#### Transcript Extensive Form - London School of Economics

Prerequisites Almost essential Welfare and Efficiency Frank Cowell: Microeconomics November 2006 Efficiency: Waste MICROECONOMICS Principles and Analysis Frank Cowell Agenda Frank Cowell: Microeconomics Build on the efficiency presentation Start from the “standard” efficiency rules Focus on relation between competition and efficiency 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? Efficiency: Waste Overview... Frank Cowell: Microeconomics Background How to evaluate inefficient states Basic model Model with production Applications The approach Frank Cowell: Microeconomics 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 A reference point Frank Cowell: Microeconomics Address the question: how much waste? Need a reference point Any efficient point would do But it is usual to take a CE allocation where there is zero waste quantify departures from this point 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 A model of price distortion Frank Cowell: Microeconomics Assume there is a competitive equilibrium If so, then everyone pays the same prices But now we have a distortion Distortion What are the implications for MRS and MRT? p1 p2 p3 consumer prices ... pn ~ = p1 [1+d] ~ = p2 ~ = p3 = ... ~ = pn firms' prices Price distortion: MRS and MRT For every household marginal rate of substitution = price ratio Frank Cowell: Microeconomics Consumption: Production: for commodities 2,3,...,n MRSij MRT1j But for commodity 1... MRT2j h pj = — pi pj = — [1+ d] p1 pj = — p2 pj MRT3j = — p3 ... ... ... pj MRTnj = — pn Illustration.... Price distortion: efficiency loss Frank Cowell: Microeconomics Production possibilities An efficient allocation Some other inefficient allocation x2 At x* producers and consumers face same prices. At x producers and x x* consumers face different prices. Producers Price "wedge" forced by the distortion. How to measure importance of this wedge .... p* Consumers 0 x1 Waste measurement: a method Frank Cowell: Microeconomics To measure loss we use a reference point Take this as competitive equilibrium... 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 : ...which defines a set of reference prices 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… Efficiency: Waste Overview... Frank Cowell: Microeconomics Background Taking producer prices as constant… Basic model Model with production Applications If producer prices constant… Frank Cowell: Microeconomics 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 value of output at consumer prices Measure cost in terms of C(p*,u) good 2. x Losses to consumers are C(p*,u) C(p,u) x* p 0 p* L is difference between C(p*,u) C(p,u) and DP u x1 Model with fixed producer prices Frank Cowell: Microeconomics 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 h hi h h h xi = H (p,u ) = Ci (p,u ) Take a Taylor expansion to evaluate L: L is a sum of areas under compensated demand curve. Efficiency: Waste Overview... Frank Cowell: Microeconomics Background Allow supply-side response… Basic model Model with production Applications Waste measurement: general case Frank Cowell: Microeconomics 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 value of output at consumer prices Measure cost in terms of C(p*,u) good 2. x Losses to consumers are C(p*,u) C(p,u) x* p L is difference between C(p*,u) C(p,u) and DP p* u 0 x1 Model with producer price response Frank Cowell: Microeconomics 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: Efficiency: Waste Overview... Frank Cowell: Microeconomics Background Working out the hidden cost of taxation and monopoly… Basic model Model with production Applications Application 1: commodity tax Frank Cowell: Microeconomics Commodity taxes distort prices Simplified model: 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? 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: A model of a commodity tax Frank Cowell: Microeconomics 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 measured by L Dp1 size of triangle Sum over h to get total waste Commonly known as deadweight loss of tax. p1* x1 * Dx1h x1 h Tax: computation of waste Frank Cowell: Microeconomics The tax imposed on good 1 forces a price wedge h’s demand for good 1 is lower with the tax: e := p1Dx1h / x1hDp1< 0 Net loss from tax (for h) is DCSh = ∫ x1h dp1 ≈ x1** Dp1 − ½ Dx1hDp1 = Th + ½Dx1hDp1= Th − ½ t p1* Dx1h > Th Use the definition of elasticity x1** rather than x1* where x1** = x1* + Dx1h and Dx1h < 0 Revenue raised by government from h: Th = tp1* x1** Loss of consumer’s surplus to h is Dp1 = tp1* > 0 where is p1* is the untaxed price of the good 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 Size of waste depends upon elasticity Frank Cowell: Microeconomics 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 Application 1: assessment Frank Cowell: Microeconomics Waste inversely related to elasticity Suggests a policy rule Low elasticity: waste is small High elasticity: waste is large 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 Application 2: monopoly Frank Cowell: Microeconomics Monopoly power is supposed to be wasteful… We know that monopolist… but why? 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 Monopoly: computation of waste (1) Frank Cowell: Microeconomics Monopoly power in market for good 1 forces a price wedge * * − p * > 0 where Dp1 = p1 1 ** 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: h loss imposed on household h: −½Dp1Dx1 > 0 loss overall: − ½Dp1Dx1, where x1 is total output of good 1 2 * */p * * using definition of elasticity e, loss equals − ½Dp1 e x1 1 To evaluate this need to examine monopolist’s action… Monopoly: computation of waste (2) Frank Cowell: Microeconomics Monopolist chooses overall output 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: use first-order condition MR = MC: ½ p1* * x1* * / |e| Waste from monopoly is greater, the more inelastic is demand Highly inelastic demand: substantial monopoly power Elastic demand: approximates competition Summary Frank Cowell: Microeconomics Starting point: an “ideal” world Characterise inefficiency in terms of price distortion fine for individual OK just to add up? Extends to more elaborate models in the ideal world MRS = MRT for all h, f and all pairs of goods Measure waste in terms of income loss pure private goods no externalities etc so CE represents an efficient allocation straightforward in principle but messy maths Applications focus on simple practicalities elasticities measuring consumers’ price response but simple formulas conceal strong assumptions