lect7 - Production Functions Intermediate Microeconomics...

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Unformatted text preview: Production Functions Intermediate Microeconomics Amy Brown University of California, Los Angeles August 25, 2008 A. Brown (UCLA) Econ 11 Lecture 7 08/25/08 1 / 37 Outline of Lecture 1 Pro&t Maximization 2 Supply and Input Demand 3 Producer Surplus 4 Applications of Producer Theory to Growth 5 Break 6 Market Equilibrium 7 Demand and Supply Elasticities 8 E ciency and Welfare 9 E/ects of Taxation 10 E/ects of Trade Restrictions This should cover chapter 9-10 in the 9th edition, chapter 11-12 in the 10th edition A. Brown (UCLA) Econ 11 Lecture 7 082508 2 37 Review of Production Functions De&nition A production function describes the production possibilities by determining the output obtainable for given quantities of inputs. This lecture will describe how we &nd these and their relationship to cost functions. How does a &rm choose its level of output? A. Brown (UCLA) Econ 11 Lecture 7 08/25/08 3 / 37 Pro&t Maximization The &rms motive is maximizing pro&t . De&nition Pro&t is the &rms revenue less its costs. In order to determine how much input to demand and output to supply, the &rm must solve ( k , l ) = Pf ( k , l ) & vk & wl which is a simple maximization problem in two variables, giving us &rst order conditions ( k , l ) k : P f ( k , l ) k & v = ( k , l ) l : P f ( k , l ) l & w = A. Brown (UCLA) Econ 11 Lecture 7 08/25/08 4 / 37 Marginal Products in Pro&t Maximization Notice that the marginal products of capital and labor appear in the &rst order conditions of our pro&t maximization problem. The &rst order conditions give us: P f ( k , l ) k = P & MP k = v P f ( k , l ) l = P & MP l = w So we see that the producer will choose inputs such that the value of their marginal product is equal to the marginal cost of hiring that input. Just as before, we de&ne our input demand functions in terms of v and w . A. Brown (UCLA) Econ 11 Lecture 7 08/25/08 5 / 37 Supply Function 1 Set up pro&t function in terms of capital and labor hired. 2 Maximize function and solve for optimal capital and labor in terms of P , v and w . 3 Plug these input demand functions back into pro&t function ( k , l ) . 4 This give us production in terms of v , w and q . A. Brown (UCLA) Econ 11 Lecture 7 08/25/08 6 / 37 Supply Function Example Example Recall that Toyota&s technology for producing cars is given by f ( k , l ) = k 2 3 l 1 3 . Its prot function in terms of capital and labor hired is ( k , l ) = Pk 2 3 l 1 3 & vk & wl where P is the price of a Toyota car. 2 P 3 k & 1 3 l 1 3 = v P 3 k 2 3 l & 2 3 = w 2 l k = v w l = v 2 w k A. Brown (UCLA) Econ 11 Lecture 7 08/25/08 7 / 37 Supply Function Example Example Use the optimality condition to &nd the input demand functions and plug them in to the pro&t function q = k 2 3 & v 2 w k 1 3 = &...
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lect7 - Production Functions Intermediate Microeconomics...

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