Roman consumes only pies and beer. His utility is U(p, b) = 2 ln p + ln b. Pies used to cost $2 each and beer was $1 per can. His income used to be $60 per week, but he had to pay an income tax of $10. The government decided to eliminate the income tax and instead put a specific tax of $1 per can of beer.

(a) On the same diagram, draw Roman's old and new budget lines and explain what happens to his consumption of pies after the introduction of the specific tax. How much revenue did this tax raise from Roman?

(b) Suppose that instead of just taxing beer, the government had decided tax both beer and pies at the same percentage rate. That is, the price of beer becomes 1 + t, while the price of a pie becomes 2(1 + t). Find out the tax rate t that raises the same revenue from Roman as the tax on beer alone described above. Is Roman better off having just beer taxed or having both beer and pies taxed, if both sets of taxes raise the same revenue?