Quantity Tax Incidence Subsidy Welfare Effects Case Study. Equilibrium Chapter 16

Transcription

1 Equilibrium Chapter 16

2 Competitive Equilibrium: Motivating Questions Firms are price-takers in competitive markets, but how is the market price (and quantity) determined? competitive equilibrium What happens to equilibrium price and quantity when either supply or demand changes? comparative statics What are the effects of taxes and subsidies on prices and quantities? What are the welfare effects of taxes and subsidies? deadweight loss, tax incidence

3 Taxes Quantity (or excise) tax Effect on p, q Subsidy Incidence Welfare effects

4 Quantity Taxes Levied on each unit sold. E.g. gasoline tax: seller sets price at $2.05/gallon and gasoline tax is $0.35/gallon. Consumer must pay p d = = 2.40 dollars/gallon Seller gets p s = 2.05 Like any tax, this creates a wedge between what consumer pays and what producer receives The $0.35 tax, collected by the govt., is the difference between the consumer price, p d, and the producer price, p s : p d p s = 0.35

5 Equilibrium with a Quantity Tax Suppose gasoline tax is t dollars/gallon. t as a wedge: p d p s = t = p d = p s + t How does this affect equilibrium? New condition: D(p d ) = S(p s ) Rewrite as D(p s + t) = S(p s ) or D(p d ) = S(p d t) Can think of this as either shifting D or S

6 Example Inverse Demand: P d (q) = 50 + q 2 Supply: S(p) = p Suppose govt. imposes tax t = 0.90 per gallon. What is the after-tax equilibrium? We need to find D(p) first: p = 50 + D(p) 2 = D(p) = 100 2p Equilibrium condition: D(p s + t) = S(p s ) = 100 2(p s ) = p s = 9p s = = p s = = 9.80

7 Example Consumer price: p d = p s + t = = So the equilibrium quantity is q t = S(p s ) = p s = = 78.6 How much tax revenue does the government collect? R t = tq t =

8 Example Who really pays this tax? The division of t between the buyers and sellers is the incidence of the tax. Compare pre-tax equilibrium price, p, with consumer price, p d, and producer price, p s. p = 10, p d = 10.70, and p s = 9.80 So consumer pays = 0.70 per gallon and the producer pays = 0.20 per gallon.

9 Tax Incidence and Elasticity Passing Along Tax with Perfectly Inelastic Supply The incidence of a quantity tax depends upon the price-elasticities The producers pay all the tax when the supply is perfectly inelastic. of demand and supply. p d S S p * p s t D q t q * Gas The producers pay all the tax when supply is perfectly inelastic.

10 Tax Incidence and Elasticity Passing Along Tax with Perfectly Elastic Supply The incidence of a quantity tax depends upon the price-elasticities The consumers pay all the tax when the supply is perfectly elastic. of demand and supply. p d p t p * t S S D q t q * Gas The consumers pay all the tax when supply is perfectly elastic.

11 Equilibrium with a Subsidy Example What if govt. wants to keep gas prices low, e.g. p = 8? A price ceiling will leads to shortages. An alternative is to subsidize gasoline by paying sellers $s per gallon. How large must s be? Well, p d + s = p s so D(p d ) = S(p s ) = D(8) = S(8 + s) = = (8 + s) = s = 18 7

12 Equilibrium with a Subsidy Equilibrium with Subsidy Example p S(p) p s = 8 + s p d = 8 s = 18/7 D(p) q t = 100-2*8 = 84 Gas

13 Equilibrium with a Subsidy Just Equilibrium a negative tax: with q Subsidy t > q and p d < p < p s p S(p) p s p * s p d D(p) q * q t Gas

14 Total Surplus Total Surplus Price A CS = A + B + E PS = C + D + F Total surplus = A+B+C+D+E+F S(p) p * B C E F D D(p) q t q * Gas

15 Deadweight Loss: Deadweight DWL Loss (DWL) Price p t A CS = A, PS = D, Gov t = B+C Total surplus with Tax = A+B+C+D DWL = E+F S(p) t p t - t B C D E F D(p) q t q * Gas

16 adweight Loss: Example with Tax Quantity Tax Incidence Subsidy Welfare Effects Case Study Recall from previous Deadweight examples: before Loss (DWL) tax p = 10, q = 80, and after Tax taxexample: p t = 10.7, recallp that p = 10, q = 80, p t s = 9.8, q t = = 10.70, p s = 9.80, q t = Price DWL = (1/2)x( )x( ) = S(p) t= D(p) Gas

17 eadweight Loss: Example with Subsidy Quantity Tax Incidence Subsidy Welfare Effects Case Study Recall from previous examples: before subsidy and price ceiling p = 10, q = 80, Deadweight and after subsidy Loss and(dwl) price ceiling p Subsidy example: recall that p 10, q s = = 80, 7 = 10.57, p p s = = 10.57, p d = 8, q t = 84. d = 8, q t = 84. Price DWL = (1/2)x( )x(84-80) = s S(p) s=18/7 8 D(p) Gas