4. Claudia has the following preferences over two goods, c and d: U(c, d) = min{c/2, 3d) Let pc = 2 and pd=3. a. What combination of c and d will give Claudia exactly 18 units of utility at the lowest possible cost? b. How much will this bundle cost? c. If the price of c rises to 3 and the price of d stays the same, will the expenditure minimizing bundle change? Why or why not? d. Solve for Claudia’s Hicksian demand functions for c and d. e. Write down Claudia’s expenditure function E(pc, pd , U). f. Using Shephard’s Lemma, derive Claudia’s Hicksian demand function for d.

In march 2012, the state of california started requiring that all packaging for food and drink with the additive 4-methylimidazole (4-mi) be clearly labeled with a cancer warning. because of this, both pepsi and coke changed their formula to eliminate 4-mi as an ingredient. if pepsi and coke did not change their formula, holding all else constant, what would have happened to the demand for these goods, assuming pepsi and coke were in a competitive market? a. the demand curve for both pepsi and coke would have shifted to the right, causing the price of both products to decrease and the profits for the companies to fall. b. the demand curve for pepsi and coke would have remained unchanged, but the price of both products would have decreased and the profits for the companies would have fallen. c. the demand curve for pepsi and coke would have decreased, but the prices and profits would not have changed. d. the demand curve for only one of them would change because pepsi and coke are substitutes. e. the demand curve for pepsi and coke would have shifted to the left, causing the price of both products to decrease and the profits for both companies to fall.