Equilibrium and Price Regulations in Closed and Open Economy

In their 1992 article (Production Subsidy and Countervailing Duties in Vertically Related Markets: The Hog-Pork Case Between Canada and the USA, American Journal of Agricultural Economics 74(4), 48-49.) Moschini and Meilke estimated demand function for hog as Qd = 53 – 20P + 20PB + 3PP + 2Y, where P, PB and PP are prices of hog, beef and poultry. Y is per capita income. Supply function was found to be Qs = 78 + 40P – 60PHF , where PHF is price of hog feed.

1) Find equilibrium price Pe and equilibrium quantity Qe of hog if PB = 4, PP = 31/3, PHF = 1.5 and Y = 12.5 .
Qd = 53 – 20P + 20PB + 3PP + 2Y = 168 – 20P = 40P – 12 = 78 + 40P – 60PHF = Qs => Pe = 3 and Qe = 108

Alternatively use inverse demand and supply: Pd = 8.4 – 0.05Qd = 0.3 + 0.025Qs = Ps => Pe = 3 and Qe = 108

2) Find social surplus SSe (sum of consumer surplus CSe & producer surplus PSe) with no price regulations .

a. Consumer Surplus is area below demand and above price: CSe = 108(8.4 – 3)/2 = 291.6

b. Producer Surplus is area above supply and below price: PSe = 108(3 – 0.3)/2 = 145.8

SSe = CSe + PSe = 437.4

3) Find new quantity exchanged Qc, full economic price Pfe, excess demand EDc (demand less supply), dead weight loss DWLc, black market gain BMG, new producer surplus PSc & new consumer surplus CSc with price ceiling PC = 2.

a. Quantity exchanged is inverse supply at Pc: Qc = Qs|Pc = 40*2 – 12 = 68
b. Full Economic Price is inverse demand at Qc: Pfe = Ps|Qc = 8.4 – 0.05*68 = 5

c. Excess Demand is demand less supply at Pc: EDc = 168 – 20*2 – (40*2 – 12) = 60

d. Dead Weight Loss is area of triangle (Qc,Pfe), (Q,ePe), (Qc,Pc): DWLc = (108 – 68)(5 – 2)/2 = 60

e. Black Market Gain is area of rectangle 0Qc and PcPfe: BMG = 68*(5-2) = 204
f. Producer Surplus at Pc: PSc = 68*(2 – 0.3)/2 = 57.8
g. Consumer Surplus at Pc: CSc = 68*(8.4 – 5)/2 = 115.6

PSc + CSs + DWLc + BMGc = 437.4


4) Find new quantity exchanged Qf, excess supply ESf (supply less demand), government subsidy GSf, new consumer surplus CSf, new dead weight loss DWLf and new producer surplus PSf with price floor PF = 4 .

a. Quantity exchanged is inverse demand at Pf: Qf = Qd|Pf = 168 – 20*4 = 88

b. Excess Supply is supply les demand at Pf: ESf = (40*4 – 12) – 88 = 60

c. Government Subsidy is area of rectangle Esf and 0Pf: GSf = 60*4 = 240

d. Consumer Surplus at Pf: CSf = 88*(8.4 – 4)/2 = 193.6

e. DWL is area of triangle (Qf,Pf), (Q,ePe) and (Qf,Ps|Qf): DWLf = (108 – 88)*[4 – (.3+.025*88)]/2 = 15

f. Producer Surplus at Pf is (Cse + Pse) – (CSf + DWL): PSf = (291.6 + 145.8) – (193.6 + 15) = 228.8

DWLf + CSf + PSf (33.33% lower Pc is more destructive than 33.33% higher Pf: DWLc > DWLf) = 437.4

5) Find new quantity exchanged Qt, buyer price Pbt, producer price Ppt, tax revenue TRt, new DWLt, new consumer surplus CSt & new producer surplus PSt with excise ($ amount levied on pack of cigarettes or gallon of gas) tax t = 1.5 .

