Question

There is Cournot competition between Joel (Firm 1) and Daniel (Firm 2). The inverse demand for their goods is: P(q1 +q2) = 30?2(q1 +q2), and the cost functions are: c1(q1) = 12q1, c2(q2) = 6q2. Revert to assuming that there is no capacity constraint. But now the gov- ernment imposes a price ceiling, p ? = 14, which is higher than marginal cost. As it is now illegal to sell for more than $14 per unit, the price will now be: p=min{p ?,30?2(q1 +q2)}. The most straightforward way to proceed is probably just to assume that Firm 1 will never want to produce so little q1 that: 30?2(q1 +q2)>14. (1) After all, he would then not get paid any more than $14 per unit, and he would be able to sell a little more without affecting the price he receives. a) In a new diagram, draw a line that separates the (q2,q1) combinations for which equation (1) is satisfied from those combinations for which it is not satisfied. Label the two areas that are separated by this line, so we know when the price is less than $14 and when it is not. b) In the same diagram, draw q1 = BU 1(q2), as you derived in question 1. c) Now draw and label the overall best response for Firm 1. Justify your answer, possibly with reference to the assumption proposed just before equation (1). d) What can you conclude about Nash equilibrium in this version of the game? Explain your reasoning.

Answer 1