Microeconomics Final Assignment: Two Firms In A Market

Name
Instructor
Course
Date
MICROECONOMICS FINAL: Questions 5, 6, 7, 8
5. Suppose there are two firms in a market with demand D(p) = 100-P.
Assume that there are two possible firms who can serve this market.
One has a total cost function of C1(y) = 100 + y. The other firm has a cost function of C2(y) = 12y. Suppose that Firm 1 serves this industry as a monopoly. What will be the outcome (price and quantity)?Suppose the same for Firm 2? Which maximizes total surplus?
Assuming D (p) = Q then Q=100-P
Then the D (p) = 100-P
Mathematically D(p)=Q
Q=100-P
Then P= 100-Q
TR= (100-Q)*Q= 100Q-Q2
MR=100-2Q
C1(y) = 100 + y, which is TC=100+q and MC=1
The other firm has a cost function of C2(y) = 12y, which is TC=12q and MC= 12
At profit maximizing quantity MR=MC
Firm 1 then100-2Q=1 and q= 49.5 and p= 100-49.5= $ 50.5 firm 2 then 100-2Q=12 and q=44 and p= $ 56
(a) Now assume that the right to be a monopolist will be “auctioned by price?” That is each firm will submit a price that they will charge if they are a monopolist and the lowest price will win the
firm the monopoly. [Hint: For those of you who have game theory experience you can probably predict how firms will behave in equilibrium. But as a general hint. Find the prices that will give each firm zero profits. The lowest price a firm will bid is this price. Take the firm that has the lowest breakeven price you just found. Look at all the prices between the two average costs and pick the one that maximizes their profit. This is the outcome. Pay special care to the endpoints Profit= TR-TC
Firm 1
TR-TC=100Q-Q2-100-Q and Q=97 and P=3
Firm 2
TR-TC=100Q-Q2 -12Q and Q=88 and p=12
Firm 1 has the lowest price and will bid
(b) Repeat the above example but assume a different model for auctioning off the right to be a monopolist. Suppose instead that they must bid a flat payment up front to be the monopolist. Assume that the firm that would earn more profits bids a fee equal to the profits of the less profitable potential monopolist and wins. Who wins this auction?
Of the two auction methods, which maximizes?
i. Consumer surplus-second method
ii. Government revenue-second method
iii. Output-second method
iv. Total surplus (assuming that gov’t revenues are part of total surplus)? - First method
6. Assume a monopolist with total cost C(y) = 500+20y. Market demand is Q = 100 - P.
(a) If price is set equal to marginal cost, what will the firm’s profits be?
P= 100-Q
TC=500+20Q and MC= 20
TR=100Q-Q2
Profit=100Q-Q2-500-20Q
Profit 100(20)-400-(500+400) = 700
(b) If price is set equal to average cost, what will the loss be in terms of output and total surplus from the first part?
AC= (500+20Q)/ Q= 500/Q+20 then 100-Q=500/Q+20
The Q= 6.83 or73.17, which is 7 or74 units
Plugging Q to get price then P=26.83
Loss in output= (100-20) - 74 = 6
...