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Prerequisites. Almost essential Welfare and Efficiency. Efficiency: Waste. MICROECONOMICS Principles and Analysis Frank Cowell . Agenda. Build on the efficiency presentation Focus on relation between competition and efficiency Start from the “standard” efficiency rules

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efficiency waste

Prerequisites

Almost essential

Welfare and Efficiency

Efficiency: Waste

MICROECONOMICS

Principles and Analysis

Frank Cowell

agenda
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?
overview
Overview…

Efficiency: Waste

Background

How to evaluate inefficient states

Basic model

Model with production

Applications

the approach
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
a reference point
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
a model of price distortion

~

= p1

~

= p2

~

= p3

consumer

prices

firms' prices

~

= pn

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

Distortion

  • What are the implications for MRS and MRT?

p1

[1+d]

p2

p3

= …

pn

price distortion mrs and mrt
Price distortion: MRS and MRT

For every household marginal rate of substitution = price ratio

pj

MRSijh= —

pi

  • Consumption:
  • Production:
    • for commodities 2,3,…,n

pj

MRT1j = —

p1

  • But for commodity 1…

[1+ d]

pj

MRT2j = —

p2

pj

MRT3j = —

p3

… … …

Illustration…

pj

MRTnj = —

pn

price distortion efficiency loss
Price distortion: efficiency loss
  • Production possibilities
  • An efficient allocation

x2

  • Some other inefficient allocation
  • At x* producers and consumers face same prices
  • At x producers and consumers face different prices
  • x

Producers

  • x*
  • Price "wedge" forced by the distortion

How to measure importance of this wedge …

p*

Consumers

x1

0

waste measurement a method
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…
overview1
Overview…

Efficiency: Waste

Background

Taking producer prices as constant…

Basic model

Model with production

Applications

if producer prices constant
If producer prices constant…
  • Production possibilities

C(p, u)

x2

  • Reference allocation and prices
  • Actual allocation and prices

DP

  • Cost of u at prices p
  • Cost of u at prices p*
  • 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*
  • L is difference between
  • C(p*, u)  C(p, u) and DP

p

p*

u

0

x1

model with fixed producer prices
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
overview2
Overview…

Efficiency: Waste

Background

Allow supply-side response…

Basic model

Model with production

Applications

waste measurement general case
Waste measurement: general case
  • Production possibilities

C(p, u)

x2

  • Reference allocation and prices
  • Actual allocation and prices

DP

  • Cost of u at prices p
  • Cost of u at prices p*
  • 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*

  • L is difference between
  • C(p*, u)  C(p, u) and DP

p

u

x1

0

model with producer price response
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:
overview3
Overview…

Efficiency: Waste

Background

Working out the hidden cost of taxation and monopoly…

Basic model

Model with production

Applications

application 1 commodity tax
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:
a model of a commodity tax
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
  • Sum over h to get total waste
  • Known as deadweight loss of tax

L

Dp1

p1*

x1*

x1h

Dx1h

tax computation of 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| = ∫ x1hdp1 ≈ x1**Dp1−½Dx1hDp1
    • = 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
size of waste depends upon elasticity

p1

p1

compensated

demand curve

Dp1

p1*

x1h

Dx1h

Dp1

p1

p1

p1*

Dp1

Dp1

p1*

p1*

x1h

Dx1h

x1h

x1h

Dx1h

Dx1h

Size of waste depends upon elasticity
  • Redraw previous example
  • e low: relatively small waste
  • e high: relatively large waste
application 1 assessment
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
application 2 monopoly
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
monopoly computation of waste 1
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 −½Dp12e x1**/p1**
  • To evaluate this need to examine monopolist’s action…
monopoly computation of waste 2
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
summary
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