Question

Suppose that Grinch and Grubb go into the wine business in a small country where imports are prohibited and wine is difficult to grow. The industry consists of just the two duopolists, Grinch and Grubb. The demand for wine is given by p = 420 − y, where p is the price and y is the total quantity sold (in hectoliters). The cost function for Grinch is ?1 (?1 ) = ?1² and for Grubb it is ?2 (?2 ) = ?2² + 21?2.

a) SOLVED - OUTPUT IN COURNOT-NASH EQUILIBRIUM: GRINCH y₁ = 85.5 -> PRICE 256 -> PROFIT=14620 GRUBB y2= 78 -> PRICE 256 -> PROFIT=12246

b) Suppose that Grinch and Grubb make a tacit collusion to maximize their joint profits. Calculate the output and profits of each of them. What would be the price in case of a collusion?

c) Grinch entered the market before Grubb. If he took advantage of the opportunity to choose his output first, how much he should sell to maximize his profits? What would be the output of Grubb in the Stackelberg equilibrium? Calculate the price and profits of each duopolist in the equilibrium.

Answer 1