Consumers surplus in multiple markeds

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Consumers surplus in multiple markeds

• Odd I LarsenCBA-course, Molde 4.-9. Dec 2006

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Main topics

• The trapezoid formulae - assumptions and
  approximations - Indirect utility function and
  Roys identity- Aggregation
• Income distribution and welfare functions
• Benefits and cost in primary and secondary
  markets

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Multiple markes

• A public policy measure may affect several
  markets, directly or indirectly.
• Sometimes we need to evaluate a package of
  different policy measures.
• This will involve a mixture of shifts in demand
  schedules and movement along demand schedules.

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The solution use the trapezoid formulae over all
markets
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What are the implicit assumptions and
approximations?

• One consumer
• The notion of indirect utility- Utility -
  function of quantities - Maximisation of utility
  function with budget constraint gt demand
  functions that depends on prices and income. -
  Insert the demand-functions in the utility
  function and we get the indirect utility function

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Indirect utility-function

• The maximum utility obtainable from given prices
  and income.

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Equivalent income change
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Roys identity
or
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Taylor expansion of U(P0,R) and the derivative of
Roys identity
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Combining
1. order approximation of demand-functions
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If marginal utility of income is constant than
ß0 and we have
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The trapezoid formulae on the level of the
individual are based on

• A second order approximation of the indirect
  utility function.
• A first order approximation of the demand
  functions.
• An assumption of constant marginal utility of
  income.
• The trapezoid formulae is an estimate of the
  equivalent change in income.
• The approximations should be good provided that
  the price changes are sufficiently small and/or
  the curvature of the functions involved are
  small.
• As long as all consumers faces the same price
  changes, the trapezoid formula used on the
  aggregate demand function gives an estimate of
  the sum of equivalent income changes over all
  affected.

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Can we aggregate with good conscience?

• We are adding utility changes for all affected,
  rich and poor have the same weight. A change may
  actually make the rich better of and the poor
  worse off!!
• ?CSgt0 only implies that winners should in
  principle be able to compensate loosers and
  still be better off in the new situation.

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A social welfare function

• Public authorities have many measures that can be
  used to obtain a distribution of income or
  material well being that are in accordance with
  objectives.
• Let Ri be disposable income for individual i.
• Welfare function WWU1(R1),..,Un(Rn)

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Maximize W subject to SiRiR
µLangrange multiplier on constraint

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Change in welfare function
Provided income distribution is in accordance
with the social welfare function and the changes
are sufficiently small, the sum of individual
changes in CSP is a first order approximation of
the change in the social welfare function!
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Is this a tenable assumption?

• If redistribution of income or material well
  being do not have any adverse effect on the
  economy we must expect that the income
  distribution is in accordance with the ruling
  political preferences.
• But, what about incentives

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Total disposable income depending on the
distribution
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Weighting
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Non-market variables
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Same method

• Needs shadow prices, i.e. trade-offs with market
  goods (or income changes)

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Correction of market failure

• Monopoly
• Natural monopoly
• Information asymmetri
• Externalities
• Public goods
• High transaction costs
• Decreasing returns to scale
• Intrapersonal externalities

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Valuing the use of resources-opportunity cost.

• The market for a resource (input) is efficient
  and price effects are negligible.
• Efficient, but project purchases affects prices.
• Market for resources are inefficient, i.e. prices
  do not properly reflect marginal social cost

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The marginal cost of public funds

• Net impact on government budget- Increased
  expenditure must in the end be financed by higher
  taxes.- Decreased expenditure can reduce taxes
• Constant taxes and budget, opportunity cost net
  social benefits of marginal projects.

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Secondary markets

• Unaffected prices the issue is any difference
  between price and social marginal cost.
  (p-smc)?x
• Affected prices gttrapezoid formulae and
  accounting for the cost of externality.
• Local and global impacts of infrastructure.
• Services user costs