#### Transcript Efficiency: Waste

Prerequisites Almost essential Welfare and Efficiency EFFICIENCY: WASTE MICROECONOMICS Principles and Analysis Frank Cowell Frank Cowell: Efficiency-Waste Agenda Build on the efficiency presentation • Focus on relation between competition and efficiency Start from the “standard” efficiency rules • MRS same for all households • MRT same for all firms • MRS=MRT for all pairs of goods What happens if we depart from them? How to quantify departures from them? Frank Cowell: Efficiency-Waste Overview… Efficiency: Waste Background How to evaluate inefficient states Basic model Model with production Applications Frank Cowell: Efficiency-Waste The approach Use standard general equilibrium analysis to… • Model price distortion • Define reference set of prices Use consumer welfare analysis to… • Model utility loss Use standard analysis of household budgets to… • Model change in profits and rents Frank Cowell: Efficiency-Waste A reference point Address the question: how much waste? Need a reference point • where there is zero waste • quantify departures from this point Any efficient point would do But it is usual to take a CE allocation • gives us a set of prices • we’re not assuming it is the “default” state • just a convenient benchmark Can characterise inefficiency as price distortion Frank Cowell: Efficiency-Waste A model of price distortion Assume there is a competitive equilibrium If so, then everyone pays the same prices But now we have a distortion What are the implications ~ for MRS and MRT? Distortion p1 = p1 [1+d] ~ p2 = p2 ~ p3 = p3 consumer prices … = … ~ pn = p n Frank Cowell: Efficiency-Waste firms' prices Price distortion: MRS and MRT For every household marginal rate of substitution = price ratio Consumption: MRSij Production: • for commodities 2,3,…,n • But for commodity 1… MRT1j MRT2j h pj = — pi pj = — [1+ d] p1 pj = — p2 pj MRT3j = — p3 … … … pj MRTnj = — pn Frank Cowell: Efficiency-Waste Illustration… Price distortion: efficiency loss Production possibilities An efficient allocation Some other inefficient allocation x2 At x* producers and consumers face same prices At x producers and consumers face different prices •x •x* Producers Price "wedge" forced by the distortion p* Consumers 0 x1 How to measure importance of this wedge … Frank Cowell: Efficiency-Waste Waste measurement: a method To measure loss we use a reference point Take this as competitive equilibrium… • …which defines a set of reference prices Quantify the effect of a notional price change: • Dpi := pi – pi* • This is [actual price of i] – [reference price of i] Evaluate the equivalent variation for household h : • EVh = Ch(p*,u h) – Ch(p,u h) – [y*h – yh] • This is D(consumer costs) – D(income) Aggregate over agents to get a measure of loss, L • We do this for two cases… Frank Cowell: Efficiency-Waste Overview… Efficiency: Waste Background Taking producer prices as constant… Basic model Model with production Applications Frank Cowell: Efficiency-Waste If producer prices constant… C(p, u) Production possibilities Reference allocation and prices Actual allocation and prices Cost of u at prices p Cost of u at prices p* x2 DP Change in valuation of output Measure cost in terms of good 2 •x C(p*, u) Losses to consumers are C(p*, u) C(p, u) •x* p 0 L is difference between C(p*, u) C(p, u) and DP p* u x1 Frank Cowell: Efficiency-Waste Model with fixed producer prices Waste L involves both demand and supply responses Simplify by taking case where production prices constant Then waste is given by: Use Shephard’s Lemma • xih = Hhi(p,uh) = Cih(p,uh) Take a Taylor expansion to evaluate L: L is a sum of areas under compensated demand curve Frank Cowell: Efficiency-Waste Overview… Efficiency: Waste Background Allow supply-side response… Basic model Model with production Applications Frank Cowell: Efficiency-Waste Waste measurement: general case C(p, u) Production possibilities x2 Reference allocation and prices Actual allocation and prices Cost of u at prices p Cost of u at prices p* DP Change in valuation of output C(p*, u) Measure cost in terms of good 2 •x Losses to consumers are C(p*, u) C(p, u) •x* p p* u 0 L is difference between C(p*, u) C(p, u) and DP x1 Frank Cowell: Efficiency-Waste Model with producer price response Adapt the L formula to allow for supply responses Then waste is given by: • where qi (∙) is net supply function for commodity i Again use Shephard’s Lemma and a Taylor expansion: Frank Cowell: Efficiency-Waste Overview… Efficiency: Waste Background