EconS 301, Spring 2015, Dr. Rosenman
Test 3, April 23, 2015
Name ____________________________
ID#_______________________________
Do any three of questions 1, 2, 3 and 4, and do question 5. The three questions you do out of 1-4 are
worth 10 points each, and question 5 is worth 20 points. I am figuring 10 minutes each for the first 3,
and 30 minutes for question 5. That leaves 15 minutes for panic and other activities. There is also an
extra credit section on game theory at the end of the test.
1. Three firms in the local Pullman area are Avista, which sells electricity, Time-Warner Cable, which
provides cable TV and internet services, and the Black Cyprus, a restaurant.
a. Discuss the characteristics of the market facing each firm.
b. How much market power do you think each firm might have? Defend your answer. Be sure to
think about how much competition each might face, and what the market demand for the
product looks like.
c. What is the likelihood that each firm is making a profit? Again, defend your answer.
Answer
A. The market facing Avista is a monopoly because it does not have any competitors in the market
meaning it is a price setter (ignoring any regulation that it might face) and has the entire market
demand.
Time-Warner Cable/Internet is in an Oligopoly because there are a few competitors such as
Dish, DirecTV, and Frontier that provide similar services. These four firms share the market
power and are also price setters.
Black Cyprus is in a monopolistic competition because there are many substitutes but all of
them have differentiated goods which might induce brand loyalty.
B. Avista as a monopoly likely has lots of market power, especially since there are no good
substitutes for electricity so the demand is likely very steep. Hence, understanding that a
measure of market power is how far P exceeds MC, we should expect price>>MC .
Time-Warner Cable has less market power than Avista both because of the availability of
substitutes for the specific good it provides and because there are other sources of
entertainment. Hence its demand curve will be more elastic than that of Avista but will still be
relatively inelastic in comparison to other markets with more competitors. Hence, we would
expect P>MC.
Because of the large number of other restaurants Black Cyprus’s market power depends on how
much brand loyalty it has developed. It likely faces an elastic demand curve but not a perfectly
elastic demand curve, so P is above but close to MC.
C. Although this really depends on costs and demand, we would expect that Avista is making the
most profit because of its strongest market power. The profit Time-Warner makes depends on
how the firms behave. For example, if they compete Bertrand, we would expect profit=0, while
Cournot they will make some profit but not as much as a monopoly. While Black Cyprus could
be making positive profits in the short run, because of free entry, in the long run it will make no
economics as that is the long run equilibrium in a monopolistic competition.
2. The Antitrust division of the FTC is looking into a particular industry. The market is
made up of 52 firms, the two largest of which have shares (in terms of quantity sold) of
25% each. The remaining 50 firms make up a competitive fringe, having 1% each. The
market elasticity is about 1.5%, the weighted Lerner's Index is 0.0867.
a. Find the Herfindahl index for this industry.
b. Find the C2 and the C4.
c. Using “equal-sized firms” rules, which measure shows the most
concentration in the industry?
d. Find the elasticity of demand for the industry.
e. Find the Lerner’s index for the largest firm in this industry.
f. The FTC claims with 2 firms holding half the industry the market is overly
concentrated. If you were arguing for the industry, how would you respond?
Answer
A.
B.
C.
D.
E.
F.
H = .25^2 + .25^2 +50 (.01^2) = 0.13
C2=.5, C4=.52
M=1/H=7.6923, M=2/C2=4, M=4/C4=7.6923
0.0867 = 0.13/|e| , |e| = |1.499|
LI = .25/|1.499| = 0.1668
The FTC is ignoring how much the ½ of the industry that consists of small firms
affects the concentration in the industry. While C2 is large, and describes an
industry that consists of only 4 firms, both the H and C4 describe industries with
almost twice that number of firms.
3. Consider a two-person economy (Bill and Sue) with two goods (A and B) where both individuals have
a utility function U=A*B. The PPF for A and B is a normal curved shape. A is produced by a
monopoly which can always set the price of A so PA=2*MCA. B is produced in a competitive market
so PB=MCB. (HINT: Think about MRS and MRT when answering this question)
a. Will this economy be Pareto efficient in equilibrium? Explain why or why not.
b. Does it produce too much of A or too much of B, or the right amount of each?
c. Suppose the government uses its anti-trust powers so that good A is now produced as a perfect
competition, but imposes a tax of t on good A to raise money to enforce the anti-trust action.
