Question

The market demand is given by P = 130 – 2Q, where P ($/unit) is the price and Q is the market quantity demanded (units). The marginal cost of producing the good is flat MC = $10 per unit. Use these for all the questions below.

1. In a Cournot duopoly market equilibrium,

   1. what is the price ($/unit)?

   2. what is the market quantity (units)?

   3. what is the Herfindahl-Hirschman Index HHI?

   4. what is the Lerner Index LI?

   5. what is the (social) surplus from trade (the sum of consumer surplus and profits)?

   6. what is the deadweight loss DWL?

Answer 1

Solution:

a) In a perfectly competitive market, price and quantity are determined by equating price with the marginal cost that is in a perfect competition, a producer maximizes his profit by setting price equal to marginal cost.

so, Price = Marginal cost which means that the price charged in a perfect competition is equal to the marginal cost which in this case is $10. So, the equilibrium price is $10.

b) Price = 130 - 2Q

Putting the value of price = marginal cost = $10 in the above equation,

10 = 130 - 2Q

130 - 10 = 2Q

120 = 2Q

Q = 120/2

Q = 60 is the answer.

c) Hirschman Herfindahl Index calculated the degree of market concentration and its value ranges from 0 to 10,000. The closer the index is to 0, it indicates perfect competition as there are thousands of firms competing as a result of which each firm would have almost 0% market share. So, in case of perfect competition the value of this index is 0 which means 0 market concentration.

d) Lerner index is the index which indicates the degree of monopoly power. The index is calculated as follows,

(P - MC)/P = (10 - 10)/10 = 0/10 = 0.

In case of perfect competition, the degree of monopoly power is 0 which means the the firm has no control over the market like in case of monopoly.

I hope this helps if you find any problem. Please comment below......