1. Utility and Social Choice
1. Suppose your utility function has two inputs: studying time (s) and 'leisure' time (l). Draw a set of indifference curves (say 3 of them) representing your preferences with studying on the y-axis and leisure on the x-axis. Be honest.
2. Suppose you have a society of n identical individuals and the environment. Each individual likes his or her material possessions as well as access to parks and wilderness areas. In fact, the utility function of each individual is given by: U(x, H) = x + H - 1/x - 1/H.
where x is consumption goods and H is environmental health. H attains its highest level when it is pristine: H = 100. Consumption of goods degrades the environment but the environment has some ability to heal itself. In fact, the environment has health: Ht = Ht-1 + g(100 - Ht-1) - nx, where Ht is todays level of H and Ht-1 is yesterday's level. The environment's ability to cleans itself, g, is fixed. Answer the following questions. Hint: although not required, you may find that spreadsheet software such as excel will help with this problem.
(a) Suppose we start at H = 100. Assume g = 1 and n = 1. Plot how H would evolve for x = 0.01, 0.1, 1, and 2.
(b) Repeat part (a), except plot the utility function U instead. Feel free to try other values of x. Can you reach any conclusion about the level of consumption that maximizes utility?
(c) How would the optimal consumption be different if the ability of the environment to clean itself, g, decreases? How about if the number of people in the economy, n, increases?
3. Suppose we have a small inhabited island with three residents and a volcano that generates air pollution.
Two people live upwind of the volcano and one person lives downwind. For $21,000 we can clean up the volcano with a patented "smoke guzzler". The two upwind people would pay $1,000 each to get rid of the smoke whereas the downwind person would be willing to bay $15,000. Consider two plans to finance the "smoke guzzler". Plan A calls for a head-tax of $7,000. Plan B calls for the affected party (the downwind person) to pay $21,000 and everyone else nothing. Compare each plan to the status quo and indicate society's choosing using:
(a) the Pareto criterion
(b) the majority rule
(c) potential Pareto improvement.
4. In the Figure on the next page, using the Pareto criterion, which of the labeled points are social preferred to W? Explain your answer.
2. SO2 Cap-and-Trade
1. Briefly explain how the Cap-and-Trade system worked.
2. What was the goal of the SO2 Cap-and-Trade system? (generally speaking).
3. Draw a graph for the market for SO2 tradable permits (supply and demand). Make the supply of permits is fixed at the CAP and the demand downward sloping.
(a) From 2006-2010, the demand for permits started to drop. Demonstrate how this affected the price of permits using your graph.
(b) What are some of the possible explanations for this drop in demand?
4. The Cap-and-Trade program reduced emissions of SO2 by nearly 60% in 20 years. Is this a positive or a normative statement?
5. The success of the SO2 program implies that we can reduce CO2 emissions by 60% using a Capand-Trade program. Is this a positive or normative statement? What are some of the flaws in this argument?
