202-4
Post on 07-Apr-2018
216 Views
Preview:
TRANSCRIPT
-
8/3/2019 202-4
1/11
Rilwan Dawodu
1awith no tax equilibrium values are
Q = 140,000 - 25,000P demandQ = 20,000 + 75,000P supply
subtract supply from demand
0 = 120,000 -100,000P
100,000P = 120,000
P = 120/100 = 1.2Q = 140,000 - 25,000(1.2) = 20,000 + 75,000(1.2) = 110,000
with no tax equilibrium values arePeq = $1.2Qeq = 110,000 packs per day
1bwith tax the 4 equations areQ = 140,000 - 25,000Pb demandQ = 20,000 + 75,000Ps supplyQd = Qs
Pb - Ps = tax = 0.40
140,000 - 25,000Pb = 20,000 + 75,000PsPb = Ps + 0.40
140,000 - 25,000(Ps + 0.40) = 20,000 + 75,000Ps120,000 - 10,000 = 100,000Ps
110,000 = 100,000PsPs = 1.1Pb = Ps + 0.40 = 1.5
Q = 140,000 - 25,000Pb = 140,000 - 25,000*1.5 = 102,500Q = 20,000 + 75,000Ps = 20,000 + 75,000*1.1 = 102,500
with tax the seller's price isPs = $1.1with tax the buyer's price isPb = $1.5
1
-
8/3/2019 202-4
2/11
with tax the quantity bought and sold isQ = 102,500 packs per day
what portion of the tax is borne by buyers and sellers respectively?compared to the no tax equilibrium price P = $1.2
buyer's pay 1.5 - 1.2 = $0.30 moreseller's receive $0.10 less( 1.1 - 1.2 = - 0.10 )$0.30 + $0.10 = $0.40 = tax
1cthe deadweight loss from the tax isthe area of the triangle (which is the sum of the 2 triangles)whose base is the tax and whose height is the difference in Q (Qeq - Qtax)
1/2 * 0.40 * (110,000 - 102,500) = $1500 per day
the deadweight loss from the tax is $1500 per day
1dthe tax revenue generated istax * quantity
= 0.40 * 102,500 = $41,000 per day
2aIf there were no imports, domestic equilibrium P and Q would be
P = 100 cents per poundQ = 50 million pounds
P = 50 + Q supplyP = 200 - 2Q demandsubtracting0 = - 150 + 3QQ = 150/3 = 50P = 50 + 50 = 100
the world price isPw = 60 cents per poundthe tariff of 40 cents per pound would raise the price of imports to100 cents per poundwhich equals the domestic equilibrium price with no imports
Therefore there will be no imports and the domestic equilibrium price of 100 cents perpound
2
-
8/3/2019 202-4
3/11
will be the domestic price of hula beans if the tariff is imposed
2bthe domestic quantity demanded without the tariff is
P = 200 - 2Q demandwhere P = 60
60 = 200 - 2Q-140 = -2QQ = 70
consumer surplus is reduced by the amount
(40 cents per pound )(50 million pounds) = 2000 million cents+ 1/2 * (70 - 50)million pounds * 40 cents per pound = 400 million cents
= 2400 million cents = $24 million
consumer surplus is reduced by $24 million
the domestic quantity supplied without the tariff isP = 50 + Q supplywhere P = 60
Q = 60 - 50 = 10 million pounds
producer surplus is increased by
10 million pounds * 40 cents per pound = 400 million cents+ 1/2 * (50 - 10)million pounds * 40 cents per pound = 800 million cents
