EC426: Class 8 Question 1 Consider the pollution externality from the production of cars, but assume that the externality damage is uncertain. Illustrate the ex post welfare loss from a tax policy that is based on the expected damage. Do the same for a policy that regulates car production based on the expected damage. Which policy seems better when the demand becomes more price-inelastic? Standard Model of Externalities • Produce: f(c(x)) = x units • Pollute: p(x) units – p(x) = x  constant MD • Demand = PMB = SMB • PMC • SMC = PMC + MD SMC = PMC + MD Cost/$ PMC DWL MD • Firms maximise profits • Consumers maximise utility • Compve Equilibrium (xCE): PMB = PMC • Pareto Efficiency (x*): SMB = SMC MD D= PMB = SMB x* xCE Quantity of Cars / x Standard Model of Externalities • Find optimal level of pollution using MC & MD • MC: Marginal Cost of Pollution Reduction (Private Utility of Pollution) • MD: Marginal Benefit from Pollution Reduction (Damage from Pollution) • Problem: min D – C ------- (1) • Solution: MD = MC – Set tax at t – Regulate pollution at x* Cost/$ MD t MC p(x*) Qty of Pollution / p(x) Externalities under Uncertainty • Assume government knows MC • But is uncertain about MD • Then, it assumes MD = MDE MDE = E(MD) = ½MDH + ½MDL • Uses MDE to optimise (1) • (Pareto Efficient)E at C • Knows that the required tax to be set is t • Or that production of cars and hence pollution should be regulated at x* MDH MDE MDL Cost/$ t C MC p(x*) Qty of Pollution / p(x) Welfare Loss under Tax Policy Suppose government sets tax t Then, firms will choose to produce up to x* • Given MDT = MDH, • (Pareto Efficient)T at B • Welfare loss: Δ ABC MDT • Given = • (Pareto Efficient)T at D • Welfare loss: Δ CDE MDL MDH MDE MDL Cost/$ A B t C D E MC • Note: Δ ABC = Δ CDE p(x*) Qty of Pollution / p(x) Welfare Loss under Regulation Suppose government regulates production at x* MDH MDE MDL Cost/$ • Given MDT = MDH, • (Pareto Efficient)T at B • Welfare loss: Δ ABC A B • Given MDT = MDL • (Pareto Efficient)T at D • Welfare loss: Δ CDE • Note: Δ ABC = Δ CDE C D E MC p(x*) Qty of Pollution / p(x) When demand becomes more price inelastic … • • • • More inelastic demand means  same increase in tax (price) induces a smaller decrease in the quantity demanded of cars New PE outcome requires higher tax (t’) but optimal quantity of cars slightly closer to the CE outcome than before (x’) Won’t affect comparative welfare loss under uncertainty about MD But might be easier to regulate production than to implement tax Cost/$ t SMC = PMC + MD PMC t' D= PMB = SMB D’ x* x' xCE Quantity of Cars / x EXTENSION • In the class, we assumed the MD function (“marginal benefit of pollution reduction”) was uncertain • This results in no ex post welfare difference between price and quantity measures • But if it was the MC function (“marginal cost of pollution reduction”; see slide 3) that was subject to uncertainty, then price and quantity measures do differ in terms of their ex post welfare losses • The following slides illustrate what that difference would be Uncertain Marginal Cost of P.R. • • • • • • • • Begin with the same set up on slide 3 Then assume government is uncertain w.r.t. MC So we have either MCH or MCL Government’s expectation of MC, given equal likelihood of MCH and MCL is MCE = E(MD) = ½MDH + ½MDL Uses MCE to optimise (1) (Pareto Efficient)E at C Like before, knows that the required tax to be set is t Or that production of cars and should be regulated at x* (to generate p(x*) of pollution Cost/$ t MD C MCH MCL p(x*) MCE Qty Welfare Loss under Tax Suppose government sets tax t • • • • • • • • • Given MCTRUE = MCH, Firms produce up to A, i.e. x = xH (Pareto Efficient)TRUE at CH Welfare loss: Δ ABCH Given MDTRUE = MDL Firms produce up to E (Pareto Efficient)TRUE at CL Welfare loss: Δ CLDE Note: Δ ABC = Δ CDE Cost/$ t MD CH E D C B A CL MCH MCE MCL p(xL) p(x*) p(xH) Qty Welfare Loss under Regulation Suppose government regulates production at x* • • • • Given MCTRUE = MCH, Firms produce at A (i.e. x*) (Pareto Efficient)TRUE at B Welfare loss: Δ ABC • • • • Given MDTRUE = MDL Firms produce at E (i.e. x*) (Pareto Efficient)TRUE at D Welfare loss: Δ CDE • Cost/$ MD A B C D E MCH MCL Note: Δ ABC = Δ CDE p(xL) p(x*) p(xH) MCE Qty Welfare Loss Comparison Comparing ex post welfare loss from the price (green) and quantity (purple) measures, we see that the tax policy in this case would generate a relatively smaller deadweight loss compared to the policy of regulating car production. Cost/$ t MD C MCH MCL p(x*) MCE Qty Welfare Loss Comparisons (Uncertain MC) • As we can see, when MC is uncertain, the sizes of ex post welfare loss triangles under tax and regulation differ • The question of “which is better” depends on the slopes of MC and MD • In the example in slides 8-10, a relatively inelastic MC shows us that quantity measures would generate a higher welfare loss compared to taxes • If you repeat the analysis varying the slopes of both the MC and MD curves respectively, you would get different outcomes (e.g. tax would generate more ex post welfare loss under a relatively elastic MD curve) Inelastic MD curve • Here, we have the same MC curves (still in uncertain MC world) but MD curve is now more inelastic than before. • Notice that now the green (price regulation) welfare loss triangles are much larger than the purple ones (quantity regulation) than in the previous example! Cost/$ t MDinelastic C MCH MCL p(x*) MCE Qty