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practice_midterm - Practice Midterm I Short Answer 1 10 You...

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Practice Midterm I. Short Answer 1. (+10) You are the Director of the Los Angeles Environmental Agency. The only source of emissions in the city is vehicles. Your Statistics nerds have given you the following information. 1990 2008 2030 Population (in Millions) 4 6 8 Probability own Vehicle .90 .95 1 Annual Miles Driven Conditional that own vehicle in 1000s 10 12 Q Average Emissions per Mile 4 X Z You have promised the Mayor to reduce vehicle emissions in 2008 and 2030 back to 1990s levels. Solve for X such that you achieve this goal. If you expect that Q will equal 14, what must Z equal to achieve this goal? Briefly explain the role of scale and technique effects in determining pollution levels. 2. Mike owns one tree. Its height, measured in feet, is a function of the tree’s age, measured in years, with production function ( 29 age Feet 50 = . Assume that the real price per foot of wood is always equal to \$40. Suppose the cost of cutting down the tree is \$10. (note that this is a fixed cost) Assume that the interest rate always equals 4%. Mike’s goal is to maximize the PDV of his profits. a. (+4) Write down the profit function as a function of age, and describe how you will find the optimal tree cutting age. (you need not actually find the age)

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b. (+4) Now suppose the interest rate is increase to 8% permanently. Will the optimal tree cutting age increase or decrease? Explain. (You need not solve for the new optimum) c. (+4) Now suppose that each year there is a 8 1 ( or 12.5%) chance that Kahn will sneak into the forest and cut down Mike’s tree. In which case Mike will receive \$0. Assume the interest rate is 8%. Write down the new profit function and describe how you will find the optimal tree cutting age. (Again you need not actually solve for the optimum, just characterize the solution) d. (+5) Will the optimal tree cutting age be sooner or later in question (c) than in question (b)? Explain. 3. Consider two vehicles called the Prius and the Hummer. Assume the Prius will get 40mpg and the Hummer will get 10mpg (miles per gallon). Assume gasoline is \$2.00 per gallon: Roundtrip Distance to Work Roundtrip Distance to the Beach Chris 1 mile 10 miles Jeff 11 miles 0 miles Assume they each drive to work 5 days a week, and go to the beach once a week. Chris’ green friends convince him to sell his Hummer to Jeff and buy a Prius. Can you determine if Chris’ decision decreased the total carbon footprint in Los Angeles? If not, what else would you need to know? 4. A steel factory produces 3 units of pollution for every unit of steel it produces. If 400 identical people live near the factor and each suffers 2 sick days per unit of pollution exposure. Suppose each person values not being sick at “w” dollars per sick day. a. (+5) If the steal factory produces “X” units of steel each year, write down an expression for the total monetary value of the yearly aggregate damage that this firm is causing by its pollution? (The answer will be in terms of “X” and “w”)
b. (+5) Assume that X=100. The city has recently unanimously passed a measure to

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