{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

12. Cost Min

# 12. Cost Min - Cost Minimization Professor John Diamond...

This preview shows pages 1–12. Sign up to view the full content.

Cost Minimization Professor John Diamond ECON 370: Microeconomic Theory Lecture 12

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Cost Minimization: Introduction Cost-minimizing firm produces y 0 at min total cost Min cost for each y yields: Total cost function - c(y) With input prices w = (w 1 ,w 2 ,…,w n ), Total cost function is c(w 1 ,…,w n ,y)
3 The Cost-Minimization Problem Consider a firm using 2 inputs to make 1 output Production function is y = f(x 1 ,x 2 ) Take output level y 0 as given. Given input prices w 1 and w 2 , Total cost of input bundle (x 1 ,x 2 ) is w 1 x 1 + w 2 x 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 The Cost-Minimization Problem So, for given w 1 , w 2 and y, firm’s cost - minimization problem is to solve 2 2 1 1 0 x , x x w x w min 2 1 subject to y ) x , x ( f 2 1
5 The Cost-Minimization Problem Solution x 1 *(w 1 ,w 2 ,y) and x 2 *(w 1 ,w 2 ,y) are firm’s conditional demands for inputs 1, 2 Smallest possible total cost for producing y is To solve for conditional input demands ) y , w , w ( x w ) y , w , w ( x w ) y , w , w ( c 2 1 * 2 2 2 1 * 1 1 2 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6 Iso-cost Lines: Introduction Iso-cost curve contains all input bundles that cost same amount E.g., given w 1 and w 2 , the \$100 iso-cost line has equation 100 x w x w 2 2 1 1
7 Iso-cost Lines: Equation Generally, given w 1 and w 2 , the equation of the “c” iso -cost line is 2 1 2 1 2 w c x w w x c x w x w 2 2 1 1 Slope is - w 1 /w 2 Intercept is c/w 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
8 Iso-cost Lines: Graph 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
9 The Cost-Minimization Problem: Graph x 1 x 2 Cost minimizing bundle that will produce y’: f(x 1 ,x 2 ) y’ x 1 * x 2 *

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
10 The Cost-Minimization Problem: Graph x 1 x 2 f(x 1 ,x 2 ) y’ x 1 * x 2 * At an interior cost-min input bundle: (a) f(x 1 *,x 2 *) = y’ (b) slope of isocost = slope of isoquant ) x , x ( at MP MP TRS w w * 2 * 1 2 1 2 1
11 Cobb-Douglas Example of Cost Min.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}