Consumption, Production, Welfare B:Consumer Behaviour

Univ. Prof. dr. Maarten JanssenUniversity of Vienna

Winter semester 2013

Consumer Theory without preferences

• Revealed preference: We can look at choices made of individuals and ask whether they satisfy some natural consistency requirements

• General: if in two choice situations, x and y were both included, and in one choice situation the agent chose x, then he cannot uniquely choose y in the other situation

• Under a budget constraint: if at prices p and wealth level w, individual chose x(p,w) and if at prices p’ and wealth level w’ individual chose x(p’,w’), then px(p’,w’) ≤ w implies p’x(p,w) > w’

• Graphical illustration budget constraint two goods

Implications for demand theory

• Does RP imply that demand curves are downward sloping?

• Graphical illustration• Only if price changes are compensated by wealth

changes• Slutsky compensation: you compensate agent so

that she can just afford old consumption bundle, i.e., p’x(p,w) = w’

• RP in this case implies (p’ – p)[x(p’,w’) - x(p,w)] ≤ 0

Recent study by Wieland Müller et al. (AER 2013, forthcoming)

• Internet experiments with large sample of Dutch population, of which researchers know many features (age, education, wealth, etc.)

• They perform RP tests in choice situations• Who is more rational (is more consistent with RP)?– Younger, more educated people

• Doing well in RP tests correlates well with wealth of individuals (if corrected for age, education and other features)

Implication Equivalence

• RP has empirical implications (that can be violated)

• Utility maximization under a budget constraint has empirical implications

• These empirical implications are almost identical

Maximization implication

• Budget set has a slope of • Utility function has indifference curve given

by implying (if only and change) • In optimum ratio of marginal utilities has to be

equal to price ratio• Helps to derive demand functions

Application: gasoline tax proposal under president Carter

• Carter proposed to increase gasoline tax to reduce use of gasoline in USA

• Critique: the poor can then not afford to have a car (as they cannot afford to pay gigher gasoline price)

• Carter reacted by saying that the poor will be income compensated for the tax increase

• Critique’s then said that the whole proposal is then ridiculous as it is ineffective: if people can afford the same amount as before, they will.

• Who is right?

Econ Questions and Analysis

Gasoline consumption

Other goods

Original budget line

1. Will the consumption of gasoline decrease after an gasoline price tax?

2. If consumers are compensated will they consume less gasoline?

- How are they compensated?3. If they are Slutsky compensated, will

they consume less? 4. How to reconclide answers to 1 and

3?5. If they are Slutsky compensated, will

government run a deficit over this policy?

Further concepts in consumer theory• Indirect utility function v(p,w): maximum utility an

individual agent can get at prices p and wealth level w.– Increasing in w, non-decreasing in p

• Expenditure function e(p,u): minimum wealth level you need to be able to reach utility level u at price p.– Increasing in w, non-decreasing in p

• Hicksian demand h(p,u) and Walrasian demand x(p,w): – If at prices p and wealth level w consumer chooses x(p,w),

then h(p,v(p,w)) = x(p,w). Similarly, if at (p,u) consumer chooses h(p,u), then x(p,e(p,u)) = h(p,u)

Relation between h(p,u) and e(p,u)

• Expenditure • LHS gives the minimum wealth you need to

reach u at prices p; RHS gives expenditure if you keep a certain demand level.

• = )• Main idea: at some prices, demand ) is optimal

and there .• If e(p,u) is differentiable, then you have result.• Show figure

Property of Hicksian demand • If price of y becomes relatively

lower than that of x and consumer is compensated such that he can achieve same utility level, then consumption of y has to be nondecreasing and of x nonincreasing

• In terms of Hicksian demand: (p’ – p)[h(p’,u) - h(p,u)] ≤ 0

• This is the substitution effect (and is always nonpositive)

• When can it be zero?

X

y

Income effects

• Where can demand be after a decrease in income, wealth?

• Normal goods • Inferior goods • All coloured choices are

possible

X

Y

Income and substitution effects

• A price change has a substitution and income effect on demand

• Total effect of a price change from A to B can be decomposed into a substitution effect (from A to C) and an income effect (from C to B)

A

C

B

Income and substitution effects: Mathematically

• Demand can be written as h(p,u) = x(p,e(p,u)) • Thus,

= • As sign of LHS is negative, if income effect is

positive (normal goods), then first term on RHS has to be negative. If income effect is strongly negative, then this first term may be positive (Giffen good, Veblen effect)

Relationship h(p,u) and x(p,w)

Normal goods Inferior goods

p

Q

h(p,u)

x(p,w)

p

Q

x(p,w)

h(p,u)

Welfare evaluations• How do consumers appreciate price changes. A pure economist‘s

response would be to say: v(p‘,w) – v(p,w) is appropriate measure• But how big is this?• Money-metric measure should come in handy: e(p,v(p,w)) is how

much money you need to be able to reach utility level v(p,w) when price are p

• How much did consumer becomes better off because of a price change from p to p‘?: e(p,v(p‘,w)) - e(p,v(p,w))

• Depends on choice of p. Two obvious choices:– P is old price p: Equivalent variation. How much money should you

comepnsate to consumer to make him just willing to stay with old prices?– P is new price p: Compensating variation. How much money should you

comepnsate to consumer to make him just willing to accept new prices?

Equivalent Variation: graphically• Suppose price of good y is

normalized to 1• Shift from A to B is due to price

decrease in price of x• How much money should

consumer get to stay with old prices? EV measured on vertical axis

• Can you draw CV systematically?

A B

EV

X

Y

Equivalent variation: more detail for this price decrease of x

Mathematically• EV = e(p,u’) – e(p,u)

= e(p,u’) – w= e(p,u’) – e(p’,u’) =

Graphically

X

𝑝𝑥

h(p,u’)

p

p’EV

Compensating variation when x is a normal good

Mathematically• CV = e(p’,u’) – e(p’,u)

= w - e(p’,u) = e(p,u) – e(p’,u) =

• Relation with EV: is u higher than u’ or not?

• With price decrease we are analyzing here u is smaller than u’ and so we have

Graphically

X

𝑝𝑥

h(p,u’)

p

p’EVCV

h(p,u)

x(p,w)

What measures consumer surplus?

Interpretation• If we use consumer surplus as

a measure of welfare change due to a price decrease, then we have figure on right

• For normal goods this is smaller than EV and larger than CV (see previous slides)

• It is equal to both if there are no income effects

• Good exercise: try to depict EV, CV, CS with inferior goods

Graphically

X

𝑝𝑥

x(p,w)

p

p’CS