Cournot & Stackelberg

Suppose there are two restaurants selling gyros on the same block in Davis, Sam's and Ali Baba's, and they are competing with each other following the rules of the Cournot Oligopoly Model. Suppose inverse market demand for gyros is p = 600Q. Suppose Sam's has cost function C(qs) = q2 s and Ali Baba's has cost function C(qab) = 9qab.

A. What is the Nash-Cournot equilibrium in this market (quantities) and what is the price in the market?

B. What are the prots of the two restaurants at the equilibrium (assume zero xed cost)?

C. Graph the marginal cost, demand, residual demand, and marginal revenue curve for Sam's. Show the equilibrium price and quantity for that restaurant.

Now suppose Sam's is the rst mover following the Stackelberg Oligopoly Model, but everything else stays the same as in the above problem.

D.What is the Nash-Stackelberg equilibrium in this market (quantities) and what is the price in the market?

E. What are the prots of the two restaurants at the new equilibrium?

F. Graph the marginal cost, demand, residual demand, and marginal revenue curve for Sam's. Show the equilibrium price and quantity for that restaurant.