Will the economy be Pareto efficient? Explain.
d. Describe a tax scheme that will allow the economy to be Pareto efficient while still raising
revenue? Explain why it will work.
Answers
A. In this situation the economy is not Pareto efficient in equilibrium because
MRS=Pa/Pb=2MCa/MCb>MCa/MCb=MRT which means that the slope of the point on the
contract line meets with the two indifference curves is steeper than the slope of the PPF at this
point.
B. We have the MRS=MUa/MUb>MCa/MCb=MRT. The value (MUa) consumers place on the last
unit of A (relative to how much they value the last unit of good B) is more than it costs the
society to provide it (again, relative to another unit of good B). Hence, society is producing too
much B and should provide more of good A (giving up B). This means MUa will fall (and MUb
will increase) and MCa will increase (as MCb falls) moving the economy towards the condition
needed for Pareto efficiency.
C. No because now the economy is in a situation where
MRS=MUa/MUb=Pa(1+t)/Pb>Pa/Pb=MCa/MCb=MRT and it will still under produce good A
relative to good B.
D. If the government were to tax both goods A and B were taxed the same percent so that the
consumers price ratio was equal to the firm’s price ration then the outcome would be Pareto
efficient. MRS=MUa/MUb=Pa(1+t)/Pb(1+t)=Pa/Pb=MCa/MCb=MRT.
4. Suppose we have a market with an inverse demand curve P=100-Q and MC is constant so MC=10.
a. If the market is a perfect competition, what will be the equilibrium price, what would be the
market output, and how much profit would firms make?
b. Now suppose it is a monopoly. What will be the equilibrium price, what would be the market
output, and how much profit would the firm make?
c. Now suppose it is a Cournot duopoly. What will be the equilibrium price, what would be the
market output, and how much profit would each firm make?
d. Find the market price, each firms’ quantity, and profit if one firm acts as a Stackelberg leader
and the other a follower.
e. Find the market price, each firms’ quantity, and profit if both firms act as a Stackelberg leader
Answers
A. P=100-Q=10, Q=90, P=10 Profits=0 because P=MC=AC as MC is constant
B. Profits = (100-Q)Q -10Q  Marginal Profit = 90-2Q = 0  Q=45 P=55 Profit = 2,025
C. Profit = (100-q2-q1)q1-10q1  Marginal Profit = 90-q2-2q1  RF1 is q1=45-1/2q2 and RF2 is
q2=45-1/2q1  plug RF2 into RF1 to get q1=30  q2=30 P=40 and profits for both firms is 900
D. Let firm 1 be the leader, Profit=(100-q1-(45-1/2q1))q1-10q1  Marginal profit = 100-45-102q1+q1=0  q1 = 45 so RF2 is the same q2 =45-1/2(45)=22.5  P=32.5, Profit1=1,012.5,
Profit2=506.25
E. If both firms are Stackelberg leaders then:
Profit function for 1 = (100-q1-(45-1/2q1))q1-10q1
Profit function for 2 = (100-q2-(45-1/2q2))q2-10q2
We solved for 1 in the first part
q1 = 45  q2 = 45
P=10
Profit1=Profit2=0
5. For any FIVE (5) of the statements below, indicate if it is True, False or Uncertain, and explain why.
(Your explanation needs to give reasoning, not just a different statement). Each is worth 4 points.
a. The PPF for an economy that produces two goods, A and B, is a straight line with a slope of -1. Both
residents of the economy have utility functions U=A0.5*B0.5. A Pareto efficient general equilibrium
will have both residents consuming so A=B.
True, we went over this example in class. The MRS = B/A = 1 because MRT = - Slope of the PPF=1
therefore MRS=B/A=1 implying B=A when in a Pareto efficient general equilibrium.
b. A multiplant monopolist has plants in Seattle and Tacoma. When Seattle raised its minimum wage
to $12 an hour (much more than the minimum wage in Tacoma) the best move for the monopolist
will be to close the Seattle plant and move all production to Tacoma.
False, a multiplant monopolist produces so that MC is equal in all plants. In this case the MC in
Seattle has gone up so the firm should move some production to Tacoma until the MC are equal
again.
c. Water service provides water to households for a set price of $20 then $0.03 per a gallon. This is a
form of perfect price discrimination.
