Lecture11 -2012Welfare Measures POST [Compatibility Mode](1)

# Lecture11 -2012Welfare Measures POST [Compatibility...

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1 Welfare Effects of Price Changes Consumer Surplus Compensating Variation, and Equivalent Variation (B&B Chapter 5) Notes for Lecture #11 Northwestern University ¤ Econ 310-1: Microeconomics Theory ¤ Professors Jim Hornsten and Ron Braeutigam

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2 Consumer Surplus An individual must pay \$10 per hour for court time to play tennis. Suppose her monthly demand curve for court time is: P, price of court time Q, number of hours of court time 25 10 2 23 Demand 21 19 17 15 13 11 9 7 34 5 67 89 1 10 Hour Willingness to pay (\$) Price (\$) Consumer Surplus (\$) 12 5 1 0 15 22 3 1 0 13 32 1 1 0 11 41 9 1 0 9 51 7 1 0 7 61 5 1 0 5 71 3 1 0 3 81 1 1 0 1 All 144 80 64 The consumer surplus is the area under the demand curve and above the price the consumer must pay for each unit consumed. Northwestern University ¤ Econ 310-1: Microeconomics Theory ¤ Professors Jim Hornsten and Ron Braeutigam
3 Consumer Surplus (Smooth Demand Curve) Question: How do we measure the monetary value that a consumer places on a change in a price? Suppose the consumer's monthly demand curve for milk is: Q = 40 - 4P P = price in \$/gallon Q = number of gallons / month Question: What is the consumer surplus when the price is \$3? Answer: Area of triangle G. This area is (0.5)(10 - 3)(28)=\$98. Question: What is the increase in consumer surplus if price drops from \$3 to \$2? Answer: Consumer surplus increases by H + R = \$28+ \$2 = \$30. Observation: It turns out that consumer surplus is a correct measure of the welfare effect of a price change when there is a zero income effect. When the income effect is positive or negative, consumer surplus does not exactly measure the welfare effect of a change in price. We may need to measure the welfare effect using more exact measures compensating variation or equivalent variation. Northwestern University ¤ Econ 310-1: Microeconomics Theory ¤ Professors Jim Hornsten and Ron Braeutigam P, price of milk (\$/gallon) Q, number of gallons of milk Demand for Milk 3 2 G H R 28 32 40 10

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y x A B C U 2 =324 U 1 =144 4 6 9 36 72 24 Initial BL Slope = -9 CV Decomposition BL Slope = - 4 Final BL Slope = - 4 48 4 Demand: Nonzero Income Effect Suppose price decreases: P x1 =\$9 P x2 =\$4 How can we see that there is a nonzero income effect when the price falls from 9 to 4? Given: I = \$72 per day. P y = \$1. The demand curve is x = 36/P x (see text, Learning-By-Doing Exercise 5.2). Basket x y U(x,y) MU x /MU y =P x /P y Expenditure = P x •x+P y •y A (initial) 4 36 144 9 9(4)+1(36)=72 B 6 24 144 4 4(6)+1(24)=48 C (final) 9 36 324 4 4(9)+1(36)=72 Northwestern University ¤ Econ 310-1: Microeconomics Theory ¤ Professors Jim Hornsten and Ron Braeutigam 0 2 4 6 8 2468 1 0 Quantity of Food Demand for Food 36 x x P Price of Food 9 Example: U = xy If we measure the shaded area to estimate the monetary value of the increase in welfare, we would calculate an increase in “consumer surplus” of \$29.2.
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Lecture11 -2012Welfare Measures POST [Compatibility...

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