Frank Cowell: Efficiency-Waste EFFICIENCY: WASTE MICROECONOMICS Principles and Analysis Frank Cowell Almost essential Welfare and Efficiency Almost essential Welfare and Efficiency Prerequisites

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 Basic model Applications Overview… Background Model with production Efficiency: Waste How to evaluate inefficient states

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 = p 1 ~ p1p1 [1  = p 2 ~ p2p2 = p 3 ~ p3p3 pnpn = …… = p n ~ consumer prices firms' prices  But now we have a distortion A model of price distortion  Assume there is a competitive equilibrium  If so, then everyone pays the same prices  What are the implications for MRS and MRT? Distortion

Frank Cowell: Efficiency-Waste Price distortion: MRS and MRT  Consumption: p j MRS ij h = — p i For every household marginal rate of substitution = price ratio  Production: for commodities 2,3,…,n p j MRT n j = — p n p j MRT 3 j = — p 3 p j MRT 2 j = — p 2 p j MRT 1 j = — p 1 [1+  ] … … … But for commodity 1… Illustration…

Frank Cowell: Efficiency-Waste x1x1 0 x2x2 Consumers Price distortion: efficiency loss  Production possibilities  An efficient allocation  Some other inefficient allocation How to measure importance of this wedge … x x* p* Producers  At x * producers and consumers face same prices  At x producers and consumers face different prices  Price "wedge" forced by the distortion

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:  p i := p i – p i * This is [actual price of i] – [reference price of i]  Evaluate the equivalent variation for household h : EV h = C h (p*,  h ) – C h (p,  h ) – [y* h – y h ] This is  (consumer costs) –  (income)  Aggregate over agents to get a measure of loss,  We do this for two cases…

Frank Cowell: Efficiency-Waste Basic model Applications Overview… Background Model with production Efficiency: Waste Taking producer prices as constant…

Frank Cowell: Efficiency-Waste x1x1 0 x2x2 If producer prices constant…  Production possibilities  Reference allocation and prices  Actual allocation and prices x x* p*  Measure cost in terms of good 2  Losses to consumers are C(p*,  )  C(p,  )  Cost of  at prices p C(p,  ) l  Cost of  at prices p* l C(p*,  )  Change in valuation of output  p p    is difference between C(p*,  )  C(p,  ) and 

Frank Cowell: Efficiency-Waste Model with fixed producer prices  Waste  involves both demand and supply responses  Simplify by taking case where production prices constant  Then waste is given by:  Use Shephard’s Lemma x i h = H hi (p,  h ) = C i h (p,  h )  Take a Taylor expansion to evaluate  :   is a sum of areas under compensated demand curve

Frank Cowell: Efficiency-Waste Basic model Applications Overview… Background Model with production Efficiency: Waste Allow supply-side response…

Frank Cowell: Efficiency-Waste x1x1 0 x2x2 Waste measurement: general case  Production possibilities  Reference allocation and prices  Actual allocation and prices x* p*  Measure cost in terms of good 2  Losses to consumers are C(p*,  )  C(p,  )  Cost of  at prices p C(p,  ) l  Cost of  at prices p* l C(p*,  )  Change in valuation of output  p p    is difference between C(p*,  )  C(p,  ) and  x

Frank Cowell: Efficiency-Waste Model with producer price response  Adapt the  formula to allow for supply responses  Then waste is given by: where q i (∙) is net supply function for commodity i  Again use Shephard’s Lemma and a Taylor expansion:

Frank Cowell: Efficiency-Waste Basic model Applications Overview… Background Model with production Efficiency: Waste Working out the hidden cost of taxation and monopoly…

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p1 compensated demand curve p1p1 p1*p1* x1hx1h x1hx1h x1*x1* revenue raised = tax x quantity revenue raised = tax x quantity    Equilibrium price and quantity  The tax raises consumer price…  …and reduces demand  Gain to the government  Loss to the consumer  Waste  Waste given by size of triangle  Sum over h to get total waste  Known as deadweight loss of tax

Frank Cowell: Efficiency-Waste Tax: computation of waste  An approximation using Consumer’s Surplus  The tax imposed on good 1 forces a price wedge  p 1 = tp 1 *  > 0 where is p 1 * is the untaxed price of the good  h’s demand for good 1 is lower with the tax: x 1 ** rather than x 1 * where x 1 ** =  x 1 *  x 1 h and  x 1 h < 0  Revenue raised by government from h: T h = tp 1 *  x 1 ** = x 1 **  p 1  > 0  Absolute size of loss of consumer’s surplus to h is  CS h  = ∫ x 1 h dp 1 ≈ x 1 **  p 1  −  ½  x 1 h  p 1 = T h  −  ½ t p 1 *  x 1 h > T h  Use the definition of elasticity  := p 1  x 1 h / x 1 h  p 1 < 0  Net loss from tax (for h) is  h =  CS h  − T h = − ½tp 1 *  x 1 h = − ½t  p 1 x 1 ** = − ½t  T h  Overall net loss from tax (for h) is ½ |  tT uses the assumption that all consumers are identical

Frank Cowell: Efficiency-Waste p1p1 compensated demand curve p1p1 p1*p1* x1hx1h x1hx1h Size of waste depends upon elasticity   low: relatively small waste   high: relatively large waste  Redraw previous example p1p1 p1p1 p1*p1* x1hx1h x1hx1h p1p1 p1p1 p1*p1* x1hx1h x1hx1h p1p1 p1p1 p1*p1* x1hx1h x1hx1h

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  p 1 = p 1 * * − p 1 * > 0 where p 1 ** is price charged in market p 1 * is marginal cost (MC)  h’s demand for good 1 is lower under this monopoly price: x 1 **  x 1 *  x 1 h, where  x 1 h < 0  Same argument as before gives: loss imposed on household h:  −½  p 1  x 1 h > 0 loss overall:  − ½  p 1  x 1, where x 1 is total output of good 1 using definition of elasticity , loss equals −  ½  p 1 2  x 1 * *  p 1 * *  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: p 1 * * [ /  ] FOC is therefore p 1 * * [ /  ] = MC hence  p 1 = p 1 * * − MC = − p 1 * * /   Substitute into triangle formula to evaluate measurement of loss:  ½ p 1 * * x 1 * * / |   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