Ch. 21. COST MINIMIZATION - Summary - Intermediate Microeconomics - Varian

Ch. 21.  COST MINIMIZATION

The profit-maximization problem can be split into two pieces.

First step in the problem is how to minimize the costs of producing any given level of output.
Second step is to choose the most profitable level of output.

In this chapter the first step—minimizing the costs of producing any given level of output is discussed.


A. Max profits require minimize costs

1. Minimize w1x1 +w2x2 s.t. f(x1, x2)=y

2. Geometric solution

    Isocost curves and isoquant for f(x1, x2)=y

    w1/w2=MP1/MP2



3. Optimal choice (X1*) is the conditional factor demand function

Function of input-prices

Conditional of level of production (y)



4. Examples

Perfect susbstitutes
Fixed proportions
Cobb-Douglas


B. Returns to scale and the cost function

(1) Increasing returns (to scale) - decreasing AC

(2) Constant returns - constant AC

(3) Decreasng returns - increasing AC



C. Long run and short run costs

(1) Long run: all inputs variable

(2) Short run: some inputs fixed



D. Fixed and quasi-fixed costs

(1) Fixed: must be paid, whatever the output level

(2) Quasi-fixed: only paid when output is positive




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