Cournot & Stackelberg.

Suppose there are two restaurants selling pizzas on the same block, Tominos and Huts, and they are competing with each other following the rules of the Cournot Oligopoly Model. Suppose inverse market demand for pizzas is p = 600 - Q. Suppose Dominos has a cost function C( q_t ) = q²_t and Huts has a cost function C( q_h ) = 9q_h.

1. What is the Nash - Cournot equilibrium in this market (quantities) and what is the price in the market?
2. What are the profits of the two restaurants at the equilibrium assuming zero fixed costs?
3. Graph the marginal cost, demand, residual demand, and marginal revenue curve for Tominos. Show the equilibrium price and quantity for that restaurant.

Now suppose Tominos is the first mover following the Stackelberg Oligopoly Model, but everything else stays the same.

1. What is the Nash - Stackelberg equilibrium in this market (quantities) and what is the price in the market?
2. What are the profits of the two restaurants at the new equilibrium?
3. Graph the marginal cost, demand, residual demand, and marginal revenue curve for Tominos. Show the equilibrium price and quantity for that restaurant.