Uncertain, but likely true. Each consumer will buy additional water until their MU=0.03. The fixed
fee is put into place to take consumer surplus away.
d. Movie theaters they give older people a discount but the symphony gives students a discount but
not older people. Movie theaters think students have a less elastic demand for movies and the
symphony thinks older people are less elastic demand for the symphony.
True, This can be seen using the rule P=MC(e/(1+e)) assuming that the MC is the same for each
group.
e. A monopoly practicing 2nd degree price discrimination will produce the same amount as a
monopoly practicing 1st degree price discrimination but will make a greater profit.
False, under 1st degree price discrimination there is no consumer surplus because it is all captured
by the monopolist whereas in 2nd degree price discrimination there is still some consumer surplus
left that is not captured by the producer. So they produce the same amount, but the profit is bigger
for the firm practicing 1st degree price discrimination.
f.
It is possible to have a Pareto efficient allocation where one person is worse than he is at an
allocation that is not Pareto efficient.
True. Look at the following graph:
Point 2 is not Pareto efficient. Point 9 is Pareto efficient (it is on the contract curve) but leaves
Bronte worse off than at 2. Similarly, point 10 leaves Spenser worse off than at 2, although 10 is
Pareto efficient.
g. Firms in monopolistic competitions have no market power because P=AC.
False. Market power is measured by the ability to set P>MC. In equilibrium P=AC but we could
expect AC>MC. For example see graph (although graph is not needed to get full credit, just
understanding that P=AC>MC. LR equilibrium is at P1.
h. Toyota faces competition from many other car companies, hence Toyota does not have any market
power.
Likely False but really uncertain. Both acceptable with good explanation, if consumers have brand
loyalty to Toyota then they will have some market power. However, if Toyota is seen as a perfect
substitute with other car companies then there is no product differentiation and they will have no
market power.
i.
If the MRS(A for B)>MRT(Afor B), an economy can make its members better off by increasing the
production of B.
False, in this situation MRS=MUA/MUB>MCA/MCB=MRT. Given the law of diminishing marginal
utility you could lower MRS by increasing consumption of A and decreasing consumption of B. At the
same time, the MRT would increase as MCA goes up and MCB goes down.
j.
In a Hotelling beach model where firm A faces a higher marginal and average cost than firm B, firm A
will locate at one end of the beach and firm B will locate at the other end of the beach.
False – they will still compete by location to attract the middle buyer, even with different costs, and
tend towards the center of the beach.
k. In an oligoloply market, if both firms follow Bertrand behavior, output will be less than if they both
follow Cournot behavior.
False, Betrand behavior leads to competitive prices (P=MC) and thus larger outputs which are
greater than Cournot output where P>MC.
l.
The Kenworthy theater in Moscow charges $6 for a single entry, but sells ticket books at the rate of
$50 for 10 entries. This is likely an example of 1st degree price discrimination.
False, this is an example of 2nd degree price discrimination or step pricing because the first few units
sell for $6 and then subsequent untis are cheaper.
m. A firm in a kinked-demand curve oligopoly passes all cost increases on to consumers.
False, if the firm is on the vertical portion of the MR curve then any increase in cost will not be
passed onto the consumers resulting in lower profits for the firm.
Extra Credit: Each of the following questions is worth 2.5 XC points.
XC1. Suppose you have the following game:
Payoffs are A,B
Player A
Top
Bottom
Player B
Left
-3,-3
-6,0
Right
0,-6
-1,-1
Does either player have a dominant strategy? Explain why or why not?
Find any Nash Equilibria that exist in this game.
What type of game is this?
Top is dominant strategy for player A
Left is dominant strategy for player B
Nash: (Top, Left)
Battle of the Sexes
XC2. Suppose you have the following game:
Payoffs are A,B
Player A
Top
Bottom
Player B
Left
2,1
0.0
Right
0,0
1,2
Does either player have a dominant strategy? Explain why or why not?
Find any Nash Equilibria that exist in this game.
There are no dominant strategies. Given Player B chooses left then Player A will want to choose top but
if Player B chooses right then Player A will want to choose Bottom.
If player A chooses Top player B will want Left, but if player A chooses Bottom Player B will want Right.
There are Nash Equilibria in this instance similar to the battle of the sexes example in the lecture slides.
If Player B chooses left then Player A will choose top. If Player B chooses right then Player A will choose
bottom. There is no incentive to change given the others choice in either of these situations.