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After a decade long advertising war, NIK and REB are the only two surviving firms in the sport-shoe market. The yearly demand in this market is given by P=100-0.5q. Both firms produce shoes at a constant marginal cost of $10 per pair and have no fixed costs. Your analysis of the industry suggests that they are engaged in monopolistic competition.

a) If NIK and REB split the market equally, what are the price and quantity chosen by each firm? What are the total profits in the market?

b) Suppose that NIK gets 2/3 of the market. What are the price and quantity chosen by NIK in this case? What are its profits?

NewBal, one of the losers from the advertising wars, is exploring re-entering the market. NewBal's CEO is convinced that if they enter they (1) will be able to capture 1/3 of the market, (2) NIK will get 1/2of the market, and (3) REB will keep the last 1/6. Suppose that the (annualized) cost of entering is $E. Assume that the market will remain monopolistically competitive, whether or not NewBal enters the industry.

c) What is the maximum value of E at which NewBal would enter the industry?

Suppose that NewBal decides not to enter the industry, that the government imposes a $1 tax per/shoe-pair sold that is paid by NIK and REB, and that the market is split as in
part (a).

d) What are the new equilibrium price and quantity in the market?

e) What is the impact of the tax on the total profits in the industry?

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This solution offers both the new equilibrium price and quantity in the market for the attached case.

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Answer:
Given that,
P=100-0.5q
Marginal Cost (MC)=$10
For monopolistic competition the profit maximization condition is:
P=MC
Or,
100-0.5q=$10
Or,
0.5q=90
Or,
q=90/0.5=180
If NIK and REB split the market equally,
Quantity for NIK=90
Hence,
Price for NIK=100-0.5*90=$55
Similarly price for RBK is $55.
So,
Total ...

Solution provided by:
Jayant Kumar, MBA
Education
  • MBA, Indian Institute of Finance
  • Bsc, Madras University
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