Once upon a time there was a market in a kingdom far far away. This market could

Question

Once upon a time there was a market in a kingdom far far away. This market could be expressed by the demand Q = 200 P in which Q =Ni=1 qi was the aggregate quantity. There were N 1 firms in this market, and the marginal cost for each firm i was a constant ci.

After a little while the Antitrust Agencies were concerned with the effect on market concentration generated by this regulation, so they decided to open exceptions for new entrants creating a competitive fringe with marginalcostMCCF =30+Q.Sincetheincumbentwasalreadythereas a monopolist, it retained its price-maker status. The previous investment made by the incumbent were then sunk costs.

(a) What is the dominant firm’s residual demand?

(b) What is the level of output the dominant firm chooses to produce?

(c) What is the market price determined by the dominant firm?

(d) What is the dominant firm’s profit in equilibrium?

(e) How much is the competitive fringe producing?

(f) How much is consumer surplus in this case? How did it change compared with the monopolist case? Why is that so?

(g) What is the Herfindahl Hirschman Index in this market?

Explanation / Answer

In a market, if there is a firm holding a large share of the market, then this firm is called the dominant firm. Typically, a dominant firm's share in the market is much higher than that of its next rival in the market. Usually, dominant firms have a market of atleast 40% or more.

In such cases where a market has a dominant firm, the competition that this firm faces due to the smaller firms in the market is called the competitive fringe.

It is given to us that the demand function in the market is Q = 200 - P and that the marginal cost with competitive fringe is MCcf = 30 + Q

The inverse demand function is P = 200 - Q. We know that one of the assumptions in competitive market with a dominant firm is that the quantity produced by the market is determined at the point where MC = P. On equating the MC function and the inverse demand function we get :

30 + Q = 200 - Q

Q + Q = 200 - 30

2Q = 170 or Q = 170/2 or Q = 85

This is the supply in the market or S(p).

(a) Residual demand for a dominant firm is the difference between demand and supply in the market. It is given by the following function :

DR = D(p) - S(p)

= 200 - P - 85

= 115 - P

Residual demand is DR = 115 - P

(b) A profit maximising firm will produce at a point where MR = MC. Marginal revenue can be calculated from the inverse demand function. Since it is a liner demand function, for marginal revenue, the intercept of the inverse demand function remains the same but the slope is doubled. So, MR = 200 - 2Q.

A profit-maximising firm produces at a point where MR = MC. So,

200 - 2Q = 30 + Q (MCcf is given to us in the question)

200 - 30 = Q + 2Q

170 = 3Q or Q = 170/3 or Q = 56.66 or 57

(c) The market price P given by the dominant firm can be determined by the inverse demand function P = 200 - Q. Since Q = 57,

P = 200 - 57 = 143

(d) Profit for a dominant firm is determined by the following equation :

Profit = (P - MCcf) Q

= (143 - 30 - Q) x Q

= (113 - Q) x Q

= (113 - 57) 57

= 56 x 57 = 3,192

So profit for the dominant firm in equilibrium is $3,192

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