Question

Consider the case of a single product incumbent firm that is currently facing demand qm = 2400−30pm and marginal cost cm = 12 and no fixed cost.

(a) What price will M set, how many units does it sell?

(b) What is total surplus here?

Suppose further that there is a potential single product entrant E that could decide to enter at a cost Ce ≥ 0. If E enters then M and E choose prices simultaneously and independently and demand is given by {qm = 2400 − 40pm + 20pe , qe = 2400 + 20pm − 40pe . E’s marginal cost is the same as M’s.

(c) For what values of Ce is it in E’s interest to enter?

(d) For what values of Ce would total surplus be greater if E entered?

(e) What does this question have to do with mergers?

Answer 1

The incumbent firm will set a price of $796.67 and sell 2170 units. Total surplus can be calculated by adding consumer surplus and producer surplus. E's interest to enter depends on the comparison of its profit with and without entry. Total surplus will be greater if E enters if the total surplus with E's entry is higher than the total surplus without E's entry. The question is related to mergers as it considers the impact of competition and entry on market outcomes and total surplus.

Step-by-step explanation:

(a) To maximise profit, the incumbent firm will set the price where its marginal cost equals the demand curve. The marginal cost is given as cm = 12. Setting the marginal cost equal to the demand equation 2400 - 30pm, we have 12 = 2400 - 30pm. Solving for pm, we get pm = $796.67. Substituting this price into the demand equation gives us qm = 2400 - 30(796.67), so qm = 2170. These are the values that the incumbent firm will set for price and quantity sold.

(b) Total surplus is the sum of consumer surplus and producer surplus. Consumer surplus is the area above the demand curve and below the price, while producer surplus is the area below the demand curve and above the marginal cost. In this case, the consumer surplus is (1/2)(796.67)(2170) and the producer surplus is (1/2)(796.67)(2170 - 12). Adding these two values gives us the total surplus.

(c) E's interest to enter is determined by comparing its profit if it enters with its profit if it doesn't enter. If the difference between the two is positive, then it is in E's interest to enter. We can calculate E's profit based on the price and quantity it chooses.

(d) Total surplus will be greater if E enters if the total surplus with E's entry is higher than the total surplus without E's entry.

(e) This question is related to mergers because it considers the impact of competition and entry on market outcomes and total surplus. The entry of a new competitor can potentially change market dynamics and affect the allocation of resources.