Consumer s surplus CV/EV Examples. Consumer s surplus. Intermediate Micro. Lecture 9. Chapter 14 of Varian

Transcription

1 Consumer s surplus Intermediate Micro Lecture 9 Chapter 14 of Varian

2 Welfare analysis Last few lectures: how does p i affect demand? Today: how does p i (or other change) affect consumers s well-being? Bad news: multiple methods Good news: Agree on good/bad Good news: Similar magnitude

3 Consumer s surplus: a micro principles review Start with discrete goods model Reservation price: r j, price (per unit) at which consumer is indifferent between buying j and j 1 units of the good Gives $-value of consumption of 1 unit

4 Consumer s surplus: a micro principles review Suppose price is p (purple line) Choice: x = 2 Gross consumer surplus: $-valuation of total benefit from chosen x. Area of 2 left-most bars r1 + r 2

5 Consumer s surplus: a micro principles review Suppose price is p (purple line) Choice: x = 2 Consumer s surplus: $-valuation of benefit from chosen x net of foregone consumption of other goods. Area above the price line r1 + r 2 2 p

6 Non-discrete goods Can find CS when x is not discrete good Use demand function: x i (p i, p i, m) CS = p x(p, p i, m)dp

7 Non-discrete goods Or, use inverse demand function p i (x i, p i m) p i so that x i (p i, p i, m) = x i CS = x 0 p(x, p i, m) pdx

8 Welfare analysis CS alone not very interesting CS with policy change is informative $-value (-cost) of price change Example: p, from p to p

9 Multiple consumers Units for CS are $s We can sum CSs across many individuals Can also add in producer surpluses Note PS is income for households

10 Great, let s stop here Issues with CS 1. It requires taking integrals It can be done! 2. How well do Purchase costs represent utility? Income effect Quasilinear utility - perfectly Other utility functions - well, maybe not

11 Great, let s stop here Issues with CS 1. It requires taking integrals It can be done! 2. How well do Purchase costs represent utility? Income effect Quasilinear utility - perfectly Other utility functions - well, maybe not

12 Using the indifference curve Other ways to measure impact of price increase 1. Compensating variation: Increase in m needed, after price increase to restore utility to pre-change level Price change and m happen How much to compensate for price change? 2. Equivalent variation: Decrease in m sufficient, before price change, to bring utility to post-change level m happens instead of price change What cost is equivalent to effect of price change? CV and EV can also be used for price decreases

13 Compensating variation p 1 from p to p p 2 = 1 CV is m so that budget line with slope p tangent to old indifference curve x2 max = m p 2 = m

14 Equivalent variation p 1 from p to p p 2 = 1 EV is m so that budget line with slope p tangent to new indifference curve x2 max = m p 2 = m

15 What we re doing How far has the indifference curve moved? Like, in $ terms Use budget lines to measure

16 CV vs EV CV EV (Almost always) CV: in post-change $s EV in pre-change $s They don t have same buying power For p CV EV, usually > Equal with quasilinear utility = CS, too Equal if CV, or EV, = 0

17 Example: Cobb-Douglas utility Example: Cobb-Douglas utility p x changes from p = 5 to p = 4 Find the CV and EV u(x, y) = x 2 y m = 300, p y = 1

18 Example: Cobb-Douglas utility

19 Example: Quasilinear utility Example: Quasilinear utility u(x, y) = 4 x + y p x changes from p = 0.8 to p = 1 Find the CV and EV m = 40, p y = 1

20 Quasilinear utility - a general result Compensating variation v(x ) + [m + CV p x ] = v(x ) + [m px ] CV = [v(x ) px ] [v(x ) p x ] CV = [v(x ) v(x )] [px p x ] CV = [ utility from x] [ expenditure on x]

21 Quasilinear utility - a general result Equivalent variation v(x ) + [m p x ] = v(x ) + [m EV px ] EV = [v(x ) px ] [v(x ) p x ] EV = [v(x ) v(x )] [px p x ] EV = [ utility from x] [ expenditure on x] So, CV = EV

22 Example: Quasilinear utility

23 Quasilinear utility and CS FOC for x: p = v (x) Loss of direct utility when x falls from x to x is x x v (x)dx = v(x ) v(x ) Blue area For p

24 Quasilinear utility and CS Reduced spending from x goes to y Green area Increased spending from p comes from y Red area Total effect: CS = CV = EV Only for quasilinear utility CS = v(x ) v(x ) p[x x ] +x [p p] blue area green box +red box