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lect6

lect6 - Production and Cost Functions Intermediate...

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Production and Cost Functions Intermediate Microeconomics Amy Brown University of California, Los Angeles August 25, 2008 A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 1 / 39

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Outline of Lecture 1 Production Functions of Single Output 2 Graphical Representation of Production Function 3 Marginal Rate of Technical Substitution 4 Returns to Scale 5 Production Possibility Frontier 6 Break 7 Cost Minimization This should cover chapters 7-8 in the 9th edition, chapters 9-10 in the 10th edition A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 2 / 39
Theory of Production and Supply Production of goods and services takes place inside °rms . Microeconomics studies how market prices in°uence production decisions. Characterize ±rm as a process using a given set of inputs to produce other goods as outputs. De±nition A production function describes the production possibilities by determining the output obtainable for given quantities of inputs. A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 3 / 39

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Rationality Principle We abstract from the processes of decision-making within a ±rm, assume these are optimal. A ±rm is de±ned by its technology for transforming inputs into outputs. The de±nition reduces the ±rm to a mathematical description. Example Suppose we have a ±rm that makes cars. Then that ±rm makes the single output, "cars," from the two inputs "capital" and "labor." q = f ( k , l ) A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 4 / 39
Marginal Product of an Input Measures the change in output due to a marginal change in an input. MP k = f ( k , l ) k MP l = f ( k , l ) l Usually assumed to be decreasing in the input. 2 f ( k , l ) k 2 < 0 2 f ( k , l ) l 2 < 0 A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 5 / 39

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Isoquant Curves De±nition Isoquant curves represent a production function by its level curves, or the quantities of the inputs that can produce a given level of output. Shape of the isoquants determines the substitutability of inputs in a given production function. A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 6 / 39
Marginal Rate of Technical Substitution De±nition The marginal rate of technical substitution is the ratio of marginal products of inputs, measuring the slope of the isoquant. MRTS l , k = f ( k , l ) l f ( k . l ) k = MP l MP k Another use of the implicit function theorem. ° dk dl ° ° ° ° f ( k , l )= q = f ( k , l ) l f ( k . l ) k Measures the rate at which inputs can be substituted for each other. A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 7 / 39

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Assumption About Marginal Rate of Technical Substitution Assume that MRTS is decreasing. As the ratio of k to l increases, the marginal product of capital decreases relative to the marginal product of labor. Gives us the shape of the isoquant curves. A. Brown (UCLA) Econ 11 Lecture 6 08/25/08 8 / 39
Elasticity of Substitution De±nition For a production function f ( k , l ) , the elasticity of substitution ( σ ) measures the proportionate change in k l relative to the proportionate change in the MRTS along an isoquant.

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