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ERE HW 4 Solution

# ERE HW 4 Solution - AEM 2500(Fall 2009 Environmental and...

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AEM 2500 (Fall 2009): Environmental and Resource Economics Homework 4 – Market Failure (Public Goods) SOLUTIONS 1. a., b., and d. Treatment Level WTP = 6 - T (Consumer 1) WTP = 6 - ½T (Consumer 2) Aggregate WTP MC = T 0 6.00 6 12.00 0 2 5.33 5 10.33 2 4 4.67 4 8.67 4 6 4.00 3 7.00 6 8 3.33 2 5.33 8 10 2.67 1 3.67 10 12 2.00 0 2.00 12 14 1.33 0 1.33 14 16 0.67 0 0.67 16 18 0.00 0 0.00 18 20 0.00 0 0.00 20 c. Aggregate WTP: Over the range T = 0 to T = 12: Total WTP = WTP C1 + WTP C2 = (6 – T) + (6 – ½ T) Total WTP = 12 – 5/6 T Over the range T = 12 to T = 20: Total WTP = WTP C1 = 6 – T The kink in the function occurs because consumer 2 only has a positive WTP up to 12 units of treatment. At 12 units this WTP=0. After 12 units, consumer 2 has dropped out of the market, so the aggregate WTP is equal to consumer 1’s WTP. e. By inspecting the table, we can see that the marginal benefits (Aggregate WTP) equals the marginal costs at a treatment level between T = 6 and T = 8. We could also find the exact point by setting the WTP function equal to the MC function: 12 – 5/6*T = T 6.55 = T

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NOTE: YOU SHOULD THINK FURTHER ABOUT VARIANTS TO THIS QUESTION AS THE SOLUTION OCCURS ABOVE THE KINK IN THE CURVE WHEREIN YOU USED THE TOTAL WTP FUNCTION FOR THE [0,12] RANGE. What would happen if MC=1/10 T (Hint: the intersection of MC and Total WTP curve would occur at a point greater than T=12. Thus the appropriate Total WTP function would be TotalWTP = 6- T.) What would happen if Total WTP and MC intersected exactly at the kink in the WTP curve? Graph of WTP C1 , WTP C2 , WTP TOTAL and MC
2. (Answers adapted from Harris, 2006) a. The output, total revenue, average revenue, and marginal revenue (in pesos) for each number of wells is expressed in the table below. Note that the marginal revenue is the value between two values. For example, the marginal revenue of 600 pesos for 40 wells is actually the marginal revenue per well between 30 and 40 wells. The value of 600 is obtained by taking the difference between the total revenue at 30 wells and the total revenue at 40 wells, and dividing by 10. b. If each well is independently operated, farmers will operate their well as long as their revenue exceeds their costs, which are given as 600 pesos per well. So, if revenue per well is above 600 pesos, farmers will continue to operate their wells. Average revenues are around 600 pesos between 60 and 70 wells, meaning that between 60 and 70 wells will operate when the wells are subject to free market conditions. This number of wells is greater than the economically efficient outcome because wells are brought into operation past the point where marginal costs exceed marginal revenues. This number of wells is also not ecologically sustainable because a daily withdrawal of around 400,000 gallons per day exceeds the natural recharge rate of 340,000 gallons per day. c. The economically efficient number of wells sets marginal revenue equal to marginal cost. With a marginal cost per well of 600 pesos, the economically efficient number of wells is between 30 and 40 wells (the marginal revenue of 600 pesos occurs between 30 and 40 wells). We can calculate the net social benefit by

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subtracting the total cost from the total revenue, as shown in the table below. The
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