4. Follow the link to read the article, "Ethanol a big factor, among several, driving up food prices." Consider a good like lasagna which is made up of beef and cheese (we'll ignore the other ingredients). Suppose that Q = 100 units of lasagna are produced each week using 50 units of beef and 50 units of cheese, and that, before the increase in the price of corn, the prices were pb = pc = 1, where pb and pc are the prices of beef and cheese, respectively.

a. Suppose the increase in the price of corn increased both beef and cheese prices by 100% to pb = pc = 2. If the lasagna maker minimizes the cost of producing 100 units of lasagna, how much beef and cheese will the cafeteria use? What will be the impact of the price increase on the its total production cost? (Hint: what does a uniform price increase do to the price ratio (i.e., the slope of the iso-cost lines?)

b. In the article, the lasagna manufacturer says that it has changed its recipe to use more beef and less cheese. If the firm is a cost-minimizer, what does this imply about the change in the relative prices of cheese and beef?

c. Start with the information above (Q=100, and 50 units of beef and cheese are used), and suppose that the price of cheese increases from 1 to 2, and the price of beef increases from 1 to 1.5. If the maker does not change its recipe, how will its total cost of production change? If it can change its recipe, how will it do so? Will the adjustment in the recipe result in total cost being higher or lower than the cost of the original recipe at the new prices?

d. Briefly discuss the difference in the cost of lasagna when the recipe changes and when it doesn't.