= 1200 million cents = $12 milllion
producer surplus is increased by $12 milllion
the change in total surplus (producer + consumer)is minus $12 millliontotal surplus is reduced by $12 milllion
Since the import price with tariff, 100 cents per pound, equals the domestic equilibriumprice without imports,there are no imports and thus the government revenue from the tariff is $0
3
-
8/3/2019 202-4
4/11
3aThe monopoly operates where MR = MCMR = 28 - 0.0016QMC = 0.0012Q
28 - 0.0016Q = 0.0012Q28 = 0.0028QQ = 10,000
P = 28 - 0.0008QP = 28 - 0.0008*10,000P = 28 - 8P = 20
unregulated firm will operate atP = 20
Q = 10,000
3bThe price and quantity that would be most socially efficientis the competitive equilibrium price and quantity whereMC = PThis is because at the competitive equilibrium price and quantity,total surplus, producer plus consumer surplus is greatest.As seen in the diagram in 3c, the monopolist's higher P and lower Qresult in a deadweight loss, reducing total surplus from thecompetitive equilibrium level
P = 28 - 0.0008QMC = 0.0012QMC = P
0.0012Q = 28 - 0.0008Q0.002Q = 28
Q = 14,000P = 28 - 0.0008*14,000P = 16.8
P = 16.8Q = 14,000
4
-
8/3/2019 202-4
5/11
3c
4MC1 = 20 + 2Q1MC2 = 10 + 5Q2
First find the MCtotal = MCt curvewhich is the horizontal sum of the 2 MC curves
let MC1 = MC2 = MC andsolve for Q1 and Q2 above
Q1 = MC / 2 - 10Q2 = MC / 5 - 2
Qt = Q1 + Q2 = MC / 2 + MC / 5 -12
10Qt = 7MC - 120
MCt = 120/7 + 10/7 Qt
set MCt = MR to solve for Qt
P = 20 - 3QR = PQ = 20Q - 3Q^2MR = 20 - 6Q
MR = MCt20 - 6Q = 120/7 + 10/7 Q
140/7 - 42/7 Q = 120/7 + 10/7 Q
20/7 = 52/7 Q
Q = 20/52 = 10/26 = 5/13
5
-
8/3/2019 202-4
6/11
Q = 5/13
MR = 20 - 6QMR = 20 - 30/13
P = 20 - 3QP = 20 - 15/13
solve for Q1 and Q2 from
MR = MC120 - 30/13 = 20 + 2Q1
Q1 = - 15/13
MR = MC220 - 30/13 = 10 + 5Q2
Q2 = 2 - 6/13
Q1 = - 15/13Q2 = 2 - 6/13 = 1.54P = 20 - 15/13 = 18.85
Q = Q1 + Q2 = 5/13should not be a negative value for Q1
5Set the MR curve for each demand curve equal to MC = $10and solve for each Q and P
MRb = MRp = MC = 10
Pb = 70 - 0.0005QbPp = 20 - 0.0002Qp
MRb = 70 - 0.001QbMRp = 20 - 0.0004Qp
10 = 70 - 0.001QbQb = 60,000Pb = 70 - 0.0005*60,000 = 40
6
-
8/3/2019 202-4
7/11
10 = 20 - 0.0004QpQp = 25,000Pp = 20 - 0.0002*25,000 = 15
The prices are not optimalOptimal prices are
Pb = 40Pp = 15
6aThe monopolist maximizes profitwith the condition MR = MC
hereMC = 0
R = PQ = 1200Q - Q^2MR = 1200 - 2Q
MR = MC is1200 - 2Q = 0Q = 1200/2 = 600
P = 1200 - Q = 1200 - 600 = 600
For monopolistQ = 600P = 600
6bP = 1200 - QFirm 1's total revenue is
R1 = PQ = ( 1200 - Q )Q1
= 1200Q1 - (Q1 + Q2)Q1= 1200Q1 - Q1^2 - Q2Q1
MR1 = 1200 - 2Q1 - Q2
set MR1 = MC = 0 and solve for Q1
7
-
8/3/2019 202-4
8/11
1200 - 2Q1 - Q2 = 0
Q1 = 600 - Q2 / 2this is firm 1's reaction curve
in the same wayfirm 2's reaction curve isQ2 = 600 - Q1 / 2
