It is common in many countries that governments subsidize the production of goods in certain large oligopolistic industries. Common examples include aircraft industries and car industries.
A: Suppose that a 2-firm oligopoly faces a linear, downward sloping demand curve, with each firm facing the same constant marginal cost and no recurring fixed cost.
(a) If the intent of the subsidy is to get the industry to produce the efficient output level, what should be the subsidy for Bertrand competitors?
(b) How would your answer to (a) change if each firm faced a recurring fixed cost?
(c) What happens (as a result of the subsidy) to best response functions for firms who are setting quantity (rather than price)? How does this impact the Cournot equilibrium?
(d) How would you expect this to impact the Stackelberg equilibrium?
(e) Suppose policy-makers can either subsidize quantity-setting oligopoly firms in order to get them to produce the efficient quantity, or they can invest in lowering barriers to entry into the industry so that the industry becomes competitive. Discuss how you would approach the trade-offs involved in choosing one policy over the other.
(f) How would your answer be affected if you knew that it was difficult for the government to gather information on firm costs?
(g) Suppose there are recurring fixed costs that are sufficiently high for only one firm to produce under quantity competition. Might the subsidy result in the entry of a second firm?
B: Suppose demand is given by x (p) = A−αp, that all firms face constant marginal cost c and there are no recurring fixed costs.
(a) If the government introduces a per-unit subsidy s < c, what happens to the marginal costs for each firm?
(b) How do the Monopoly, Bertrand, Cournot and Stackelberg equilibria change as a result of the subsidy?
(c) Suppose A = 1000, c = 40 and s = 15. What is the economic incidence of the subsidy in each economic environment—i.e. what fraction of the subsidy is passed onto consumers and what fraction is retained by producers?
(d) How would your answer to (c) change if the government instead imposed a per unit tax t = 15?
(e) How much of a tax or subsidy has to be set in order to get the efficient level of output under each of the four market conditions?
(f) Suppose you are advising the government on policy and you have two choices: Either you subsidize the firms in the oligopoly, or you lower the barriers to entry that keep the industry from being perfectly competitive. For each of the four market conditions, determine what cost you would be willing to have the government incur to make the industry competitive rather than subsidize it?
(g) Suppose that pollution was produced in this industry—emitting a constant level of pollution per unit of output, with a cost of b per unit of output imposed on individuals outside the market. How large would b have to be under each of the market conditions in order for the outcome to be efficient (without any government intervention)?