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 P=20-Q/N. Each firm chooses output in Cournot fashion and assumes that price is given by the inverted market demand curve. Each firm faces constant marginal cost equal to 10 per unit and a fixed cost equal to 100.
a) Solve for the Cournot equilibrium level of (i) output per firm, (ii) industry output, (iii) price (iv) profit per firm as functions of the number of firms n and the number of buyers N.
b) If Cournot firms enter until profits are driven to zero then the find the level of N required for (i) one firm to enter (ii) two firms to enter and (iii) 3 firms to enter.
c) Suppose that N= 20 and n = 2. Use your solutions in a) to find welfare. If a third firm were to enter (n= 3) then determine whether this firm would earn positive profits and whether the entry of this firm would raise or lower welfare.