Movies and Popcorn

Tilly Technicolor consumes only two goods: movies and popcorn. In fact, she always eats exactly 2 servings of popcorn for each movie she sees. Let x be the quantity of movies she sees and let y be the servings of popcorn she eats.

1. Suppose the price of movies is Px, the price of popcorn is Py and Tilly's income is I. Show that her demands for movies and popcorn are given by: x = I/(Px + 2*Py) and y = 2*I/(Px + 2*Py). Explain why you could answer this problem without being told Tilly's utility function.
2. Are movies normal or inferior goods? How can you tell? What is her income elasticity of demand?
3. If the price of movies is $6, the price of popcorn is $1 per serving, and Tilly spends $24 in total, graph her equilibrium. Show her budget constraint and two of her indifference curves. Be careful to get the slope of each curve right.
4. Now suppose the price of movies falls to $4. Graph Tilly's new equilibrium. Calculate the changes in her consumption of movies due to the income and substitution effects and show them in your diagram. Explain anything unusual.
5. Calculate the compensating variation for the price change in part (4).