文档介绍：Chapter Twenty
Cost Minimization
Cost Minimization
A firm is a cost-minimizer if it produces any given output level y ³ 0 at smallest possible total cost.
c(y) will denote the firm’s smallest possible total cost for producing y units of output.
c(y) is the firm’s total cost function.
Cost Minimization
When the firm faces given input prices w = (w1,w2,…,wn) the total cost function will be written as c(w1,…,wn,y).
The Cost-Minimization Problem
Consider a firm using two inputs to make one output.
The firm’s production function is y = f(x1,x2).
Take the output level y ³ 0 as given.
Take the input prices w1 and w2 as given. Then the cost of an input bundle (x1,x2) is w1x1 + w2x2.
The Cost-Minimization Problem
For given w1, w2 and y, the firm’s cost-minimization problem is to solve
subject to
The Cost-Minimization Problem
The levels x1*(w1,w2,y) and x1*(w1,w2,y) in the least-costly input bundle are the firm’s conditional demands for inputs 1 and 2.
The firm’s total (smallest possible) cost for producing y output units is therefore
Conditional Input Demands
For given w1, w2 and y, how are the levels of inputs 1 and 2 in the least costly input bundle located?
And how is the firm’s total cost puted?
Iso-cost Lines
A curve which contains all of the input bundles which cost the same amount is an iso-cost curve.
., given w1 and w2, the $100 iso-cost line has the equation
Iso-cost Lines
In general, given w1 and w2, the equation of the $c iso-cost line is which rearranges to
The slope is - w1/w2.
Iso-cost Lines
c’º w1x1+w2x2
cӼ w1x1+w2x2
c’< c”
x1
x2