Econ 510
Final Exam Study Guide
You are responsible for the theoretical concepts covered in class after the midterm exam
and the readings indicated in the syllabus. In addition, make sure you know how to solve
problems similar to the following:
I.
Perfect Competition
1. Suppose there are 100 identical firms in a perfectly competitive industry.
Each firm has a short-run total cost function of the form:
C y 
1 3
y  0.2 y 2  4 y  10
300
a) Calculate the typical firm’s short-run supply curve with y as a function of
the market price p.
Answer: y  10 p  20
b) Calculate the short-run industry supply curve.
Answer: Y  1000 p  2000
2. Suppose the demand for good X is given by y  1000  5 p and the supply
by y  4 p  80 .
a) Find the equilibrium quantity and the equilibrium price in this market.
Answer: y e  400 p e  120
b) Compute the consumer surplus and the producer surplus.
Answer: Cs  16000 , Ps  20000
c) Suppose the market produces 300 units, how much in total consumer and
producer surplus would be lost?
Answer: 2250
II.
Price-Maker Firm
1. A price-maker firm can produce at constant average and marginal costs of
AC = MC = 5. The firm faces a market demand given by y  53  p .
a) Calculate the profit-maximizing price-quantity combination for the firm.
Answer: p  29 , y  24
b) Compare the price-quantity combination obtained in a) with the pricequantity combination that would be obtained under perfect competition.
Answer: Under perfect competition the result would be p  5 , y  48
2. Suppose a price-maker firm can produce any level of output it wishes at
constant average and marginal costs of 5. Assume the firm sells its goods
in two different markets separated by distance. The demand curves for the
markets are given by
y1  55  p1
y 2  70  2 p 2
a) If the firm can maintain the separation between the two markets, what level
of output should be produced in each market, and what price would
prevail in each market?
Answer: p1  30 , y1  25 and p 2  20 , y 2  30
III.
Game Theory
1. Consider the following simultaneous-move, one-shot game:
Player A
Up
Down
Left
10,20
-10,7
Player B
Right
15,8
10,10
a) Identify the dominant strategies for Players 1 and 2.
b) Is there dominant strategies equilibrium in the game?
c) Find the Nash equilibrium
Answers given in class
2. Consider the following simultaneous-move infinitely repeated game
Firm A
Price
Low
High
Firm B
Low
High
0,0
50,-40
-40,50
10,10
Suppose the interest rate is 40%. The firms agree to charge the high price each
period.
a) Compute the present value of the payoff to Firm A if it cheats on the
agreement.
Answer: Firm A earns 50 today and 0 forever after.
b) Compute the present value of the payoff to Firm A if it honors the
agreement indefinitely.
Answer: 10 
101  .4
10
10

 ... 
 35
2
1  .4 1  .4
.4
c) Identify the conditions under which a (high price, high price) equilibrium
prevails.
Answer: Since the present value of cooperating is less than the value of
cheating, Firm A cheats. Similarly, Firm B cheats. For the (high price, high
price) equilibrium to prevail the present value of cooperation must be greater
than the value of cheating.
IV.
Oligopoly
Suppose the inverse demand function in a market composed of 2 firms is
p  1000   y1  y 2  . The cost function of each firm is identical and given by
Ci  y i   4 y i .
a) Derive the equilibrium quantities produced and prevailing price if the
firms compete under a Bertrand framework.
Answer: Firms price at marginal cost, 4. The industry output is 996, each firm
produces 498.
b) Derive the equilibrium quantities produced and prevailing price if the
firms compete under a Cournot framework.
Answer: y1  y 2  332 , p  336
c) Derive the equilibrium quantities produced and prevailing price if the
firms compete under a Stackelberg (leading-firm) framework.
Answer: y1  498 , y 2  249 , p  253