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AGEC 608: Lecture 12. Objective: Illustrate how to value project impacts via direct estimation of demand curves Readings: Boardman, Chapter 12 Homework #4: Chapter 7, problem 3 Chapter 10, problems 1 + 2 Chapter 13, problem 3 due: April 10 Homework #5: T.B.A. due: April 24.
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AGEC 608: Lecture 12 • Objective: Illustrate how to value project impacts via direct estimation of demand curves • Readings: • Boardman, Chapter 12 • Homework #4: Chapter 7, problem 3 Chapter 10, problems 1 + 2 Chapter 13, problem 3due: April 10 • Homework #5: T.B.A. due: April 24
Direct estimation of demand curves Measurement of changes in social surplus are given by the triangles and trapezoids bounded by the supply and demand curves. Estimating these areas is relatively straightforward when we know the shape and position of the supply and demand curves. Given adequate empirical data, the shape and position of these curves can be obtained using statistical procedures.
Linear demand Quantity demanded (q) can be written as a function of price (p): q = a + b*p a = demand when price is zerob = change in demand as a result of increase in price If you know one point on the demand curve, and the slope, you can easily compute other points on the demand curve.
Linear demand If the demand curve is linear, then the elasticity changes along the curve, and depends on the price and quantity. The price elasticity εd measures how “responsive” demand is to changes in price. The more responsive, the higher the elasticity. εd = (Δq/Δp)*(p/q) For a linear demand curve: εd = b*(p/q).
Linear demand: example Demand for refuse disposal under a fee system: Town A Current cost of disposal = $0Current rate of disposal is 2.60 lb/p/dCurrent marginal cost = $0.06/lb (= collection cost + tipping fee) Current cost of disposal < MC If fee is levied at $1 per 20 lb container of waste, what will be the change (increase) in social surplus? (Note: fee of $0.05/lb < MC, but the fee will still increase surplus by reducing amount of waste generated).
Linear demand: example We only know 1 point on demand curve (p=0, q=2.60) Use data from study by Jenkins to estimate demand curve 9 communities with fees from $0 to $1.73 $1 increase in fee (per container) reduced waste by 0.40 lb/p/d on average The estimate of b = -0.40 If fee of $1/container ($0.05/lb) is introduced, demand (waste) will fall from 2.60 to 2.20 lb/p/day. See Figure 12.1
Linear demand: example Change in surplus: abc = social surplus loss at p = 0 = 0.5(2.6-2.12)(0.06-0.00) = $0.0144 /p/d aed = social surplus loss at p = $0.05 = 0.5(2.2-2.12)(0.06-0.05) = $0.0004 /p/d debc = net gain in surplus from the price increase = 0.0144 – 0.0004 = $0.014 /p/d for 100,000 people, gain in surplus is: ($0.014 )(365 days)(100,000) = $511,000
Linear demand How valid is this approach? 1. Internal validity: Is the design appropriate? Are the econometric methods appropriate? Is demand linear? 2. External validity: Are the data from Jenkins’ study applicable to our example? Time periods covered Similarity of study sites Out of sample prediction
Non-linear demand For linear demand, elasticity is non-constant: it depends on the price and quantity at which the elasticity is estimated. Many studies suggest that this is an inappropriate assumption: for many goods, price elasticity is closer to constant over a relevant range of prices. A demand curve with constant elasticity of demand is: q = apb or ln(q) = ln(a) + b*ln(p)
Non-linear demand If the demand curve has constant elasticity, then the elasticity does not depend on price and quantity. The price elasticity εd measures how “responsive” demand is to changes in price. The more responsive, the higher the elasticity. εd = (Δq/Δp)*(p/q) For a constant elasticity demand curve: εd = b
Non-linear demand: example Demand for refuse disposal under a fee system: Town B Current cost of disposal = $0.05 lb/p/dCurrent rate of disposal is 2.25 lb/p/dCurrent marginal cost = $0.06/lb (= collection cost + tipping fee) Current cost of disposal < MC If fee is raised to $0.08 lb/p/d what will be the change (loss) in social surplus (assuming demand has a constant elasticity form)?
Non-linear demand: example Assume previous research shows price elasticity of -0.15 We only know 1 point on demand curve (p=0.05, q=2.25) a = (2.25)/(0.05) -0.15 a≈ 1.44 So demand curve is: q = 1.44p-0.15 If price is increased to 0.08, then q will fall to: q = 1.44(0.08)-0.15 q ≈ 2.10 lb/p/day (See Figure 12.2)
Non-linear demand: example Change in consumer surplus is represented by the area fbag bah = CS lost on garbage previously dumped = abcd – hadc = $0.0022fbhg = increase in fees on remaining quantity = (0.08 – 0.05)(2.12) = $0.636Net impact = loss of $0.0652 /p/d For population of 100,000 ($0.0652 )(365)(100,000) = $2.38 million Main drawback with constant elasticity demand curve: if initial price = 0, then it is impossible to use the elasticity estimate
Non-linear demand: example Main drawback with constant elasticity demand curve: if initial price = 0, then it is impossible to use the elasticity estimate
Issues in estimation 1. Level of aggregation in data 2. Cross-section data (heteroskedasticity problems) 3. Time series data (autocorrelation problems) 4. Panel data (cross-section + time series) 5. Endogeneity and the identification problem 6. Statistical precision and confidence intervals 7. Prediction (BCA) vs. hypothesis testing (statistics)
