This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: © 2010 W. W. Norton & Company, Inc. 20 Cost Minimization © 2010 W. W. Norton & Company, Inc. 2 Cost Minimization A firm is a costminimizer if it produces any given output level y 0 at smallest possible total cost. c(y) denotes the firm’s smallest possible total cost for producing y units of output. c(y) is the firm’s total cost function. © 2010 W. W. Norton & Company, Inc. 3 Cost Minimization When the firm faces given input prices w = (w 1 ,w 2 ,…,w n ) the total cost function will be written as c(w 1 ,…,w n ,y). © 2010 W. W. Norton & Company, Inc. 4 The CostMinimization Problem Consider a firm using two inputs to make one output. The production function is y = f(x 1 ,x 2 ). Take the output level y 0 as given. Given the input prices w 1 and w 2 , the cost of an input bundle (x 1 ,x 2 ) is w 1 x 1 + w 2 x 2 . © 2010 W. W. Norton & Company, Inc. 5 The CostMinimization Problem For given w 1 , w 2 and y, the firm’s costminimization problem is to solve min , x x w x w x 1 2 1 1 2 2 subject to f x x y ( , ) . 1 2 © 2010 W. W. Norton & Company, Inc. 6 The CostMinimization Problem The levels x 1 *(w 1 ,w 2 ,y) and x 1 *(w 1 ,w 2 ,y) in the leastcostly input bundle are the firm’s conditional demands for inputs 1 and 2. The (smallest possible) total cost for producing y output units is therefore c w w y w x w w y w x w w y ( , , ) ( , , ) ( , , ). * * 1 2 1 1 1 2 2 2 1 2 © 2010 W. W. Norton & Company, Inc. 7 Conditional Input Demands Given w 1 , w 2 and y, how is the least costly input bundle located? And how is the total cost function computed? © 2010 W. W. Norton & Company, Inc. 8 Isocost Lines A curve that contains all of the input bundles that cost the same amount is an isocost curve. E.g., given w 1 and w 2 , the $100 iso cost line has the equation w x w x 1 1 2 2 100 . © 2010 W. W. Norton & Company, Inc. 9 Isocost Lines Generally, given w 1 and w 2 , the equation of the $c isocost line is i.e. Slope is  w 1 /w 2 . x w w x c w 2 1 2 1 2 . w x w x c 1 1 2 2 © 2010 W. W. Norton & Company, Inc. 10 Isocost Lines c’ w 1 x 1 +w 2 x 2 c” w 1 x 1 +w 2 x 2 c’ < c” x 1 x 2 Slopes = w 1 /w 2 . © 2010 W. W. Norton & Company, Inc. 11 The CostMinimization Problem x 1 x 2 All input bundles yielding y’ units of output. Which is the cheapest? f(x 1 ,x 2 ) y’ © 2010 W. W. Norton & Company, Inc. 12 The CostMinimization Problem x 1 x 2 All input bundles yielding y’ units of output. Which is the cheapest? f(x 1 ,x 2 ) y’ © 2010 W. W. Norton & Company, Inc. 13 The CostMinimization Problem x 1 x 2 All input bundles yielding y’ units of output. Which is the cheapest?...
View
Full
Document
This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Dee during the Spring '10 term at Andhra University.
 Spring '10
 dee
 International Economics

Click to edit the document details