Consumer Surplus and Welfare Measurement (Chapter 14) cont. & Market Demand (Chapter 15)

Transcription

1 Consumer Surplus and Welfare Measurement (Chapter 14) cont. & Market Demand (Chapter 15)

2 Outline Welfare measures example Welfare effects of interference in competitive markets Market Demand (Chapter 14) Deriving market demand from individual demands How responsive is q d to a change in price? (elasticity) What is the relationship between revenue and demand elasticity?

3 CV & EV: Example Consider a utility function U(c 1, c 2 ) = c 1 c 2, original prices p 1 = p 2 = 1, and income m = 100. Find CV, EV when p 1 increases to p 1 = 2. Need to find consumption, utility before and after. Do this by deriving a demand function for each good. Solve: subject to p 1 c 1 + p 2 c 2 = m. MRS = price-ratio: max (c 1,c 2 ) c 1c 2 MU 2 MU 1 = c 1 c 2 = p 2 p 1 = p 1 c 1 = p 2 c 2 Substituting back into the budget constraint give us c 1 = m and c 2 = m 2p 1 2p 2

4 CV & EV: Example Consumption & Utility under before and after the price change. p 1 = 1, p 2 = 1, m = 100 (before) c 1 = m 2p 1 = 50; c 2 = m 2p 2 U = = 2500 p 1 = 2, p 2 = 1, m = 100 (after) c 1 = 25 and c 2 = 50 U = = 1250

5 Compensating Variation CV = the amount of extra money needed to bring the budget line back up to the old indifference curve. m+cv CV m As well off as before c 2 u u c 1

6 CV & EV: Example Compensating Variation How much money to we have to pay the consumer to make her as well off as she was before (U = 2500)? If income is m, then consumption (with the new prices) is c 1 = m 2p 1 c 2 = m 2p 1 = m 4 = m 2 and utility is U = c 1 c 2 = m 2 8 For what value of m is U = U = 2500? m 2 So CV = m m 41 8 = 2500 = m =

7 Equivalent Variation EV: how much money we would have to take away from the consumer before the price change to leave her just as well off as she would be after. c 2 m EV As well off as after m-ev u u c 1

8 CV & EV: Example Equivalent Variation If we don t change the prices, how much money would we have to take away from the consumer to bring her utility down an equivalent amount? At original prices, consumption with income m is c 1 = c 2 = m 2 and utility is then U = c1 c 2 = m 2 4. For what value of m is U = U = 1250? m 2 4 = 1250 = m = So EV = m m 29

9 Welfare in Competitive Markets Q: How can we measure the gain or loss caused by market intervention/regulation? A: Use consumer and producer surplus: total surplus = CS + PS. Our benchmark will be competitive, free-market equilibrium Supply p CS PS Demand q Snuggly blankets

10 Welfare in Competitive Markets Any regulation that causes the units from q 1 to q 0 to be not traded destroys some of the gains from trade. Loss p CS PS q 1 q 0 Q D, Q S This loss is the net cost of regulation.

11 Welfare in Competitive Markets Example: per unit tax of $t Loss p b CS t Tax Revenue p s PS q 1 q 0 Q D, Q S

12 Welfare in Competitive Markets Example: price floor p f Loss p f CS PS q 1 q 0 Q D, Q S

13 Welfare in Competitive Markets Example: price ceiling p c Loss CS p c PS q 1 q 0 Q D, Q S

14 Welfare in Competitive Markets Example: rationing (only q 1 units allowed to be traded) p b p s CS Ration coupon Revenue PS Loss q 1 q 0 Q D, Q S

15 From Individual Demands to Market Demand Let D i (p) be the demand function of person i and suppose that D 1 (p) = max{20 p, 0} D 2 (p) = max{10 2p, 0} 20 D 1 (p) 5 D 2 (p) 20 Cats 10 Cats Demand of Agent 1 Demand of Agent 2

16 From Individual Demands to Market Demand The market demand is the horizonal sum (for a given p) of all individual demand: D(p) = D i (p) i = D 1 (p) + D 2 (p) 20 D 1 (p) Market Demand 5 D 2 (p) kink Cats