There are only two suppliers of courses in finance in Brisbane, two private univ

Question

There are only two suppliers of courses in finance in Brisbane, two private universities: University A and University B. Given its available lecture halls, Uni- versity A can let either 80 or 240 students enrol. University B can let either 40 or 160 students enrol. For simplicity, assume that costs are zero for both universities, and that all students view a finance course from University A as equivalent to a finance course from University B. Further, assume that the market always clears no matter which enrolment caps University A and University B set, the market price enrolment fees) adjusts so that there is no excess demand or excess sup- ply of seats The aggregate demand for courses in finance is given below (price in $1,000). $ 400 $2 340 $3 280 $4 240 5 200 $6 160 7 120 $8 90 . Fil ll out the payoffs (in $1,000) in the following game matrix. ECON 7002 SEMESTER 1.2018 40 160 80 240 2. If University B sets an enrolment cap of 160, then which enrolment cap will University A prefer to set? 3. What are the enrolment caps of University A and University B in the Nash equilibrium of this game?

Explanation / Answer

We will add up the seats for both universities

Then 80+40=120; 80+160=240; 240+40=280; 240+160=400 is an aggregate demand. Now let's find corresponding price from tables for aggregate demand payoff matrix can be written as below

40. 160

80. 7,7 . 4,4

240. 3,3. 1,1

If B chooses 160 then A will choose 80 otherwise they have lower payoff.

Nash equilibrium will be 80,40

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