as functions of exogenous variables only. e.Write this consumer’s indirect utility function. f. If the price of food is $20, the price of clothing is $80, and annual income is $60,000, determine the number of units of food and clothing the consumer purchases and the amount of utility the consumer derives from the optimal combination.
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