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464math1 - M Muniagurria Econ 464 Microeconomics...

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-1- TECHNOLOGY q L M. Muniagurria Econ 464 Microeconomics Handout (Part 1) I. : Production Function, Marginal Productivity of Inputs, Isoquants (1) Case of One Input : L (Labor): q = f (L) Let q equal output so the production function relates L to q. (How much output can be produced with a given amount of labor?) Marginal productivity of labor = MPL is defined as = Slope of prod. Function Small changes i.e. The change in output if we change the amount of labor used by a very small amount. How to find total output (q) if we only have information about the MPL: “In general” q is equal to the area under the MPL curve when there is only one input. Examples : (a) Linear production functions. Possible forms: q = 10 L | MPL = 10 q = ½ L | MPL = ½ q = 4 L | MPL = 4 The production function q = 4L is graphed below.
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-2- q 8 Notice that if we only have diagram 2, we can calculate output for different amounts of labor as the area under MPL: If L = 2 | = Area below MPL for L Less or equal to 2 = = in Diagram 2 Remark : In all the examples in (a) MPL is constant . (b) Production Functions With Decreasing MPL. Remark: Often this is thought as the case of one variable input (Labor = L) and a fixed factor (land or entrepreneurial ability) (2) Case of Two Variable Inputs : q = f (L, K) L (Labor), K (Capital) • Production function relates L & K to q (total output) • Isoquant: Combinations of L & K that can achieve the same q
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