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eep101ps4 _1_

# eep101ps4 _1_ - Problem Set —4 Due Date 1 Environmental...

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Unformatted text preview: Problem Set —4 Due Date: 05/06/2010 1. Environmental Kuznets Curve: A researcher testing for the existence of Environmental Kuznets Curve in 002 emission Latin America uses data from 15 countries over 40 years.She claims that there exists "N"-shaped curve for 002. Explain what this shape implies regarding individual’s consumption of 002 as a function of their income. (2) Hotelling’s Rule for Nonrenewable Resources extraction 1 Consider inverse demand function, p(q) = qi. Suppose the interest rate is r, and solve for this two period model: max p(q1)q1 + 1—lTP(q2)q2 (11,42 where q1 + q2 = 1, and r = 0. Solve for his optimal rate of extraction and the price he charges. Repeat this exercise for a competitive ﬁrm by replacing inverse demand function p(q,-) 2 p,. (a) Find the elasticity of demand function faced by the monopolist. Is it constant? (b) Are the price evolution under monopoly same as in competitive case? (c) Does your result for (b) change if r2005? (3)Pesticide Economics. A representative farmer faces a production func— tion of a particular crop f (:13,A) = Qx‘J‘AB where (2,05, ,3 are parameters, and x is the level of pesticide used in the ﬁeld and A is another input which costs 1) dollar per unit. The pesticide is pestillential, and the risk factor from farm to household is given by following functions: health risk in farm activities is given by f (B1,.r) = \$4331, risk due to aversion activities off ﬁeld is given by f (B2) = 3% and risk from medical treatment, f (B3) = Bis. All these three risks are independent, so total probability of incurring health risk is the product of these three risks, and the cost function for risk is given by CO“) 2 7T2 — 7' where ”y is a scalar parameter. Total joint cost of implementing prevention scheme (31,32,33) is given by C(Bl, B2, B3) = 313233. Price of pesticide per unit is w. (a) Set up the optimization problem for the representative farmer. (b) Derive the ﬁrst order conditions. (4) Risk Aversion And Willingness To Pay(WTP) When a risk averse person is facing uncertain future, he is willing to pay a certain amount (risk premium) to avoid the uncertainty. Suppose people of a region A are facing with a threat by a monster, M, which threatens to release a poisonous material M. The economic impact of this material is known probabilistically (i.e. they know the distribution of this impact). If people of region A are known to be risk averse, will their WTP to avoid this threat by the monster be equal to the risk premium? (While answering this question, discuss the difference between WTP and risk premium.) ...
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