solving for Q1 and Q2
Q1 = 600 - (600 - Q1 / 2) / 2Q1 = 300 + Q1 / 4
4Q1 = 1200 + Q1
3Q1 = 1200Q1 = 400
Q2 = 600 - Q1 / 2 = 600 - 200 = 400
level of output produced by each firmin a Cournot duopoly in the long run isQ1 = Q2 = 400
(P = 1200 - 800 = 400)
6cFor perfect competitionset P = MC = 0
P = 1200 - Q = 0
long run output and price for perfectly competitive industryQ = 1200P = 0
revenue = profit = 0
7Qm = 140,000 - 32,000P market demandQf = 60,000 + 8,000P competitive fringe supplyDd is the dominant firm's demand curve relating Qd to P
8
-
8/3/2019 202-4
9/11
Qd = market demand - competitive fringe supply = Qm - Qf = dominant firm's output
Qd = 140,000 - 32,000P - (60,000 + 8,000P)
Qd = 80,000 - 40,000P dominant firm's demand curve
P = 2 - 0.000025 Qd dominant firm's demand curve
Rd = Qd*P = 2Qd - 0.000025 Qd^2
MRd = 2 - 0.00005 Qd dominant firm's MR curve
set MRd = MCd
2 - 0.00005 Qd = 0.75
Qd = 25,000 = dominant firm's output
for Qd = 25,000 find P on the dominant firm's demand curve
P = 2 - 0.000025 Qd = 2 - 0.000025 * 25,000 = $1.375
at P = $1.375the market output isQm = 140,000 - 32,000P market demandQm = 140,000 - 32,000*1.375
Qm = 96,000 = market output
output of the competitive fringe at P = $1.375 isQf = 60,000 + 8,000P competitive fringe supplyQf = 60,000 + 8,000*1.375 = 71,000
Qf = 71,000 = competitive fringe supply
checkQd = market demand - competitive fringe supply = Qm - QfQd = 25,000 = 96,000 - 71,000 = 25,000
8a
Q = 1800 - 200PMR = 9 - 0.01Q
9
-
8/3/2019 202-4
10/11
MC = $1.50
perfect competitionset MC = P
Q = 1800 - 200P200P = 1800 - QP = 9 - 0.005 Q(MR = 9 - 0.01Q)
P = 9 - 0.005 Q = 1.50 = MC
Q = (9 - 1.5 ) / 0.005 = 1500
Q = 1500P = $1.50
consumer surplusfrom the demand curvewhen Q = 0 P = 9
consumer surplus = 1/2 * (9 - 1.5) * 1500 = $5625
producer surplusMC = constant = 1.5 = horizontal supply curve
willing to sell any amount at P = $1.5producer surplus = 0
8bpure monopoly
set MC = MR
MC = 1.5 = 9 - 0.01Q = MR
Q = (9 - 1.5) / 0.01 = 750
P = 9 - 0.005 Q = 9 - 0.005 (750) = $5.25
pure monopolyQ = 750P = $5.25
consumer surplus
10
-
8/3/2019 202-4
11/11
from the demand curvewhen Q = 0 P = 9
consumer surplus = 1/2 * (9 - 5.25) * 750 = $1406.25
producer surplusMC = constant = 1.5 = horizontal supply curve
willing to sell any amount at P = $1.5
producer surplus = (5.25 - 1.5) * 750 = $2812.5
8cperfect price discrimination
quantity is sold until P = MC
P = 9 - 0.005 Q = 1.50 = MC
Q = (9 - 1.5 ) / 0.005 = 1500
Q = 1500Price is variable along the demand curveall prices are charged whereP = 9 - 0.005 Qand 0 < Q =< 1500
consumer surplus is 0every customer pays maximum they're willing to payfirm captures all consumer surplus
from the demand curvewhen Q = 0 P = 9
profit is1/2 (9 - 1.5) 1500 = $5625
11
top related