Suppose Alice's utility for Vegemite and other consumption is given by U (q, c ) = 24log(q + 1) + c , where q is Alice's consumption of Vegemite, and c is the level of Alice's other consumption. Normalize the price of other consumption to 1 and let p denote the price of Vegemite. Assume Alice's income I is larger than 24.

(a) What is Alice's optimal consumption of Vegemite? [Hint: Note that Alice does have a choke price. You will need this in the next part.]

(b) Suppose p = 12. How much additional income would Alice need to just compensate her for the absence of Vegemite?

(c) How does your answer to part 2b compare to Alice's consumer surplus when p = 12?

(d) Suppose there are n consumers with preferences identical to Alice. Suppose moreover that each consumer's income is greater than 24. What is the market demand for Vegemite for general p? For what value of n is market demand equal to 5 when p = 12?

(e) Suppose the market for Vegemite is as described on the supply side in Question 1d and on the demand side in part 2d. What price will maximize total surplus (that is consumer surplus plus profits)? [Hint: What is special about p = 12?]