1. (25 points total) Suppose you are a monopolist able to produce your chosen output at a constant average (and thus marginal) cost of ATC = MC = $5. You face a market demand curve given by Q = 53 â P or inverse demand given by P = 53 â Q, where Q is the output provided to the market by supplying firms, in this case you!
a.Please calculate the profit maximizing quantity you should supply to the market along with the price youâll be able to charge. Calculate your firmâs profit.
Dâ/dQ = -2Q +48 = 0 or Q =24
24 = 53 â P, P = $29
P = TR â TC = (29)(24) â (5)(24) = $576
Profit maximizing quantity is 24, Price is 29, Profits are $576
Suppose now that a second firm enters the market. Let Q1 be the output of the first firm, yours, and Q2 the output level of the second firm. Market demand is now given by Q1 + Q2 = 53 â P or inverse demand can be expressed as P = 53 â Q1 â Q2. Also assume the second firm has adopted the same technology as you and thus has the same costs (both in total and per unit) as you. As in the Cournot model, with simultaneous choices of Qi, each firm chooses its profit maximizing level of output on the assumption that its competitorâs output is fixed at itsâ profit maximizing level.
b.Find each firmâs âreaction functionâ or âreaction curve,â the statement that expresses a firmâs desired output in terms of its competitorâs output [i.e., Q1 = f(Q2) and Q2 = f(Q1)].
âr = 53 â 2Q1 â Q2 â 5 = 0, or Q1 = 24 â Q 2/2
Q2 = 24 â Q2/2
c.Calculate the Cournot equilibrium, the levels of each firmâs output at which each firm is doing as well as it can.
Q1 = 24 â (1/2)(24 â Q1/2)
Q1 = 16 Q2 =16
d.What are the resulting market price and profits for each firm?
P = 53 â 16 â 16 = $21
Profits (21)(16) â (5)(16) = $256
e.What tactics might your firm, the original monopolist, employ to deter the other firm from entering? How much (maximum) might you be willing to pay, this period, to employ these tactics?
The firm will need to have a better quality and quantity to stay ahead of the competition. The implementation of technology, and competitive prices will be needed to stay ahead and this will ensure a profit maximization within the industry so they wonât become bankrupt.
Now suppose there are N identical firms in the market, all with the same marginal and average costs. Using the Cournot mechanism, wherein each firm chooses its output simultaneously:
f. How much will each firm produce [Qi = f(N)] ?
g. What will be the single market price each firm will charge [P = f(N)] ?
h.Demonstrate that as N becomes large(r), the market price and profit per firm approach those that would prevail under perfect competition.
