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Question: 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) = A1/4 B3/4. The price of goods A and B are $10 and $20, respectively. The consumer has a budget of $1200 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. 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?
d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B.
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