Beer and Pizza

Irene Irongut consumes only two commodities: pizza and beer. Furthermore, she always drinks exactly three beers with each pizza. Suppose the price of a pizza is $3, the price of a beer is $1 and Irene has $24 to spend in total.

1. How many pizzas and beers will Irene consume? Graph her equilibrium showing her budget constraint and two of her indifference curves. Explain why you didn't need to be told her utility function.
2. Now suppose the government imposes a $2 tax on pizzas so the price of a pizza to Irene rises to $5. How many pizzas and beers she consume now? Graph her new equilibrium.
3. What are the income and substitution effects of the tax in part (2)? Explain anything unusual.
4. Calculate the compensating variation of the tax in part (2). Now calculate the tax revenue the government raises from Irene.