Econ 3710, Advanced Microeconomics, Winter 2007, ASSIGNMENT 2
Due in CLASS on Thursday, March 29, 2007. This assignment is worth 10% of your final mark. Explain your answers.
1. Go to http://today.caltech.edu/theater/item?story%5fid=14166
There is a video of a public lecture titled “Why are prices so bizarre” by R. Preston McAfee, the J. Stanley Johnson Professor of Business, Economics, and Management at the California Institute of Technology (Caltech). It is a 35-minute lecture available in the following formats: [cable/DSL], [broadband], [56k modem]. Listen to the entire lecture and answer the following questions:
(i) There is only one mathematical formula in the entire lecture. It is . Derive this formula. That is, prove how it is obtained from the behavior of a profit-maximizing monopolist.
(ii) Based on the lecture, explain why grocery stores advertise sale prices on items such as milk, paper, towels, and cola, even though the demand and cost of production didn't change?
(iii) Based on the lecture, explain why are turkeys cheapest just before Thanksgiving, when demand is highest?
(iv) Traditional demand/supply theory would predict that prices should be highest when demand is highest? What is missing in the traditional theory leading to its inability to explain the phenomenon in (iii)?
(v) In his lecture, Professor McAfee mentioned a phenomenon called “damaged goods”. Why would a firm engage in this behavior (i.e., produce ‘damaged’ goods)?
(vi) In class, we proved that a profit-maximizing monopolist will sell at a higher price to consumers who are less sensitive to price. We called his third-degree price discrimination. Professor McAfee discusses several examples of price discrimination. In what fundamental sense is the type of price discrimination that he describes different from what we referred to in class as third-degree price discrimination?
(vii) In class, we claimed that for price discrimination to be possible, the seller must be a monopolist. However, most of the examples of price discrimination that Professor McAfee discusses involve firms that are not monopolies. How is this possible?
(viii) According to McAfee, why may prices be unpredictable or random?
2. Consider a cereal manufacturer with two types of customers. Type 1 individuals have a reservation price $4, and using a coupon costs them $1.25 (in terms of effort/time). Type 2 individuals have a reservation price $3, and using a coupon does not cost them anything. It costs the manufacturer $2.50 to produce each a box of cereal. [note: a customer’s reservation price is the maximum that s/he is willing to pay].
Let the price with a coupon be p.
(i) What range of values must p lie in so that type 1 customers do not use the coupon but type 2 customers do? What price should the manufacturer charge the type 1 customers?
(ii) Does it make sense for the firm to use a coupon? If yes, explain why? If no, how would you tweak the model to explain why firms in the real world indeed use coupons?
3. Consider a market with two types of buyers: A buyer in group 1 has an inverse demand function of p = 5 – 0.5q and a buyer in group 2 has an inverse demand function of p = 10 – q. There are ni > 1 buyers in group i, i = 1, 2. Let c = 2 be the constant marginal cost. The seller of the good charges a common fixed fee, F, for the right to use the good and a common per unit price, p.
Suppose n1 = n2, what is the optimal F and p? Will both groups purchase the good?
4. A firm’s cost function is homogenous of degree one in input prices. Explain this statement in plain English and then prove it mathematically.
5. In an economy there are equal proportions of two types of workers: type-α workers who have productivity of 2 and type-β workers who have productivity of 1. Workers’ productivities are unobservable by firms but workers can spend resources to acquire educational certificates in order to signal their productivity. It is common knowledge that the cost of acquiring an education level, z, equals 0.5z for type-α workers and equal z for type-β workers. Workers are paid their true productivity if their type is known with certainty. Otherwise, they are paid the average productivity.
(i) Construct a separating equilibrium such that type-α workers invest in education to signal their type but type-β do not. [Hint: your equilibrium must be such that when a firm sees a worker with education, z ≥, then it believes that the worker is type-α and when it sees z <, it believes that the worker is type-β. You need to determine ].
(ii) What is the efficient level of education required to achieve a separating equilibrium?
J. Atsu Amegashie, Department of Economics, University of Guelph, March 6, 2007