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**Molly W. Dahl Georgetown University Econ 101 – Spring 2009**

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

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**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 p1 what is the quantity demanded of x1?” But we could also ask the inverse question “Given that the quantity demanded is x1, what must p1 be?”

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**Inverse Demand Functions**

p1 Given p1’, what quantity is demanded of commodity 1? Answer: x1’ units. p1’ x1’ x1*

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**Inverse Demand Functions**

p1 Given p1’, what quantity is demanded of commodity 1? Answer: x1’ units. The inverse question is: Given x1’ units are demanded, what is the price of commodity 1? Answer: p1’ p1’ x1’ x1*

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**Consumer’s Surplus p1 CS**

Consumer’s surplus is the consumer’s utility gain from consuming x1’ units of commodity 1. CS

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**Change in Consumer’s Surplus**

The change to a consumer’s total utility due to a change to p1 is approximately the change in her Consumer’s Surplus.

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**Change in Consumer’s Surplus**

p1(x1), the inverse ordinary demand curve for commodity 1

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**Change in Consumer’s Surplus**

p1(x1) CS before

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**Change in Consumer’s Surplus**

p1(x1) CS after

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**Change in Consumer’s Surplus**

p1(x1) Lost CS

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**In Class: Calculating Consumer Surplus**

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

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

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

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**Producer’s Surplus y Output price (p) S = Marginal Cost Revenue =**

(output units)

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**Producer’s Surplus y Output price (p) S = Marginal Cost**

Variable Cost of producing y’ units is the sum of the marginal costs y (output units)

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**Producer’s Surplus y Output price (p)**

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

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**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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**Cost-Benefit Analysis**

Price The free-market equilibrium Supply p0 Demand q0 QD, QS

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**Cost-Benefit Analysis**

Price The free-market equilibrium and the gains from trade generated by it. CS Supply p0 PS Demand q0 QD, QS

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**Cost-Benefit Analysis**

Price The gain from freely trading the q1th unit. CS Supply Consumer’s gain p0 PS Producer’s gain Demand q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price The gains from freely trading the units from q1 to q0. CS Supply Consumer’s gains p0 PS Producer’s gains Demand q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price The gains from freely trading the units from q1 to q0. CS Supply Consumer’s gains p0 PS Producer’s gains Demand q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price CS Any regulation that causes the units from q1 to q0 to be not traded destroys these gains. This loss is the net cost of the regulation. Consumer’s gains p0 PS Producer’s gains q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss CS pb t Tax Revenue ps PS q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss So does a floor price set at pf CS pf PS q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss So does a floor price set at pf, a ceiling price set at pc CS pc PS q1 q0 QD, QS

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**Cost-Benefit Analysis**

Price An excise tax imposed at a rate of $t per traded unit destroys these gains. Deadweight Loss So does a floor price set at pf, a ceiling price set at pc, and a ration scheme that allows only q1 units to be traded. CS pe pc PS q1 q0 QD, QS Revenue received by holders of ration coupons.

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**Compensating Variation and Equivalent Variation**

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

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**Compensating Variation**

p1 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.

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**Compensating Variation**

p1=p1’ p2 is fixed. x2 u1 x1

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**Compensating Variation**

p1=p1’ p1=p1” p2 is fixed. x2 u1 u2 x1

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**Compensating Variation**

p1=p1’ p1=p1” p2 is fixed. x2 u1 u2 x1

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**Compensating Variation**

p1=p1’ p1=p1” p2 is fixed. x2 u1 CV = m2 - m1. u2 x1

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**Equivalent Variation p1 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.

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Equivalent Variation p1=p1’ p2 is fixed. x2 u1 x1

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Equivalent Variation p1=p1’ p1=p1” p2 is fixed. x2 u1 u2 x1

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Equivalent Variation p1=p1’ p1=p1” p2 is fixed. x2 u1 u2 x1

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**Equivalent Variation EV = m1 - m2. p1=p1’ p1=p1” p2 is fixed. x2 u1 u2**

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**Consumer’s Surplus, Compensating Variation and Equivalent Variation**

When the consumer has quasilinear utility, CV = EV = DCS. Why? There are no income effects with quasilinear utility. Otherwise, EV < DCS < CV.

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