Download CEVAPLAR 1. Conigan Box Company produces cardboard boxes

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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
CEVAPLAR
1.
Conigan Box Company produces cardboard boxes that are sold in bundles of
1000 boxes. The market is highly competitive, with boxes currently selling for
$100 per thousand. Conigan's total and marginal cost curves are:
TC = 3,000,000 + 0.001Q2
MC = 0.002Q
where Q is measured in thousand box bundles per year.
a.
b.
Calculate Conigan's profit maximizing quantity. Is the firm earning a
profit?
Analyze Conigan's position in terms of the shutdown condition. Should
Conigan operate or shut down in the short-run?
Solution:
a.
Given the competitive nature of the industry, Conigan should equate P to MC.
100 = 0.002Q
Q = 50,000
To determine profit:
π = TR - TC
TR = PQ
TR = $100 • 50,000
TR = 5,000,000
TC = 3,000,000 + 0.001(50,000) 2
TC = 3,000,000 + 2,500,000
TC = 5,500,000
π = 5,000,000 - 5,500,000
π = - 500,000
Conigan is losing 500,000 per year.
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
b.
To determine if the firm should operate or shutdown, we must compare P to
AVC.
TVC
Q
TVC = TC - TFC
TVC = 5,500,000 - 3,000,000
TVC = 2,500,000
2,500,000
AVC =
= $50
50,000
AVC = 50; P = $100
AVC =
The firm should operate since P > AVC .
2.
Homer's Boat Manufacturing cost function is: C ( q ) =
marginal cost function is: MC ( q ) =
75 4
q + 10, 240 . The
128
75 3
q . If Homer can sell all the boats he
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produces for $1,200, what is his optimal output? Calculate Homer's profit or
loss.
Solution: The profit maximizing output level is where the market price equals marginal
cost (providing the price exceeds the average variable cost). To determine the
optimal output level, we need to first equate marginal cost to the market price.
75 3
q = P = 1, 200 ⇔ q = 8. The average variable cost at this
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75 ( 512 )
75
3
output level is: AVC (8 ) =
= 300. Since P > AVC ( 8 ) , Homer will
(8 ) =
128
128
That is, MC ( q ) =
maximize profits at 8 units. Homer's profits are:
 75 ( 8 )4