a. y intercept of Ps increases by t: Pst = 1.8 + 0.025Q = 8.4 – 0.05Q = Pd => Qt = 88

b. Buyer’s P is new equilibrium P: Pbt = Pd|Qt = 8.4 – 0.05*88 = 4

c. Producer’s P is Pbt less tax: Ppt = 4 – 1.5 = 2.5

d. Tax Revenue is area of rectangle: TRt = tQt = 1.5*88 = 132

e. DWL is area of triangle: DWLt = 1.5(108 – 88)/2 = 15

f. CS at t is: CSt = 88(8.4 – 4)/2 = 193.6

g. PS at t is: PSt = 88(2.5 – 0.3)/2 = 96.8

TRt + DWLt + CSt + PSt = 437.4

6) Find new quantity exchanged Qv, new buyer price Pbv, new producer price Ppv, new Tax Revenue TRv, new dead weight loss DWLv, new consumer surplus CSv & new producer surplus PSv with ad valorem (sales) tax v = 60% .

a. v% increases entire Ps: Psv = Ps(1 + v) = 0.48 + 0.04Q = 8.4 – 0.05Q = Pd => Qv = 88

b. Buyer’s P is: Pbv = Pd|Qv = 8.4 – 0.05*88 = 4

c. Producer’s P is: Ppv = Ps|Qv = 0.3 + 0.025*88 or = Pbv/(1 + v) = 4/1.5 = 2.5

d. Tax Revenue is: TRv = Qv(Pbv – Ppv) = 88(4 – 25) = 132

e. DWL is: DWLv = (108 – 88)(4 – 25)/2 = 15

f. CS at v is: CSv = 88(8.4 – 4)/2 = 193.6

g. PS at v is: PSv = 88(2.5 – 0.3)/2 = 96.8

TRv + DWLv + CSv + PSv = 437.4


7) Find domestic quantity demanded Qd, domestic quantity supplied Qs, imports M and domestic consumer surplus losses CSl if world price Pw = 2, tariff r = 0.5 and quota q = 30 .

a. Free Trade: Pw = 2, Qdw = 168 – 20Pw = 128, Qsw = 40Pw – 12 = 68, Mw = Qdw – Qsw = 60

b. Tariff (r): Pr = 2.5, Qdr = 168 – 20Pr = 118, Qsr = 40Pr – 12 = 88, Mr = Qdr – Qsr = 30
G = rMr = 15, PIr = r(Qsr – Qsw)/2 = 5, Tr = rQsr – PIr = 39, CIr = r(Qdw – Qdr)/2 = 2.5

CSlr = G + PIr + Tr + CIr = 61.5

c. Quota (q): Qd=168–20P=30–12+40P=q+Qs => Pq = 2.5, Qdq = 118, Qsq = 88, q = 30, W = q(Pq–Pw) = 15
PIq = (Qsq–Qsw)(Pq–Pw)/2 = 5, Tq = Qsq(Pq–Pw)–PIq = 39, CIq = (Qdw–Qdq)(Pq–Pw)/2 = 2.5
CSlq = W + PIq + Tq + CIq = 61.5


8) Find new equilibrium price Pe’ & quantity Qe’ & new social surplus (sum of new consumer surplus CS’ & new producer surplus PS’) if demand shifts by 12 to Qd’ = 180 – 20P & supply remains Qs, with no price regulations .

a. Qd’ = 180 – 20P = 40P – 12 = Qs Pe’ = 3.2 and Qe’ = 116

Alternatively use inverse demand and supply: Pd’ = 9 – 0.05Qd’ = 0.3 + 0.025Qs = Ps Pe’ = 3.2 and Qe’ = 116

b. CSe’ = 116(9 – 3.2)/2 = 336.4
c. PSe’ = 116(3.2 – 0.3)/2 = 168.2

CSe’ + PSe’ = 504.6

9) Find new quantity exchanged Qt’, new buyer price Pbt’, new producer price Ppt’, new tax revenue TRt’, new dead weight loss DWLt’, new consumer surplus CSt’ & new producer surplus PSt’ at higher demand Qd’ & excise tax t = 1.5

a. y intercept of Ps increases by t: Pst’ = 1.8 + 0.025Q = 9 – 0.05Q = Pd’ => Qt’ = 96

