Show that the increase in the variance of marginal cost has caused H, L and W to rise.

Need to help for these two question:

1. Cournot, Market Power and Market Concentration. Consider a market in which there are two firms who face the inverted industry demand given by P = 260 – Q. Each firm has zero fixed cost and constant marginal cost given by c1 for Firm 1 and c2 for firm 2.

a) (10 marks). Let c1 = c2 = 170. Solve for the Cournot equilibrium outputs. Use you solution to calculate the (i) Herfindahl index (H) (ii) Lerner Index (L) and (iii) industry elasticity () and (iv) Welfare (W). Verify that L = H/.

b) (10 marks). Let c1 = 150 and c2 = 190. Repeat part a). Show that the increase in the variance of marginal cost has caused H, L and W to rise.

2. Cournot and entry. Consider an industry consisting of n firms that produce identical products. There are N buyers in the market and each buyer has a demand curve given by qd = 20 – P where qd is the amount demanded by each buyer and P is the common industry price. The number of buyers N is a measure of market size. Market demand is equal to the amount demanded by all buyers and is thus given by Q = N(20 – P). The inverted market demand curve is thus given by