Question

The following equations represent the inverse supply and demand functions in the market for Good A:
PC =80-1⁄2QD
PP =14+QS
where PC and PP are the prices paid by consumers and received by producers respectively. QD and QS are the quantities demanded and supplied, respectively.
Suppose the government is considering imposing a tax of $6 per unit of Good A.
a) Compute the competitive market equilibrium price and output without the tax.
b) Compute producer surplus and consumer surplus without the tax.
c) Compute the competitive market equilibrium price and output with the tax.
d) Compute producer surplus and consumer surplus with the tax.
e) What is the incidence of this tax on consumers and producers?

Answer 1

Competitive Equilibrium is at the price level where both the quantity demanded and quantity supplied are equal.

Producer Surplus is the area below the price line and above the supply curve whereas Consumer Surplus is the area Above the price line and below the demand curve.

- Que PC = 80 - do Pc = PP = 14 + QS OD = Os = do = ds 160-apc pp - 14 160-2Pc : pp - 14 160 +14 = PP + alc At Equilibrium, PP = Pc op 174 = 3P P: 58 Hence @ D = Os = 58-14:44 160 – 116 44 - Hence Price and = 58 competitive Equilibrium quantity = 44.

(or %) зоб (+) е эс ч, ях) (", 19) Фd 20 o so (4Ч10) go op. 10 (4о бо Producer Surplus: ava OBCE = 4х чух ( 58 -н) - 88 x 44 : 461 Consumilk up : 20 а днес : х 18р -53) xчч : 22, 22 , цвч
c) To compute the Equilibrium with taxes :

Now to calculate the consumer and producer surplus, we plot the new demand curve , as it will shift leftwards because of the taxes. The Equilibrium price and quantity will be as in the above question but the amount paid by consumer and the producer will be different because of the taxes.

Assume the tax is imposed on consumer Now Pc will lee Afectively pett 3) PcHt - 80 - do 2PC +2+ 160 ; -20 op: 160 - & PC -2E (OD 160-apc- 12) Qp : 1648-2 PC) and dd = pp-14 At Equilibrium , ad=dg=d and PC= PP =P 160-apc-at= Pp-14 160 - 8P - 2+ = p-14 160 +14 - 24 = 3P 7- 6 = 100+14-19 = P . 169 = 38 ) PE 54 = 40

The amount paid by the producer will be 54 and the amount paid by the consumer will be 54+6=60.

The surplus is calculated as per the shaded area shown in the graph.

Consumer Surplus will be calculated as per the original demand curve, as the price paid by the consumer will be different from the equilibrium price and the final price will be reflected by the original demand curve.

QS En consumes suplus s producer Surplus i X Tan = 6 Od (Apres tax) 04. ) 20 ao Go 8o lo 120 140 160

општин Кирш“. 4х (во —60) x4o - 2 х 2р - Чоо Родия upші: 1x ( s4-19) Үчь * | 1 чох чо • % х чь - 8 .

E)The incidence of the tax is shown by comparing the price paid with taxes to the equilibrium price without taxes.

The price at equilibrium before taxes was 58. After taxes, consumer paid 60 and producer paid 54. Hence out of the 6 units of the tax imposed, 2 units of incidence is borne by consumer ( 60-58) and 4 units is borne by producer (58-54).