Consumption, Production, Welfare B: Consumer Behaviour Univ. Prof. dr. Maarten Janssen University 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

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)

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 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

Relationship h(p,u) and x(p,w) Normal goodsInferior goods p Q h(p,u) x(p,w) p Q 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 MathematicallyGraphically X h(p,u’) p p’ EV

Compensating variation when x is a normal good MathematicallyGraphically X 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 x(p,w) p p’ CS