Question

Suppose that Qd = 200 - 3P and Qs = 20 + 2P. If a tax is imposed on this market such that Qtax = 89, then Pbuy = , Psell = , the size of the tax is , and the deadweight loss is

Answer 1

We are given demand and supply curves and post tax quantity and asked to find price paid by sellers, price paid by buyers, size of tax and deadweight loss

When no tax is imposed, equilibrium is at point where demand is equal to supply.

Equilibrium price is 36 and equilibrium quantity is 92

Producer surplus is 2016 and consumer surplus is 1410.82

After tax is imposed, quantity sold in the market is 89

Price received by sellers is 34.5

Price paid by buyers is 37

Consumer surplus is 1320.315 and producer surplus is 1880.25

Tax revenue is 222.5 and deadweight loss is 3.75

OEMAND CURVE SUPPLY CURVE Qp = 200-3P Qs = 20 +2 p. TAX THAN O O is imOSED Post TAX UNITS ON MARKET SUCH THAT QUANTITY IN MARKET IS PRICE PAID BY BUYERS, PB = 200-Q 3 AT Q-89 PB = 200-89-11.-37 ATT PRICE RECEIVED BY SELLERS, Ps = Q-2° 2 Ps = 89-20 - 69 = 34.5 2 SIZE OF TAX= PB- Ps 34 SIZE OF TAX, t - PB - Ps = 37 - 34.5a 25 : TAY OF 2.5 per unit is imposed on the good IF NO TAX is imPOSED, THEN EQUILIBRIUM AT THE POINT WHERE DEMAND = SUPPY Cie. INTERSECTION OF SUPPLY AND DEMAND CURVE Qp = Rs - 200-3p = 20+2P 5P = 200-20 P-180 = 36 s AT P=36 Qo= 200 - 3P = 200 - 3(36) = 200-108=92 ca Scanned with CamScalas = 20 +2 - 20+ 2p - 20 + 2(36) = 20 +72 = 9 2

WILL PRICE, 66.00/2 0377 PB -- --- 1, 6) = - - - - - XE 134.5) Psl--- ---73! > QUANTITY oth 89 92 ss' Supply CURVE DD'E DEMAND CURVE WHEN NO TAX is impos EP, EQUILIBRIOM is 97 POINT E WHERE PRICE is PE = 36 AND QUANTITY is QE = 92 DPE E = CONSUMER SUR PLUS OFE PE =PRODUCER SURPLUS AREA DPE €)= 4 xDPE x PE E = (60.67 -36) (12) AREA COPE ED= (30.672(92) = 1410.82 OFE PEL COF + PEECOPE= (20+92)(36) 2 2 TOPPT Offt ARE COFELE2-2016 cow SUMER SURPLUS = 1410-82 CS Scanne PRODUCER SURPWS - 2016 CamScanner.

AFTER TAX IS IMPOSED OF 2.5 PER UND QUANTITY SOLD IN MARKET is 89 UNITS PRICE PAID BY BUYERS = 37 PRICE PAID BY SELEERS = 34.5 A PGD = CONSUMER SURPLUS = + (OP) (APB) - CONSUMER SURPLUS1666-67-377089)=1320.315 PBAPA = GOVERNMENT REVENUE FROM TAX REVENUE FROM TAX=( PB PSIC PB2 TAXREVENUE = (37-34.5) (89) = 222.5 OF BPs = PRODUCER SURPLUSE 1 COF + BPs) PGO PRODUCER SURPLUS = 1880. 25 2 DEAD WEIGHT LOSS = ABE = (AB) CCE DWL= < 37–34.5) (92-89) = 5*2.5*33.75 Scanned with CamScanner