16. A consumer's utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A,B) = A!5 B45. The price of goods A and B are $5 and $10, respectively. The consumer has a budget of $300 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. Price of good B increases by 20%. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the price increase?
16. A consumer's utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A,B) = A!5 B45. The price of goods A and B are $5 and $10, respectively. The consumer has a budget of $300 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. Price of good B increases by 20%. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the price increase?
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 8P
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Transcribed Image Text:16. A consumer's utility only depends on the consumption of goods A and B
according to the following Cobb-Douglass utility function: U(A,B) = A1/5 B4/5.
The price of goods A and B are $5 and $10, respectively. The consumer has a
budget of $300 that he can use to consume the two goods.
a. Write down the budget constraint and plot it.
b. Calculate the optimal bundle and maximized utility for the consumer.
c. Price of good B increases by 20%. Compute the new optimal bundle of
good A and B for the same consumer. What is the utility loss due to the
price increase?
d. Plot a linear approximation of the demand function for good B based on
your answers above and show the dollar equivalent of the utility loss under
the demand function.
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