Change in supply and equilibrium price .

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(c) Assume an infinite horizon, continuous time and certainty. Furthermore, assume an additively separable utility function in consumption C and pollution stock S so that, U(C,S) = u(C) + v(S), where uc > 0; Ucc 0. Note that the first derivative, and the second subscript denotes the second derivative. The evolution of the pollution stock S over time is a function of consumption, decay rate of the stock of pollution & and abatement through the function, g(S) with gs > 0 and 9ss < 0. Time subscripts are ignored for ease of notation. Show that in the case of a stock pollutant, the marginal utility of consumption should equal the present value of disutility associated with the pollution stock. Interpret the condition.

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Chapter 4, Problem 4CQQ

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Change in supply and equilibrium price.

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(c) Assume an infinite horizon, continuous time and certainty. Furthermore, assume an additively separable utility function in consumption C and pollution stock S so that, U(C,S) = u(C) + v(S), where uc > 0; Ucc 0. Note that the first derivative, and the second subscript denotes the second derivative. The evolution of the pollution stock S over time is a function of consumption, decay rate of the stock of pollution & and abatement through the function, g(S) with gs > 0 and 9ss < 0. Time subscripts are ignored for ease of notation. Show that in the case of a stock pollutant, the marginal utility of consumption should equal the present value of disutility associated with the pollution stock. Interpret the condition.

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