π = Pq − C ( q ) = 1, 200 ( 8 ) − 
+ 10, 240  = −3, 040.
 128

Homer will produce and
make a loss as losing $3,040 is better than not producing and losing $10,240.
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
3.
The market for wheat consists of 500 identical firms, each with the total and
marginal cost functions shown:
TC = 90,000 + 0.00001Q2
MC = 0.00002Q,
where Q is measured in bushels per year. The market demand curve for wheat
is Q
= 90,000,000 - 20,000,000P, where Q is again measured in bushels and P is
the price per bushel.
a.
b.
c.
Determine the short-run equilibrium price and quantity that would exist in
the market.
Calculate the profit maximizing quantity for the individual firm. Calculate
the firm's short-run profit (loss) at that quantity.
Assume that the short-run profit or loss is representative of the current
long-run prospects in this market. You may further assume that there are
no barriers to entry or exit in the market. Describe the expected long-run
response to the conditions described in part b. (The TC function for the
firm may be regarded as an economic cost function that captures all
implicit and explicit costs.)
Solution:
a.
Market supply is horizontal sum of individual firm supply (firms MC curve).
Firm's TC = 90,000 + 0.00001Q2
MC = 0.00002Q = P.
Solve for Q in terms of P to express as supply curve
P = 0.00002Q
Q = 50,000P
Market supply curve is horizontal sum of firm supply curve or N-times the
firm supply curve
(N is the number of firms).
QS = 500(50,000)P
QS = 25,000,000P
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
equate QS and QD to determine price and quantity
25,000,000P = 90,000,000 - 20,000,000P
45,000,000P = 90,000,000
P = $2.00
Q = 25,000,000P
Q = 25,000,000(2)
Q = 50,000,000
b.
To determine the firm's output, equate price and marginal cost - Firm's MC =
0.00002Q.
P = 2 = 0.00002Q
Q = 100,000
Firm's π = TR - TC
TR = 2.00(100,000)
TR = 200,000
TC = 90,000 + 0.00001Q 2
TC = 90,000 + 0.00001(100,000) 2
TC = 190,000
π = 200,000 - 190,000 = 10,000
c.
Firms are earning economic profit so we would expect entry to occur, causing
the market supply curve to shift rightward. As the market supply curve shifts
rightward, price falls, which in turn causes each firm to reduce its output. This
will continue until we reach long-run equilibrium at zero profit.
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
4.
The elected officials in a west coast university town are concerned about the
"exploitative" rents being charged to college students. The town council is
contemplating the imposition of a $350 per month rent ceiling on apartments in
the city. An economist at the university estimates the demand and supply
curves as:
QD = 5600 - 8P
QS = 500 + 4P,
where P = monthly rent, and Q = number of apartments available for rent. For
purposes of this analysis, apartments can be treated as identical.
a.
b.
c.
Calculate the equilibrium price and quantity that would prevail without the
price ceiling. Calculate producer and consumer surplus at this equilibrium
(sketch a diagram showing both).
What quantity will eventually be available if the rent ceiling is imposed?
Calculate any gains or losses in consumer and/or producer surplus.
Does the proposed rent ceiling result in net welfare gains? Would you
advise the town council to implement the policy?
Solution:
a.
To calculate equilibrium set QD = QS and solve for P.
5600 - 8P = 500 + 4P
5100 = 12P
P = 425
Substitute P into QD to solve for Q
QD = 5600 - 8(425)
Q = 2200
Q D = 5600 − 8P
P = 700 − 0.125Q D
Q S = 500 − 4P
P = 125 + 0.25Q
C.S. = area A
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
C.S. = 0.5(700 - 425) x 2200
C.S. = 302,500
P.S. = area B
P.S. = 0.5(425 - 125) x 2200
P.S. = 330,000
Sum of producer and consumer surplus is:
302,500 + 330,000 = 632,500
b.
Eventually the market will settle at the quantity supplied corresponding to
$350 rent.
QS = 500 + 4(350)
QS = 1900
QD at P = 350
QD = 5600 - 8(350) = 2800
There will be a shortage of 900 apartments.
Gain = Consumer surplus is area A
Area A = (425 - 350) x 1900 = 142,500
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
Area B = loss in consumer surplus
To find area B, first find consumer reservation price corresponding to an
output of 1900.
P = 700 - 0.125(1900) = 462.50
Difference Q = 2200 - 1900 = 300
Area B = 0.5(462.50 - 425) x (2200 - 1900)
Area B = 5625
Loss in consumer surplus is 5625.
Area C is loss in producer surplus not offset by gain in consumer surplus.
Area C = 0.5(425 - 350) x (2200 - 1900)
Area C = 11,250
c.
Area A is a gain in consumer surplus, but it is offset by a loss in producer
surplus. The net changes are thus B (lost C.S.) and C (lost P.S.). The policy
thus results in a deadweight loss. The deadweight loss = lost C.S. + lost P.S.
or 5625 + 11250 = 16,875.
Deadweight loss = 16,875
5.
Tad's bait shop has a monopoly on the bait market at Sanderson's Lake. The
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demand curve for bait is QD = 56 − 8 P ⇔ P = 7 − QD . This implies the marginal
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revenue function is: MR ( Q ) = 7 − Q. Tad has two employees he can use to
search for bait. The marginal cost of using Amanda to search for bait is:
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QM .
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MC N ( QN ) = QN .
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The marginal cost of using Andrew to search for bait is:
MCM ( QM ) =
Determine how many units of bait each employee should
gather. What is the price Tad receives for selling the bait?
Solution: We can think of Tad's employees as two different plants that Tad owns. We
can then determine the individual plant supply and aggregate to determine
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Tad's total output. This is done as follows: MCM ( QM ) = QM ⇒ QM = 4MCM .
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8
8
3
Also, MCN ( QN ) = QN ⇒ QN = MCN . This implies that Tad's aggregate supply
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is: Q = QM + QN = 4MCM + MCN . Since marginal costs will be equivalent across
plants, Q =
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MC.
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Tad's marginal cost as a function of output at both plants is:
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ISL 805 UYGULAMALI İKTİSAT_ UYGULAMA (4) _ 9 Kasım 2012
MC ( Q ) =
3
Q.
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Since Tad is a monopolist, he will set marginal revenue equal
to marginal cost to determine optimal output. This is:
MC ( Q ) =
3
1
Q = MR ( Q ) = 7 − Q ⇒ Q = 17.5.
20
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At this output level, Tad's marginal
cost is $2.63. This means that Amanda is gathering 10.5 units of bait while
Andrew gathers 7 units of bait. Tad receives $4.81 per unit of bait.
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