Section 7 - EEP 101/Econ 125 Section 7 Diana Lee Spring...

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EEP 101/Econ 125 Section 7 Diana Lee Spring 2010 1 Economic Maximization Review Step 1 : Set up the objective function. Identify the choice variable(s). For almost all cases in this class, the objective being maximized will be profit. The choice variable is usually how much to produce, Q, but may be other things too. Sometimes a choice (variable) is dichotomous: this or that, on or off. For profit, remember: Profit = Revenue - Costs + Subsidy Payments - Tax Payments Step 2 : Write down the First Order Conditions (FOCs). Take the first derivative of the objective function with respect to (w.r.t) the choice variable(s) and set equal to zero. Step 3 : Solve the FOCs for choice variables. 2 Conservation Technology Adoption a - Input applied (water or pesticide, say), α - Land quality, some indicator between 0 and 1, h i ( α ) - Input use efficiency, which is some proportion between 0 and 1, i - Type of technology: i = 0 signifying traditional technology, i = 1 signifying modern e = ah i ( α ) - Effective input, y=f(e) - Yield. Given input price w, output price, p, and fixed cost for using technology i, κ i , profits can be expressed as π i = pf ( e ) - wa - κ i . The amount of the input that is not used, z = a [1 - h i ( α )], generates an externality. Suppose the govt imposes a pollution tax of v. Then profits 1
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using technology i are: π i = pf ( ah i ( α )) - wa - va (1 - h i ( α )) - κ i The firms (with differing land quality) choose their optimal input amount and technology. This is solved in two stages: first, find
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