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

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

2 Agenda Build on te efficiency presentation Focus on relation between competition and efficiency Start from te standard efficiency rules MRS same for all ouseolds MRT same for all firms MRS=MRT for all pairs of goods Wat appens if we depart from tese rules? How to quantify departures from efficiency?

3 Overview Efficiency: Waste Background How to evaluate inefficient states Basic model Model wit production Applications

4 Te approac 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 ouseold budgets to Model cange in profits and rents

5 A reference point Address te question: ow muc waste? Need a reference point were tere is zero waste quantify departures from tis 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 te default state just a convenient bencmark Can caracterise inefficiency as price distortion

6 A model of price distortion Assume tere is a competitive equilibrium If so, ten everyone pays te same prices But now we ave a distortion Wat are te implications for MRS and MRT? consumer prices ~ p 1 = p 1 ~ p 2 = p 2 ~ p 3 = p 3 p n = ~ = p n [1+δ] Distortion firms' prices

7 Price distortion: MRS and MRT For every ouseold marginal rate of substitution = price ratio Consumption: Production: for commodities 2,3,,n But for commodity 1 p j MRSij = pi p j MRT 1j = p1 [1+ δ] p j MRT 2j = p2 p j MRT 3j = p3 p j MRT nj = pn Illustration

8 Price distortion: efficiency loss x 2 Production possibilities An efficient allocation Some oter inefficient allocation x x* Producers At x* producers and consumers face same prices At x producers and consumers face different prices Price "wedge" forced by te distortion 0 Consumers p* x 1 How to measure importance of tis wedge

9 Waste measurement: a metod To measure loss we use a reference point Take tis as competitive equilibrium wic defines a set of reference prices Quantify te effect of a notional price cange: p i := p i p i * Tis is [actual price of i] [reference price of i] Evaluate te equivalent variation for ouseold : EV = C (p*,υ ) C (p,υ ) [y* y ] Tis is (consumer costs) (income) Aggregate over agents to get a measure of loss, Λ We do tis for two cases

10 Overview Efficiency: Waste Background Taking producer prices as constant Basic model Model wit production Applications

11 If producer prices constant C(p, υ) x 2 Π Production possibilities Reference allocation and prices Actual allocation and prices Cost of υ at prices p Cost of υ at prices p* Cange in valuation of output C(p*, υ) x x* p p* Measure cost in terms of good 2 Losses to consumers are C(p*, υ) C(p, υ) Λ is difference between C(p*, υ) C(p, υ) and Π υ 0 x 1

12 Model wit fixed producer prices Waste Λ involves bot demand and supply responses Simplify by taking case were production prices constant Ten waste is given by: Use Separd s Lemma x i = H i (p,υ ) = C i (p,υ ) Take a Taylor expansion to evaluate Λ: Λ is a sum of areas under compensated demand curve

13 Overview Efficiency: Waste Background Allow supply-side response Basic model Model wit production Applications

14 Waste measurement: general case C(p, υ) x 2 Π Production possibilities Reference allocation and prices Actual allocation and prices Cost of υ at prices p Cost of υ at prices p* Cange in valuation of output C(p*, υ) x x* Measure cost in terms of good 2 Losses to consumers are C(p*, υ) C(p, υ) p p* υ Λ is difference between C(p*, υ) C(p, υ) and Π 0 x 1

15 Model wit producer price response Adapt te Λ formula to allow for supply responses Ten waste is given by: were q i ( ) is net supply function for commodity i Again use Separd s Lemma and a Taylor expansion:

16 Overview Efficiency: Waste Background Working out te idden cost of taxation and monopoly Basic model Model wit production Applications

17 Application 1: commodity tax Commodity taxes distort prices Take te model were producer prices are given Let price of good 1 be forced up by a proportional commodity tax t Use te standard metod to evaluate waste Wat is te relationsip of tax to waste? Simplified model: identical consumers no cross-price effects (impact of tax on good 1 does not affect demand for oter goods) Use competitive, non-distorted case as reference

18 A model of a commodity tax p 1 compensated demand curve Equilibrium price and quantity Te tax raises consumer price and reduces demand Gain to te government Loss to te consumer Waste p 1 revenue raised = tax x quantity Λ Waste given by size of triangle Sum over to get total waste p 1 * Known as deadweigt loss of tax x 1 x 1 * x 1

19 Tax: computation of waste An approximation using Consumer s Surplus Te tax imposed on good 1 forces a price wedge p 1 = tp 1* > 0 were is p 1* is te untaxed price of te good s demand for good 1 is lower wit te tax: x 1 ** rater tan x 1 * were x 1 ** = x 1* + x 1 and x 1 < 0 Revenue raised by government from : T = tp 1* x 1 ** = x 1 ** p 1 > 0 Absolute size of loss of consumer s surplus to is CS = x 1 dp 1 x 1 ** p 1 ½ x 1 p 1 = T ½ t p 1* x 1 > T Use te definition of elasticity ε := p 1 x 1 / x 1 p 1 < 0 Net loss from tax (for ) is Λ = CS T = ½tp 1* x 1 = ½tε p 1 x 1 ** = ½t ε T Overall net loss from tax (for ) is ½ ε tt uses te assumption tat all consumers are identical

20 Size of waste depends upon elasticity p 1 p 1 compensated demand curve Redraw previous example ε low: relatively small waste ε ig: relatively large waste p 1 p 1 * x 1 p 1 x 1 p 1 p 1 p 1 * p 1 p 1 p 1 * p 1 * x 1 x 1 x 1 x 1 x 1 x 1

21 Application 1: assessment Waste inversely related to elasticity Low elasticity: waste is small Hig elasticity: waste is large Suggests a policy rule suppose required tax revenue is given wic commodities sould be taxed eavily? if you just minimise waste impose iger taxes on commodities wit lower elasticities In practice considerations oter tan waste-minimisation will also influence tax policy distributional fairness among ouseolds administrative costs

22 Application 2: monopoly Monopoly power is supposed to be wasteful but wy? We know tat monopolist: carges price above marginal cost so equilibrium solution is inefficient But ow inefficient? Take simple version of main model suppose markets for goods 2,, n are competitive good 1 is supplied monopolistically

23 Monopoly: computation of waste (1) Monopoly power in market for good 1 forces a price wedge p 1 = p 1 * * p 1 * > 0 were p 1 ** is price carged in market p 1 * is marginal cost (MC) s demand for good 1 is lower under tis monopoly price: x 1 ** = x 1* + x 1, were x 1 < 0 Same argument as before gives: loss imposed on ouseold : ½ p 1 x 1 > 0 loss overall: ½ p 1 x 1, were x 1 is total output of good 1 using definition of elasticity ε, loss equals ½ p 12 ε x 1 * * /p 1 * * To evaluate tis need to examine monopolist s action

24 Monopoly: computation of waste (2) Monopolist cooses overall output use first-order condition MR = MC: Evaluate MR in terms of price and elasticity: p 1 * * [ / ε] FOC is terefore p 1 * * [ / ε] = MC ence p 1 = p 1 * * MC = p 1 * * Substitute into triangle formula to evaluate measurement of loss: ½ p 1 * * x 1 * * / ε Waste from monopoly is greater, te more inelastic is demand Higly inelastic demand: substantial monopoly power Elastic demand: approximates competition / ε

25 Summary Starting point: an ideal world pure private goods no externalities etc so CE represents an efficient allocation Caracterise inefficiency in terms of price distortion in te ideal world MRS = MRT for all, 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 straigtforward in principle but messy mats Applications focus on simple practicalities elasticities measuring consumers price response but simple formulas conceal strong assumptions