HW_4_Problem_Set - 1. Suppose that Portage County...

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1. Suppose that Portage County Wisconsin’s ground water was contaminated with nitrates, and that two consumers (C1 and C2) live in this famed “sand county”. Below are their individual marginal willingness to pay functions (also known as marginal benefit functions) for a public de-nitrification plant where WTP indicates marginal willingness to pay for each additional unit of treatment and T indicates the level of treatment. Treatment is such that higher levels of treatment increase the purity of water. WTP C1 = 5 – ¼ * T WTP C2 = 5 – ½ * T a. Create a WTP (or marginal benefit) schedule for each consumer at the following treatment levels: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 in which the first column is T, the second column is the WTP for the first consumer, the third column is the WTP for the second consumer, and the 4 th and 5 th columns are identified below. If your calculated WTP is less than zero, then assume that WTP is zero. T WTP C1 WTP C2 WTP C1+C2 MC 0 5 5 10 0 2 4.5 4 8.5 .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 .5 0 .5 4.5 20 0 0 0 5 b. In the 4 th column fill in the aggregate WTP for the two consumers for each treatment level. [above] c. What is the algebraic (linear) formula for this aggregate WTP curve. Note that there may be a kink in the WTP function when WTP C2 falls to zero, so that your formula may take the form of “Over the range of T from zero to XX, the WTP function is ????. From T=XX to YY, the WTP function is ????”. Why does this kink occur? Over the range of T from 0 → 10, WTP C1+C2 = 10 – ¾*T Over the range of T from 10 → 20, WTP C1+C2 = 5 – ¼*T. Over this range of T, WTP C1+C2 = WTP C1. There is a kink in the graph when T=10 and WTP C1+C2 = 2.5 [at the point (10,2.5)] because C2’s willingness to pay (WTP) falls to zero. Since the aggregate WTP curve is formed by combining the WTP curves of C1 and C2, there will be a kink when T=10 because C2 is no longer willing to pay, and the aggregate
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WTP will just be WTP C1 . d. Assume that the marginal cost of treatment (MC) is given by the following function: MC = ¼ * T. In the 5 th column of the schedule, please enter the MC for each of the associated treatment levels. [above]
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HW_4_Problem_Set - 1. Suppose that Portage County...

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