14.42/14.420 Midterm 2011 (Solutions)

14.42/14.420 Midterm 2011 Instructions: The test begins at 2:38 and ends at 3:55 by the digital clock. There are two sections: Quantitative and Short Answer. There are 109 points in total, 53 points in the Quantitative section and 54 in the Short Answer section. You may run out of time. Make sure to allocate your time appropriately between the two sections. We expect that the most difficult question is at the end. Part 1: Short Answer Questions Each of these questions has a number of points possible. Typically, a question worth one point will take one sentence to answer, two points might take two sentences, etc. 1. Imagine a project that has benefits that accrue over a long period of time. When doing cost- benefit analysis, there are at least two ways to set the discount rate. Describe each and give a brief justification. (4 points). The market discount rate This reflects the return that we could expect for a dollar of investment today, so if an environmental project returns less it is an inferior investment We might need to risk adjust: some of the market discount rate reflects a risk premium, and returns to environmental projects may not be correlated with the market return. "Intergenerational social discount rate" The market discount rate is "too high" - it gives implausibly low weight to benefits more than a few years in the future. This makes an investment look good if it raises the sum of utility discounted by the rate of time preference б. 2. What is the difference between cost-effectiveness and efficiency? If possible, give examples of outcomes that are efficient but not cost-effective, and outcomes that are cost-effective but not efficient. (4 points) Cost-effectiveness refers to meeting some environmental goal at minimum cost. Efficiency refers to setting that goal at the point that maximizes social welfare. An outcome that is efficient is also cost- effective, so there are no examples of the former type. An outcome that is cost-effective but not efficient might be an emissions trading program that achieves a given level of emissions at minimum cost to industry, but that level of emissions is not the social optimum, ie, not the point where morginal abatement cost is equal to marginal benefit from abatement. 3. Give an example of a Pigouvian tax that has nothing to do with environmental issues. (2 points) One example is congestion pricing on roads: when people drive, they impose congestion on others. The congestion price charges drivers for that externality. 4. Imagine a pollution cap-and-trade program where one firm is responsible for a relatively large share of emissions. Denote by t the marginal social cost of emission abatement at the emissions cap. Imagine further that this large firm is allocated more allowances than the amount of pollution it emits if the allowance price were at t". Do we expect that the allowance price will be less than, equal to, or greater than t"? Why? (2 points) The allowance price will be higher than t". This is because the firm is a net seller, and it exercises market power to keep the price relatively high. It withholds allowances and under-abates. 5. Give three economic reasons why we should not have a cap-and-trade program imposed on automobile drivers for pollution from their cars. (3 points) Three example answers: Each driver would incur administrative costs in complying with the program, and these costs would be high relative to the efficiency gains. The marginal damages vary substantially across time and space, so cap-and-trade program with undifferentiated allowances would not achieve the optimum. The margin on which consumers can most easily adjust is to drive less. This outcome can be achieved through setting optimal gasoline taxes. 6. Give three factors that have determined SO2 allowance prices. Explain how they move allowances prices in one direction or another using economic logic. (6 points) Natural gas prices: higher natural gas prices increase demand for coal-fired electricity, which pushes up demand for allowances and thus increases allowance prices. Additional environmental regulations: information that the cap would be reduced lowers the expected supply of allowance prices, which increases the future expected marginal abatement cost and thus increases allowance prices in the present. Economic growth: Economic growth increases demand for electricity, which increases demand for allowances and increases allowance prices. dE*/dk < 0. k parameterizes the utility losses from one unit of pollution. More utility losses implies lower optimal emissions. a, and a, translate emissions into ambient pollution. If emissions translate into more pollution, the optimal level of emissions should be lower. g. Verify that your solution satisfies the Samuelson Condition for the optimal provision of public goods. (5 points) The Samuelsan Condition is: MRS (P) = MRT(P*) MRS can be thought of as the marginal rate of substitution between dollars of consumption of the numeraire good and units of pollution. MRT is the transformation between dollars of profit and pollution. MRT(E) = A-EB/2 MRT(P)=1/o MRT(E) (This is from equation 14.4 in Kolstad.) MRT(P)= (A+PB/(2a))/a Now plugging these values into the Samuelson Condition: NkP = (A+PB/(20))/0 PA/(B/20+ Nka) Using that P*= 20E": EA/(B+2Nka) This is the same as the socially-optimal level of emissions solved for above. h. What level of Pigouvian tax would generate this social optimum? (2 points) From above, the firm sets E The socially optimal level is E Setting these equal, we have: EA/(B+2Nka) =(Α-τ/Β r*=A-BA/(B+2Nka) (A-1)/B = A/(B+2Nka) i. Let's say we wanted to do a cost-benefit analysis of this Pigouvian tax, relative to no regulation at all. Draw a figure that shows marginal savings and marginal damages from emissions and shade the efficiency gain from the Pigouvian tax. (2 points) (Don't worry about getting the intercepts of the lines correct, but do worry about shading the correct triangles.) The shoded region is the distance between the marginal savings and marginal damages curves between the quantity of emissions where they cross and the quantity at which MS-0.