Working out the hidden cost of taxation and monopoly… Basic model Model with production Applications Frank Cowell: Efficiency-Waste Application 1: commodity tax Commodity taxes distort prices • Take the model where producer prices are given • Let price of good 1 be forced up by a proportional commodity tax t • Use the standard method to evaluate waste • What is the relationship of tax to waste? Simplified model: • identical consumers • no cross-price effects… • …impact of tax on good 1 does not affect demand for other goods Use competitive, non-distorted case as reference: Frank Cowell: Efficiency-Waste A model of a commodity tax p1 Equilibrium price and quantity The tax raises consumer price… compensated demand curve …and reduces demand Gain to the government Loss to the consumer Waste revenue raised = tax x quantity Waste given by size of triangle L Dp1 Sum over h to get total waste Known as deadweight loss of tax p1* x1 * Dx1h x1 h Frank Cowell: Efficiency-Waste Tax: computation of waste An approximation using Consumer’s Surplus The tax imposed on good 1 forces a price wedge • Dp1 = tp1* > 0 where is p1* is the untaxed price of the good h’s demand for good 1 is lower with the tax: • x1** rather than x1* • where x1** = x1* + Dx1h and Dx1h < 0 Revenue raised by government from h: • Th = tp1* x1**= x1**Dp1 > 0 Absolute size of loss of consumer’s surplus to h is • |DCSh| = ∫ x1h dp1 ≈ x1** Dp1 − ½ Dx1hDp1 • = Th − ½ t p1* Dx1h > Th Use the definition of elasticity • e := p1Dx1h / x1hDp1< 0 Net loss from tax (for h) is • Lh = |DCSh| − Th = − ½tp1* Dx1h • = − ½teDp1x1** = − ½t e Th Overall net loss from tax (for h) is • ½ |e| tT • uses the assumption that all consumers are identical Frank Cowell: Efficiency-Waste Size of waste depends upon elasticity p1 p1 Redraw previous example compensated demand curve e low: relatively small waste e high: relatively large waste Dp1 p1* x1h Dpp 1 Dx1h p1 1 p1 * Dp1 Dp1 p1* p1* x1h Dx1h Dx1h x1 h x1h Dx1h Frank Cowell: Efficiency-Waste Application 1: assessment Waste inversely related to elasticity • Low elasticity: waste is small • High elasticity: waste is large Suggests a policy rule • suppose required tax revenue is given • which commodities should be taxed heavily? • if you just minimise waste – impose higher taxes on commodities with lower elasticities In practice considerations other than waste-minimisation will also influence tax policy • distributional fairness among households • administrative costs Frank Cowell: Efficiency-Waste Application 2: monopoly Monopoly power is supposed to be wasteful… • but why? We know that monopolist… • charges price above marginal cost • so it is inefficient … • …but how inefficient? Take simple version of main model • suppose markets for goods 2, …, n are competitive • good 1 is supplied monopolistically Frank Cowell: Efficiency-Waste Monopoly: computation of waste (1) Monopoly power in market for good 1 forces a price wedge • Dp1 = p1* * − p1* > 0 where • p1** is price charged in market • p1* is marginal cost (MC) h’s demand for good 1 is lower under this monopoly price: • x1** = x1* + Dx1h, • where Dx1h < 0 Same argument as before gives: • loss imposed on household h: −½Dp1Dx1h > 0 • loss overall: − ½Dp1Dx1, where x1 is total output of good 1 • using definition of elasticity e, loss equals − ½Dp12 e x1* */p1* * To evaluate this need to examine monopolist’s action… Frank Cowell: Efficiency-Waste Monopoly: computation of waste (2) Monopolist chooses overall output • use first-order condition • MR = MC: Evaluate MR in terms of price and elasticity: • p1* * [ 1 + 1 / e] • FOC is therefore p1* * [ 1 + 1 / e] = MC • hence Dp1= p1* * − MC = − p1* * / e Substitute into triangle formula to evaluate measurement of loss: • ½ p1* * x1* * / |e| Waste from monopoly is greater, the more inelastic is demand • Highly inelastic demand: substantial monopoly power • Elastic demand: approximates competition Frank Cowell: Efficiency-Waste Summary Starting point: an “ideal” world • pure private goods • no externalities etc • so CE represents an efficient allocation Characterise inefficiency in terms of price distortion • in the ideal world MRS = MRT for all h, f and all pairs of goods Measure waste in terms of income loss • fine for individual • OK just to add up? Extends to more elaborate models • straightforward in principle • but messy maths Applications focus on simple practicalities • elasticities measuring consumers’ price response • but simple formulas conceal strong assumptions Frank Cowell: Efficiency-Waste