Problem 1)
Suppose the market for oil is characterized by the demand P = 7 – Q, where Q is the total quantity supplied at the market. Suppose there are two firms that supply for this market Shell and Caltex. Suppose that both firms has a cost of 1 per unit of oil supplied. (this is the same as to say that the marginal cost MC(Q) = 1). Assuming symmetry (the firms are identical therefore they will produce equal amounts and share the profits equally) solve for the following:
a) Cartel solution. How much each of the firms is producing and what is the resulting price? What are the firms’ profits?
b) Competitive markets solution. How much each of the firms is producing and what is the resulting price? What are the firms’ profits?
c) Cournot solution (simultaneous choice of quantity). Derive and draw the best response functions on the graph. How much each of the firms is producing and what is the resulting price? What are the firms’ profits?
d) Bertrand solution (simultaneous choice of prices). How much each of the firms is producing and what is the resulting price?
e) Stackelberg solution. Suppose Caltex moves first and chooses its quantity, then Shell observes Caltex’s quantity and decides about it s own. What are the quantities supplied and the resulting price? Show this pair of choices on the best response diagram.
f) Now suppose Caltex moves first and chooses its price, then Shell observes Caltex’s price and decides about it’s own. What are the prices chosen in equilibrium?
Problem 2.
Suppose now the demand is the same P = 7 – Q, where Q is the total quantity supplied at the market. Suppose that Shell has a cost of 1 per unit of oil supplied. (this is the same as to say that the marginal cost MC(Q) = 1) and Caltex has the cost of 3. Solve for the following:
a) Cournot solution (simultaneous choice of quantity). Derive and draw the best response functions on the graph. How much each of the firms is producing and what is the resulting price? What are the firms’ profits?
b) Stackelberg solution. Suppose Caltex moves first and chooses its quantity, then Shell observes Caltex’s quantity and decides about it s own. What are the quantities supplied and the resulting price?