1 Econ 4545 Environmental Economics Review Questions- Set 4 Global Warming, Discounting, Present Value, Social Rate of Discount, etc. 1. What is the present value of $50,000/yr for 20 years if the discount rate is .10? As part of your answer, define present value and discount rate. Why is the present value of this stream less than $1,000,000? Show all of your calculations and explain them in words. Answer: I am going to answer this and the next question assuming discrete discounting, what was presented in class. Simply put, present value is the value today of some stream of net benefits through time: what it is worth today. For example, the present value of $1 received today is $1, the present value of a $1 received a year from today is $1/(1+r) where r is the discount rate, and the present value of a $1 received a year ago is $1(1+r). The present value of $n received t years from today is trn )1/($ + . In explanation, r and the discount formula identify the rate at which the economic agent in question (individual, society, etc.) trades off net benefits of the same magnitude received today and in the future. Consider the general formula for a net benefit of $n in period t, trn )1($ + , where t=0 is the present, t<0 is t years in the future, and t>0 is t years in the past. In explanation, r and the discount formula identify the rate at which the economic agent in question (individual, society, etc.) trades off net benefits of the same magnitude received today and in the future.1 1 As an aside, one can also treat time as a continuous rather than a discrete flow. In which case ∫∞=−=0)(trtdttNBPV where )(tNB is the net benefit at point in time t.2 Put simply, discounting using the above formula assumes we discount such that present value is reduced by the same percent for each year the payment occurs in the future. Maybe this is not how preferences work. If r = .10, the present value of $50,000/yr for 20 years, starting now, is 8175......322,41454,45000,50250,468$)10.1/(000,50)10.1/(000,50...)10.1/(000,50)10.1/(000,50000,50190192++++===++++∑=tt. This PV of this stream is less that $1 million because with a positive discount rate benefits received in the future are “discounted” (worth less) than if they were received today, and discounted more the farther in the future they occur. That is, the discounter cares less about a net benefit in the future than they do about a net benefit of the same magnitude today, and the farther in the future the less they care about it today. Interestingly, many students answered the question assuming the 20 payments would start next year, rather than today. This obviously leads to a smaller PV, one losses 50,000 for the payment today) and gains 7,432 for the payment 20 years from now. 2. How much will you have in the bank after three years if you invest $1 in the bank today and the market rate of interest is 5%? Continuing to assume a market rate of interest of 5%, what is the present value of a $1 received four years from now? Show all of your calculations and explain them in words. Answer: 1576.1$)05.1(1)05.1))(05.1))(05.1(1((3==+++ The present value of a $1 received four years from now is 8227$.)05.1/(14= 3. Define the term social rate of discount, and discuss its significance for environmental policy making.34. Argue that it is not worth it to allocate current resources to reducing global warming. 5. Argue that significant resources should be allocated to reducing global warming. 6. What, if anything, do you think should be done about global warming? 7. What is global warming, what causes it, and why? 8. List some possible benefits of global warming. 9. Argue that it would be better to allocate resources to reducing poverty in those developed countries likely to be most effect by global warming than to allocate resources to reducing global warming. 10. What does a negative rate of discount imply? A rate of zero? 11. How would you determine the present value of a stream of benefits and costs? 12. Assume that the U.S. must reduce the emissions of greenhouse gases to pre-1990 levels. Suggest a method of accomplishing this task at minimum cost (efficiently) and explain why it accomplishes the task at minimum cost. 13. Provide at least four reasons why the social rate of discount should be positive. 14. At what rate do you think society should discount the future? 15. Assume that the U.S. must reduce the emissions of greenhouse gases to pre-1990 levels. Discuss the efficiency and equity implications of achieving this goal using a global permit system for greenhouse gas emissions (CO2, N2O and CH4). How might such a system work? Would such a system require different permits for different gases? As part of your discussion, consider the efficiency, equity, and political implications of different rules for distributing the permits. 16. Why are market rates of interest positive? 17. Is global warming the result of a market failure? If so, what kind and why? 18. Are automobiles a significant contributor to the production of greenhouse gases? If so, how and why? What would need to be done to reduce their contribution. Suggest a feasible method of reducing the amount of CO2 emissions produced by cars. Why are car makers concerned about policies to reduce the rate of global warming? 19. Is the cost of global warming a function of the rate of warming? Yes or no, and explain why?420. Briefly outline how the costs and benefits of global warming are likely to be distributed by location, income level, and generation. 21. Are greenhouse gases stock or flow pollutants? What are the policy implications of your answer? 22. Is there anything good about that fact that greenhouse gases are global pollutants? As part of your answer define global pollutants. 23. Could some pollutants partially offset the impact of increasing concentrations of greenhouse gases on global warming? 24. Is the marginal cost of decreasing the emissions of greenhouse gases likely greater or smaller in developing versus developed countries? Why? What are the implications for reducing these emissions in the minimum cost way? 25. Assume significant resources should be allocated to reduce CO2 emissions. Where should they be allocated on efficiency grounds and why? Assume your audience is students in a principles micro course. Convince them of your answer. Is your conclusion “as to where” fair.