16 points) Consider a homogenous good market with the following market demand cu

Question

16 points) Consider a homogenous good market with the following market demand curve:
Q=100-p

Two firms produce output at constant marginal cost = 10. Derive the Nash equilibrium outcome in terms of prices, outputs and the profits of the two firms under the following alternative situations in a)-d)

a) (3 points) Firms engage in Bertrand price competition with no capacity constraints.

b) (3 points) Firms engage in Bertrand price competition and each firm has a maximum production capacity = 15. c) (2 points) How would your answer in part (b) change if the capacity of each firm is 90?

d) (5 points) Firms engage in Cournot quantity competition (i.e., determine their capacity assuming that the price is such that market demand equals industry capacity).

e) (3 points) Compare the industry output in cases (a) and (d) to the socially optimal and the monopoly output levels.

Explanation / Answer

a). Under nash equlibrium, both the firms will charge $10 per unit; that is equal to the marginal cost. Moreover, the demand will be 90 units based on equation of Q=100-p (Q=100-10 or Q=90), this quantity of 90 will be evenly dividend among both firms that is 45 units sold by each firm. As price is equal to marginal cost, there will be no profit earned by both firms involved.

b).In this, when the production capacity is 15 units each of both firms, so each firm can sell only 15 units each. In this case, price per unit will be $85 per unit based on equation of Q=100-p where Q= 15 ( i.e. 15=100-p is equal to p=85). So as marginal cost is $10 per unit, each firm will get profit of $75 by selling one unit at $85. Total profit for each firm will be $1125 (based on total units selling of 15 at profit of $75 per unit).

c). If capacity of both firms is $90, then both firms will sell $45 units each, with no profit earned as they will sell at marginal cost of $10 per unit. Output will be 45 units by each firm.

d). Each firm will have capacity of 45 units.

e). In case a) industry output will be 90 units under socially optimal and 45 units under monoploy.

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