Consider a market with just one firm. The demand in the market is ...

[big1devin]

Consider a market with just one firm. The demand in the market is p = 18  Q and the firm has a linear cost function C(Q) = 2Q.
 
  a. How much output will this firm produce. What will be the profit and consumers surplus?
  b. Suppose a second firm with the same cost function enters the market and the two firms compete in a Cournot style (simultaneous output choice). What will be the equilibrium price and quantity in the market? What is the total market profit and CS?

Question 2

Assume a firm is a monopoly and enjoys 10 million in profits per year. The firm lobbies to have a moratorium passed by Congress on new firms in its market for the next 25 years.
 
  If there is no discount rate, how much would the firm be willing to pay to deter entry? A) 250 million
  B) 25 million
  C) 100 million
  D) 250 billion

[Hikerman221]

Answer to Question 1

a. A monopolist will produce to maximize profits given by:
= (18  Q)Q - 2Q
The derivative w.r.t Q:
- 2Q - 2 = 0
So Q = 8
The price is then 10. The profit is 10(8 ) - 2(8 ) = 64. The Consumer surplus is (18 - 10 )(8 )/2 = 32.
b. Each firm will maximize profit by:
 = (18 - Q - Qo)Q - 2Q
where Q0 is the output of the other firm. The derivative is:
18 - Qo - 2Q - 2 = 0
The best response is:
Q = 8 - Qo/2
Solving both best response functions simultaneously:
Q = 8 - (8 - Q/2 )/2
Q = 16/3 = 5.33. The total market quantity is then 10.66. The price is 18 - 10.66 = 7.34. The profit for each firm is:
5.33 (7.34 ) - 5.33(2 ) = 28.41
The total market profit is then 56.82
The consumer surplus is (18 - 7.34 )(10.66 )/2 = 56.87

Answer to Question 2

A

[big1devin]

Thank you

[Hikerman221]

Happy to help you