HW 4a - AEM 250 Environmental and Resource Economics...

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AEM 250: Environmental and Resource Economics Homework 4 – Market Failure (Public Goods) SOLUTIONS Distributed: Feb 26, 2007; Due by beginning of class on Mar. 5, 2007 1. a., b., and d. Treatment Level WTP = 5 – ¼ T (Consumer 1) WTP = 5 – ½ T (Consumer 2) Aggregate WTP MC = ¼ T 0 5 5 10 0 2 4.5 4 8.5 0.5 4 4 3 7 1 6 3.5 2 5.5 1.5 8 3 1 4 2 10 2.5 0 2.5 2.5 12 2 0 2 3 14 1.5 0 1.5 3.5 16 1 0 1 4 18 0.5 0 0.5 4.5 20 0 0 0 5 c. Aggregate WTP: Over the range T = 0 to T = 10: Total WTP = WTP C1 + WTP C2 = (5 – ¼ T) + (5 – ½ T) Total WTP = 10 – ¾ T Over the range T = 10 to T = 20: Total WTP = WTP C1 = 5 – ¼ T The kink in the function occurs because consumer 2 only has a positive WTP for up to 10 units of treatment. At 10 units this WTP=0. e. By inspecting the table, we can see that the marginal benefits (Total WTP) equals the marginal costs at a treatment level of T = 10. At this treatment level, the MC is $2.50 and the WTP is $2.50. We could also find this by setting the WTP function equal to the MC function: 10 – ¾ T = ¼ T 10 = T
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NOTE: YOU SHOULD THINK FURTHER ABOUT VARIANTS TO THIS QUESTION AS THE SOLUTION OCCURS EXACTLY AT THE KINK IN THE CURVE WHEREIN YOU COULD USE THE TOTAL WTP FUNCTION FOR THE [0,10] RANGE OR THE TOTAL WTP FOR THE T> RANGE. What would happen if MC=1/2 T (Hint: the intersection of MC and Total WTP curve would occur at a point less than T=10. Thus the appropriate Total WTP function would be Total WTP =10-3/4 T.) What would happen if MC=1/8 T (Hint: the intersection of MC and Total WTP curve would occur at a point greater than T=10. Thus the appropriate Total WTP function would be Total WTP =5-1/4 T.) 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. Number of Wells Daily Output (gallons) Total Revenue Average Revenue per Well Marginal Revenue per Well 10 100,000 10,000 1,000 1,000 20 200,000 20,000 1,000 1,000 30 280,000 28,000 933 800 40 340,000 34,000 850 600 50 380,000 38,000 760 400 60 400,000 40,000 667 200 70 400,000 40,000 571 0 80 380,000 38,000 475 -200 90 340,000 34,000 378 -400 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
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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.
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