Question

1. Assume a consumer whose demand curve is given by p = 10 – q. There is an incumbent monopolist whose marginal cost is 2.
   1. What are the monopoly price, monopoly profit, and consumer surplus?
   2. Now suppose that there is a potential entrant whose marginal cost is zero. If there is entry, the incumbent firm and the entrant compete in prices for the homogenous product. If entry, what would be the market price and what would be consumer surplus?
   3. Can the incumbent sign an exclusive contract with the customer to deter entry?
   4. Suppose that there are four customers with the same demand as above. The entrant’s marginal cost is zero as before, but it needs to incur a fixed entry cost of 40. Can the incumbent sign an exclusive contract that would deter entry? If the answer is yes, how?

Answer 1

p = 10 – q

TR = pq = q(10 – q )

TR = 10q - q²

MR = 10 - 2q

MC = 2

Setting MR = MC to determine the profit-maximizing quantity,

2 = 10 - 2q

2q = 8

q = 4

The profit-maximizing quantity = 4

To find the profit-maximizing price, substitute this quantity into the demand equation:

p = 10 – q

p = 10 – 4 = 6

The profit-maximizing price = 6

The profit of the firm is total revenue minus total cost, and the total cost is equal to average cost times the level of output produced. Since marginal cost is constant, the average variable cost is equal to marginal cost. Ignoring any fixed costs, the total cost is 2q

TC = 2q = 2*4 = 8

TR = 10q - q² = 40 - 16 = 24

Profit = TR - TC = 24 - 8 = 16

Monopoly profit = 16

In a monopolistic market, consumer surplus is the area below the demand curve, above the monopolist price.

Consumer Surplus = 1/2 * (price when demand is 0 - monopoly price)

Price when q is 0:

p = 10 – q = 10 - 0 = 10

Monopoly Price = 6

Consumer Surplus = 2

2. Setting MR = MC to determine the profit-maximizing quantity of the new entrant

MC = 0

MR = 10 - 2q

0 = 10 - 2q

2q = 10

q = 5

The profit-maximizing quantity of the new entrant= 5

To find the profit-maximizing price, substitute this quantity into the demand equation:

p = 10 – q

p = 10 – 5 = 5

The profit-maximizing price of new firm= 5

Consumer Surplus = 1/2 * (price when demand is 0 - monopoly price)

Price when q is 0:

p = 10 – q = 10 - 0 = 10

Monopoly Price = 5

Consumer Surplus when new firm operates= 2.5

c. As the new firm offers lesser price to the consumers, the incumbent is unable to sign an exclusive contract with the customers.

d. When the new firm incurs a fixed entry cost of 40, its profit become negative. The entry cost serves as an entry barrier. At this point of time, the incumbent firm will be able to sign an exclusive contract with the sellers that would deter entry