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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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