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Chapter 14 Consumer ’ s Surplus

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2 Monetary Measures of Gains-to-Trade You can buy as much gasoline as you wish at $1 per gallon once you enter the gasoline market. Q: What is the most you would pay to enter the market? A: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market. How can such gains-to-trade be measured?

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3 Three such measures are: Consumer’s Surplus Equivalent Variation, and Compensating Variation. Only in one special circumstance do these three measures coincide. Monetary Measures of Gains-to-Trade

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4 Suppose gasoline can be bought only in lumps of one gallon. Use r 1 to denote the most a consumer would pay for a 1st gallon -- call this her reservation price for the 1st gallon. r 1 is the dollar equivalent of the marginal utility of the 1st gallon. Equivalent Utility Gains

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5 Now that she has one gallon, use r 2 to denote the most she would pay for a 2nd gallon -- this is her reservation price for the 2nd gallon. r 2 is the dollar equivalent of the marginal utility of the 2nd gallon. Equivalent Utility Gains

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6 Generally, if she already has n-1 gallons of gasoline then r n denotes the most she will pay for an nth gallon. r n is the dollar equivalent of the marginal utility of the nth gallon. Equivalent Utility Gains

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7 r 1 + … + r n will therefore be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $0. So r 1 + … + r n - p G n will be the dollar equivalent of the total change to utility from acquiring n gallons of gasoline at a price of $p G each. Equivalent Utility Gains

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r1r1 r2r2 r3r3 r4r4 r5r5 r6r6

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9 What is the monetary value of our consumer’s gain-to-trading in the gasoline market at a price of $p G ? Equivalent Utility Gains

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10 The dollar equivalent net utility gain for the 1st gallon is $(r 1 - p G ) and is $(r 2 - p G ) for the 2nd gallon, and so on, so the dollar value of the gain-to- trade is $(r 1 - p G ) + $(r 2 - p G ) + … for as long as r n - p G > 0. Equivalent Utility Gains

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11 Equivalent Utility Gains r1r1 r2r2 r3r3 r4r4 r5r5 r6r6 pGpG $ value of net utility gains-to-trade Consumer’s surplus or Net consumer’s surplus

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12 If gasoline can be purchased in any quantity then... Equivalent Utility Gains

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13 Equivalent Utility Gains Gasoline ($) Res. Prices pGpG Reservation Price Curve for Gasoline $ value of net utility gains-to-trade

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14 Unfortunately, estimating a consumer’s reservation-price curve is difficult, so, as an approximation, the reservation-price curve is replaced with the consumer’s ordinary demand curve. This approximation gives the Consumer’s Surplus measure of net utility gain. Equivalent Utility Gains

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Quasi-Linear Utility One special case would be quasi-linear utility. With quasi-linear utility, calculating CS using the reservation-price curve will result in the same value with that using the ordinary demand curve. 15

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16 CS for Quasi-linear Utility Ordinary demand curve, p1p1 CS is exactly the consumer’s utility gain from consuming x 1 ’ units of commodity 1.

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Change in CS Now, what if there is a change in one of the prices? How would a price change affect the consumer’s surplus? 17

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18 Consumer ’ s Surplus p1p1 p 1 (x 1 ), the inverse ordinary demand curve for commodity 1

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19 Consumer ’ s Surplus p1p1 CS before p 1 (x 1 )

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20 Consumer ’ s Surplus p1p1 CS after p 1 (x 1 )

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21 Consumer ’ s Surplus p1p1 Lost CS p 1 (x 1 ), inverse ordinary demand; x 1 *(p 1 ), the consumer’s ordinary demand for commodity 1. measures the loss in Consumer’s Surplus.

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22 Two additional dollar measures of the total utility change caused by a price change are compensating variation (CV) and equivalent variation (EV). Compensating Variation and Equivalent Variation

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23 p 1 rises. Q: What is the least extra income that, at the new prices, just restores the consumer’s original utility level? Compensating Variation

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24 p 1 rises. Q: What is the least extra income that, at the new prices, just restores the consumer’s original utility level? A: The Compensating Variation. Compensating Variation

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

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

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

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28 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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29 p 1 rises. Q: How much money would have to be taken away from the consumer before the price change to leave him just as well off as he would be after the price change? A: The Equivalent Variation. Equivalent Variation

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

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

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

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33 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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CV and EV Both CV and EV measure “how far apart” two indifference curves are. Depend on the slope of the tangent line. CV does not equal EV in most cases. Only in quasilinear utility. Why? The distance of two indifference curves is the same no matter where it is measured. CV = EV = △ CS 34

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

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36 Producer ’ s Surplus y (output units) Output price (p) Supply Curve

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37 Producer ’ s Surplus y (output units) Output price (p) Supply Curve

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38 Producer ’ s Surplus y (output units) Output price (p) Supply Curve Producer’s Surplus.

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