Individual

There are only two institutions of public higher education in the market—Righteous Indignation College (RIC) and the Union of Rigid Institutions (URI).

The demand curve for RIC is:

            Q_ric = 20 – P_ric+P_uri

The demand curve for URI is:

                        Q_uri = 20 – P_uri + P_ric

Prices are in hundreds of dollars and Q is in thousands of students.

Both of these institutions put students in seats and talk at them, hence marginal cost is zero.  Although they differentiate their products, the two institutions compete by price.  URI has hired you as a financial consultant to set tuition levels.

·        Find the Bertrand Nash equilibrium.  The Bertrand model can be found at the end of Chapter 13 in Perloff.  How much do they charge, how much do they “produce”, and what are their profits?

There are essentially two different ways to do this.  You could use Calculus, or you could use a spreadsheet the way we did in class.  In both cases remember you are setting prices not quantities.  I don’t care which you use.

·        Construct a payoff matrix showing profits for both institutions when each institution can chose to be a Stackelberg Follower or Leader.

·        Suppose URI sets its price first, and RIC must react to it.  Find this Stackelberg equilibrium.

·        Write a memo with your recommendations including any supporting documents, charts, tables you think are helpful.

Due:  High noon, May 14, 2005