A consumer's utility only depends on the consumption of goods A and B according to the following Cobb - Douglas utility function: U(A, B) = A3/5 B 2/5. The price of goods A and B are $10 and $10, respectively. The consumer has a budget of $1500 that he can use to consume the two goods. a) Calculate the optimal bundle and maximized utility for the consumer. b) A new tax of $5 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? c) Show that the consumer would prefer a lump sum income tax that raises the same revenue of $200 as the tax on good B.
A consumer's utility only depends on the consumption of goods A and B according to the following Cobb - Douglas utility function: U(A, B) = A3/5 B 2/5. The price of goods A and B are $10 and $10, respectively. The consumer has a budget of $1500 that he can use to consume the two goods. a) Calculate the optimal bundle and maximized utility for the consumer. b) A new tax of $5 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? c) Show that the consumer would prefer a lump sum income tax that raises the same revenue of $200 as the tax on good B.
Chapter1: Making Economics Decisions
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Transcribed Image Text:A consumer's utility only depends on the consumption of goods A and B according to the following Cobb - Douglas utility
function: U(A, B) = A3/5 B 2/5. The price of goods A and B are $10 and $10, respectively. The consumer has a budget
of $1500 that he can use to consume the two goods. a) Calculate the optimal bundle and maximized utility for the
consumer. b) A new tax of $5 is imposed on the price of good B. Compute the new optimal bundle of good A and B for
the same consumer. What is the utility loss due to the tax? c) Show that the consumer would prefer a lump sum income
tax that raises the same revenue of $200 as the tax on good B.
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