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# Survey of International Economics ECON 364

UW

GPA 3.6

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This 7 page Class Notes was uploaded by April Jerde on Thursday September 17, 2015. The Class Notes belongs to ECON 364 at University of Wisconsin - Madison taught by Maria Muniagurria in Fall. Since its upload, it has received 125 views. For similar materials see /class/205134/econ-364-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.

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Date Created: 09/17/15

M Muniagurria Econ 364 Microeconomics Handout Part 1 I TECHNOLOGY Production Function Marginal Productivity of Inputs Isoquants 1 Case of One Input L Labor q fL 0 Let q equal output so the production function relates L to q How much output can be produced with a given amount of labor 0 Marginal productivity of labor MPL is de ned as A q Slope of prod Function A L Small changes ie The change in output if we change the amount of labor used by a very small amount 0 How to nd total output q if we only have information about the MPL quotIn generalquot q is equal to the area under the MPL curve when there is only one input Examples a Linear production functions Possible forms q10LgtMPL10 q12LgtMPL12 q4LgtMPL4 The production function q 4L is graphed below Diagam 2 ML 4 y Total outputforL 2 1 1 2 3 4 L Notice that if we only have diagram 2 we can calculate output for different amounts of labor as the area under MPL IfL2 gt IE Areabelow MPL for L Less or equal to 2 7 in Diagram2 Remark In all the examples in a MPL is constant b Production Functions With Decreasing MPL D E Total Output for LLD 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 0 Production function relates L amp K to q total output 0 Isoquant Combinations of L amp K that can achieve the same q 0 Marginal Productivities MPL Small changes AL K constant MPK Small changes AK L constant AK 0 MRTS Slope of Isoquant Absolute value of E Along Isoquant Examples a Linear L amp K are perfect substitutes Possible forms q10L5K MPL10 MPK5 qLK MPLl MPKl q2LK MPL2 MPKl 0 The production function q 2 L K is graphed below K Isoquant Map MPL NNwk Marginal Productivities are constant in all these examples then MRTS constant MDKA gt K b quotNice Isoquantsquot Possible Forms K KK kg x L Slope of Isoquants in absolute value 1 as L l ie l MRTS as L l as L l it becomes more and more costly to replace capital 11 COST MINIMIZATION How to choose inputs to minimize cost 1 One input Trivial Price of labor Total Cost w L where w is the price of labor 2 Two variable inputs a Fixed coefficients No substitution still easy Let r be the price of capital then the cost of producing one unit of output Average cost AC is ACaLwaKr Notice that this does not change for different levels of output The AC is constant If either w or r change the AC changes but the firm still uses aL units of L and aK units of K to produce one unit of output b Linear Isoquants perfect substitutes Hard we will skip this c quotNice Isoquantsquot Define Isocost lines Find tangency between Isoquant and Isocost lines Isocost E wL rk Combinations of L amp K that cost same amount of money Example w5r2 K Find the Isocost for 10 51 I Slope of Isocost I 3 102 5 In General I Slope of Isocost I 1 r I 05 6 L 5 Example Cost minimizing combination of K amp L to produce q 10 Islopel 1 r Effect of changes in prices 0 Tw r constant ie Twr l L ampT K Iii New Combination 74 q10 L 0T r wconstant ie l wr T L amp l K III PROFIT MAXIMIZING FACTOR DEMANDS We assume that each rm maximizes pro ts taking the product price as given P and taking input prices as given w r How many units of L amp K should the rm hire 1 Example Case of One Variable Input Labor L A pro t maximizing rm will hire L up to the point at which Marginal product x output price input price In our case MPL p w Marginal Marginal cost bene t for of hiring an extra the rm unit of labor MPL wp Prouctlon unctlon with decreasing MPL Think about a xed factor gt MPL A WP MPL gt L L 2 Case of Two Variable Inputs L amp K quotNice Isoquantsquot MPL MPK W w p 4 1 l l L L 7 L K K

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