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1 Consumer’s Surplus Molly W. Dahl Georgetown University Econ 101 – Spring 2009

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2 Inverse Demand Functions Taking quantity demanded as given and then asking what the price must be describes the inverse demand function of a commodity. Usually we ask “Given p 1 what is the quantity demanded of x 1 ?” But we could also ask the inverse question “Given that the quantity demanded is x 1, what must p 1 be?”

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3 Inverse Demand Functions p1p1 x1*x1* p1’p1’ Given p 1 ’, what quantity is demanded of commodity 1? Answer: x 1 ’ units. x1’x1’

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4 Inverse Demand Functions p1p1 x1*x1* p1’p1’ x1’x1’ Given p 1 ’, what quantity is demanded of commodity 1? Answer: x 1 ’ units. The inverse question is: Given x 1 ’ units are demanded, what is the price of commodity 1? Answer: p 1 ’

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5 Consumer’s Surplus p1p1 CS Consumer’s surplus is the consumer’s utility gain from consuming x 1 ’ units of commodity 1.

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6 The change to a consumer’s total utility due to a change to p 1 is approximately the change in her Consumer’s Surplus. Change in Consumer’s Surplus

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7 p1p1 p 1 (x 1 ), the inverse ordinary demand curve for commodity 1

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8 Change in Consumer’s Surplus p1p1 CS before p 1 (x 1 )

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9 Change in Consumer’s Surplus p1p1 CS after p 1 (x 1 )

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10 Change in Consumer’s Surplus p1p1 Lost CS p 1 (x 1 )

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11 In Class: Calculating Consumer Surplus

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12 Changes in a firm’s welfare can be measured in dollars much as for a consumer. Producer’s Surplus

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13 Producer’s Surplus y (output units) Output price (p) S = Marginal Cost

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14 Producer’s Surplus y (output units) Output price (p) S = Marginal Cost

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15 Producer’s Surplus y (output units) Output price (p) S = Marginal Cost Revenue =

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16 Producer’s Surplus y (output units) Output price (p) S = Marginal Cost Variable Cost of producing y’ units is the sum of the marginal costs

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17 Producer’s Surplus y (output units) Output price (p) S = Marginal Cost Variable Cost of producing y’ units is the sum of the marginal costs Revenue less VC is the Producer’s Surplus.

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18 Cost-Benefit Analysis Can we measure in money units the net gain, or loss, caused by a market intervention; e.g., the imposition or the removal of a market regulation? Yes, by using measures such as the Consumer’s Surplus and the Producer’s Surplus.

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19 Cost-Benefit Analysis Q D, Q S Price Supply Demand p0p0 q0q0 The free-market equilibrium

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20 CS Cost-Benefit Analysis Q D, Q S Price Supply Demand p0p0 q0q0 The free-market equilibrium and the gains from trade generated by it. PS

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21 CS Cost-Benefit Analysis Q D, Q S Price Supply Demand p0p0 q0q0 PS q1q1 Consumer’s gain Producer’s gain The gain from freely trading the q 1 th unit.

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22 CS Cost-Benefit Analysis Q D, Q S Price Supply Demand p0p0 q0q0 The gains from freely trading the units from q 1 to q 0. PS q1q1 Consumer’s gains Producer’s gains

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23 CS Cost-Benefit Analysis Q D, Q S Price Supply Demand p0p0 q0q0 The gains from freely trading the units from q 1 to q 0. PS q1q1 Consumer’s gains Producer’s gains

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24 CS Cost-Benefit Analysis Q D, Q S Price p0p0 q0q0 PS q1q1 Consumer’s gains Producer’s gains Any regulation that causes the units from q 1 to q 0 to be not traded destroys these gains. This loss is the net cost of the regulation.

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25 Tax Revenue Cost-Benefit Analysis Q D, Q S Price q0q0 PS q1q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. psps pbpb t CS Deadweight Loss

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26 Cost-Benefit Analysis Q D, Q S Price q0q0 q1q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. pfpf CS Deadweight Loss So does a floor price set at p f PS

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27 Cost-Benefit Analysis Q D, Q S Price q0q0 q1q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. pcpc Deadweight Loss So does a floor price set at p f, a ceiling price set at p c PS CS

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28 Cost-Benefit Analysis Q D, Q S Price q0q0 q1q1 An excise tax imposed at a rate of $t per traded unit destroys these gains. pcpc Deadweight Loss So does a floor price set at p f, a ceiling price set at p c, and a ration scheme that allows only q 1 units to be traded. PS pepe CS Revenue received by holders of ration coupons.

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29 Two additional dollar measures of the total utility change caused by a price change are Compensating Variation and Equivalent Variation. Compensating Variation and Equivalent Variation

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30 p 1 rises. Q: What is the extra income that, at the new prices, just restores the consumer’s original utility level? Or, after the policy has been implemented, how much must you be compensated to reach the same utility as before the policy? A: The Compensating Variation. Compensating Variation

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31 Compensating Variation x2x2 x1x1 u1u1 p1=p1’p1=p1’p 2 is fixed.

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32 Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

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33 Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

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34 Compensating Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. CV = m 2 - m 1.

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35 p 1 rises. Q: What is the extra income that, at the original prices, just restores the consumer’s original utility level? Or, how much would you pay to avoid moving to the new policy? A: The Equivalent Variation. Equivalent Variation

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36 Equivalent Variation x2x2 x1x1 u1u1 p1=p1’p1=p1’p 2 is fixed.

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37 Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

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38 Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed.

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39 Equivalent Variation x2x2 x1x1 u1u1 u2u2 p1=p1’p1=p1”p1=p1’p1=p1” p 2 is fixed. EV = m 1 - m 2.

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40 Consumer’s Surplus, Compensating Variation and Equivalent Variation When the consumer has quasilinear utility, CV = EV = CS. Why? There are no income effects with quasilinear utility. Otherwise, EV < CS < CV.

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