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Handout 2 - University of Minnesota Department of Economics...

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University of Minnesota Department of Economics Econ 3102: Intermediate Macroeconomics Handout 2 This handout continues the job of Handout 1. Here we talk about the firm’s problem. 1 The representative firm’s problem We saw in class that our representative firm had a production function of the form Y = zF ( K, N d ) . Prior to characterizing the solution to the profit-maximization problem, I’d like to make a small detour and stress out the constant returns to scale assumption. As given in class, constant returns to scale is defined as follows: Definition 1.1. A production function Y = zF ( K, N d ) has constant returns to scale (CRS) if for any number λ > 0, we have that zF ( λK, λN d ) = λzF ( K, N d ) . In other words, if the production function exhibits CRS then changing all inputs by a factor λ changes the output by the same factor λ . 2 Characterizing the profit-maximizing labor demand In class we defined the marginal products of capital and labor as the additional output that
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