b. Buyer’s P is new equilibrium P: Pbt’ = Pd’|Qt’ = 9 - 0.05*96 = 4.2

c. Producer’s P is Pbt’ less tax: Ppt’ = 4.2 – 1.5 = 2.7

d. Tax Revenue is area of rectangle: TRt’ = tQt’ = 1.5*96 = 144

e. DWL is area of triangle: DWLt’ = 1.5(116 – 96)/2 = 15

f. CS at t is: CSt’ = 96(9 – 4.2)/2 = 230.4

g. PS at t is: PSt’ = 96(2.7 – 0.3)/2 = 115.2

TRt’ + DWLt’ + CSt’ + PSt’ = 504.6

10) Find new quantity exchanged Qv’, new buyer price Pbv’, new producer price Ppv’, new tax revenue TRv’, new dead weight loss DWLv’, new consumer surplus CSv’ & new producer surplus PSv’ at higher demand Qd’ and same ad valorem tax v = 60% .

a. v% increases entire Ps: Psv’ = Ps(1 + v) = 0.48 + 0.04Q = 9 – 0.05Q = Pd’ => Qv’ = 94.67

b. Buyer’s P is: Pbv’ = Pd’|Qv’ = 9 – 0.05*94.67 = 4.27

c. Producer’s P is: Ppv’ = Ps|Qv’ = 0.3 + 0.025*94.67 or = Pbv’/(1 + v) = 4.27/1.6 = 2.67

d. Tax Revenue is: TRv’ = Qv’(Pbv’ – Ppv’) = 94.67(4.27 – 2.67) = 151.47

e. DWL is: DWLv’ = (116 – 94.67)(4.27 – 2.67)/2 = 17.06

f. CS at v is: CSv’ = 94.67(9 – 4.27)/2 = 223.89

g. PS at v is: PSv’ = 94.67(2.67 – 0.3)/2 = 112.18

TRv’ + DWLv’ + CSv’ + PSv’ = 504.6

Excise & sales tax were set to have the same econ impact for the original demand & supply. Higher demand increases social surplus in absence of price regulations. Less destructive excise tax (DWLt’ < DWLv’) has lower buyer price Pb’, higher producer price Pp’, larger quantity exchanged Qt’, higher consumer surplus CS’ & higher producer surplus PS’.

11) Find new domestic quantity demanded Qd’, new domestic quantity supplied Qs’, new imports M’ and new domestic consumer surplus losses CSl’ if world price Pw = 2, tariff r = 0.5 and quota q = 30 .

a. Free Trade: Pw = 2, Qdw’ = 180 – 20Pw = 140, Qsw’ = 40Pw – 12 = 68, Mw’ = Qdw’ – Qsw’ = 72

b. Tariff (r): Pr = 2.5 Qdr’ = 180 – 20Pr = 130, Qsr’ = 40Pr – 12 = 88, Mr’ = Qdr’ – Qsr’ = 42

G’ = rMr’ = 21, PIr’ = r(Qsr’–Qsw’)/2 =5, Tr’ = rQsr’–PIr’ = 39, CIr’ = r(Qdw’–Qdr’)/2 = 2.5

CSlr’ = G’ + PIr’ + Tr’ + CIr’ = 67.5

c. Quota (q): Qd’=180-20P=30-12+40P=q+Qs => Pq’ = 2.7, Qdq’ = 126, Qsq’ = 96, q = 30, W = q(Pq’-Pw) = 21

PIq’ = (Qsq’–Qsw’)(Pq’–Pw)/2 = 9.8, Tq’ = Qsq’(Pq’–Pw)–PIq’ = 57.4, CIq’ = (Qdw’–Qdq’)(Pq’–Pw)/2 = 4.9

CSlq’ = W’ + PIq’ + Tq’ + CIq’ = 93.1

Tariff and quota were set to have the same econ impact for the original demand and supply. However, higher demand under tariff causes lower domestic price Pr < Pq’ and lower domestic consumer surplus losses CSlr’ < CSlq’.