Consumption, Production, Welfare B:Welfare Comparisons in Consumer Behaviour Univ. Prof. dr. Maarten Janssen University of Vienna Winter semester 2013
Relationship h(p,u) and x(p,w) Normal goods Inferior goods p p h(p,u) x(p,w) x(p,w) h(p,u) Q Q
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 Y • 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? EV A B X
Equivalent variation: more detail for this price decrease of x Mathematically Graphically • EV = e(p,u’) – e(p,u) = e(p,u’) – w = e(p,u’) – e(p’,u’) = p EV p’ h(p,u’) X
Compensating variation when x is a normal good Mathematically Graphically • 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 p CV EV p’ x(p,w) h(p,u’) h(p,u) X
What measures consumer surplus? Interpretation Graphically • 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 p CS p’ x(p,w) X
Further Applications I: Price Indices • Price indices are supposed to measure inflation. Inflation numbers are important in many ways, and are used in wage negotiations • Unions demand that nominal wages are at least corrected for inflation • If wages are adjusted in this way, are people just as well off as they are without inflation (and no nominal wage increase)? • Inflation calculation uses consumer goods basket: if at prices p consumer bought bundle x, and then prices increase to p´, then inflation is p´x/px
Price Indices • Consumer has made choice under old prices (blue point) • If all prices rise (at different rates) there is new budget line (red line) • Inflation rate is calculated as ratio of red dotted line and red staight line (check) • If consumers’ wage would be compensated for inflation they would be better off! • Kind of Slutsky compensation • When would this conclusion not hold? Y X
Further Applications II: Housing Prices • Consider an individual who just bought a house. After she bought the house, consider two scenarios: • All housing prices fall • All housing prices increase • In which situation is the consumer better off?
Housing prices • Consumer has made choice under old price ratio (blue point) • If house prices rise (as he has already his house), he has other trade-off (red line) and can sell house and buy new with less square meters • Slutsky compensation • Consumer better off. • What about decrease in housing prices? Other goods Square meters
Further Applications: Direct or indirect tax Y • If government wants to raise tax revenues, do consumers prefer indirect tax or lump-sum? • Indirect tax t such that. In Figuremovefrom A to B • Ifyouwouldkeepoldprices, youcouldhave a lump sumtaxequalto EV tomakeconsumer indifferent • How large should lump sumtaxT betorise same taxrevenueasindirecttax? • This budgetlinegoesthrough B atoldprices. • Consumer better off with lump sum T EV B A X
Usingtheapparatusofconsumerbehaviour • If –EV > T consumerisbetteroff with lump sumtax. Equivalentto e(p’,u’) – e(p,u’) > = p +t h(p,u) Q