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Unformatted text preview: Answer Key
Testname: PROBLEM SET 3_SPRING2011 21) a.
Without regulation we would expect the ﬁrm to behave as a monopolist, equating MR and MC.
28  0.0016Q = 0.0012Q
Q = 10,000
P = 28  0.0008(10,000)
P = $20
b.
Economic theory suggests that price should be equal to MC to achieve allocative efﬁciency.
P = 28  0.0008Q
MC = 0.0012Q
28  0.0008Q = 0.0012Q
28 = 0.002Q
Q = 14,000
P = 28  0.0008(14,000)
P = 28  11.20
P = 16.80
c.
In (a), the price is higher ($20 as opposed to $16.80), and quantity lower (10,000 as opposed to 14,000). The
monopolist's higher price and smaller quantity result in a deadweight loss as shown below. 7 Answer Key
Testname: PROBLEM SET 3_SPRING2011 22) If Jeremy's marginal costs are constant at $50, he should charge $65 per rental.
23) Hawkins will set marginal revenue equal to marginal cost to ﬁnd optimal output.
MR(Q) = 50  Q = MC(Q) = 5 + 1 Q ⇒ Q = 30.
At this output level, Hawkins charges $35 per unit. The choke price is
2
$50 while Hawkins reservation price is $5. Consumer surplus is
CS = 1 (50  35)30 = 225. Producer surplus is PS = 0.5(20  15)(30) + (35  20)(30) = 675. Total surplus in the local
2
Oatmeal Stout market is $900 when Hawkins has monopoly power. If Hawkins did not have monopoly power, the
price of Oatmeal Stout would equal Hawkins marginal cost. We can ﬁnd this output level by setting consumer's
price as a function of output equal to Hawkins marginal cost. P = 50  1 Q = MC = 5 + 1 Q ⇒ Q = 45. At this output
2
2
level, the price of Oatmeal Stout is $27.50. Consumer surplus is CS
PS ! ! = 1 (50  27.50)45 = 506.25. Producer surplus is
2 = 1 (27.50  5)45 = 506.25. Total surplus when Hawkins does not have monopoly power would be $1,012.50.
2 Thus, society loses 112.50 of surplus due to Hawkins' monopoly power in the local Oatmeal Stout market. 8 Answer Key
Testname: PROBLEM SET 3_SPRING2011 24) Let PC = Calloway price
PA = Archwood price
EC = Calloway elasticity
EA = Archwood elasticity
a.
For an optimal price ration the following conditions must hold.
1+ 1
EA
PC
must =
PA
1+ 1
EC
PC
must = 42 = 1.68
PA
25
1+ 1
EA
1+ 1
EC = 1+ 1
4
1+ 1
2 = 3
4
1
2 = 3 = 1.5
2 The current price is not optimal.
b.
P
If the elasticities are constant C should equal 1.5.
PA
PA = $25, P C should be $37.50 9 Answer Key
Testname: PROBLEM SET 3_SPRING2011 25) a.
The monopoly level of output is found where marginal revenue equals marginal cost. The marginal revenue curve
has the same price intercept as the demand curve and twice the slope. Thus:
MR = 1,200  2Q
Setting MR equal to MC (which is zero in this problem) yields:
1,200  2Q = 0
Q = 600
P = 1,200  600 = 600
b.
The Cournot equilibrium is found by using the reaction curves of the two ﬁrms to solve for levels of output. The
reaction curve for ﬁrm 1 is found as follows:
R1 = PQ 1 = (1,200  Q)Q 1
= 1,200Q1  (Q1 + Q 2)Q1
= 1,200Q1  Q 12  Q 2Q1
The ﬁrm's marginal revenue MR1 is just the incremental revenue R1 resulting from an incremental change in output
!Q1:
MR1 = !R1/!Q1 = 1,200  2Q 1  Q 2
Setting MR1 equal to zero (the ﬁrm's marginal cost) and solving for Q1 yields the reaction curve for Q 1:
Firm 1's Reaction Curve: Q1 = 600  (1/2)Q2
Going through the same calculations for ﬁrm 2 yields:
Firm 2's Reaction Curve: Q2 = 600  (1/2)Q1
Solving the reaction curves simultaneously for Q 1 and Q2 yields: Q1 = Q 2 = 400. Thus the total output is 800 and
the price will be $400.
c.
In the industry were perfectly competitive, price will be equated to marginal cost.
P = 1,200  Q = 0 or Q= 1,200 and P = 0
26) a.
The prisoner's dilemma model is most appropriate for analyzing this situation. We can conclude that the prisoner's
dilemma is most appropriate because each ﬁrm must set its advertising strategy without knowledge of the rival's
strategy.
b.
Increasing the advertising level is the dominant strategy, since the ﬁrm is better off increasing regardless of the
rival's action. For example, if Firm B increases, Firm G earns 27 if it increases and 12 if it does not increase. G is
better off increasing. If Firm B doesn't increase, Firm G earns 45 by not increasing and 50 by increasing. Again,
Firm G is better off to increase. It is obvious that no matter what B does, G is better off to increase. Firm B faces the
same situation. 10 ...
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This note was uploaded on 12/16/2011 for the course ECON 303 at USC.
 '07
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