# Advanced Microeconomics/Production

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## Contents

### Properties of Production Sets[edit]

The production vector where represents an output, and an input

- Y is non empty
- Y is closed (includes its boundary)
- No free lunch - (no inputs, no outputs)
- possibility of inaction
- Free disposal
- Irreversability - can't make output into inputs
- Returns to scale:
- Non-increasing:
- Non-decreasing:
- Constant:

- Additivity:
- Convexity:

### Profit maximization[edit]

#### Example:[edit]

##### Single Output:[edit]

where

### marginal revenue product[edit]

Marginal revenue product is the price of output times the marginal product of input

The first order conditions for profit maximization require the marginal revenue product to equal input cost for all inputs (actually) used in production,

### marginal rate of techical substitution[edit]

### Properties of profit functions and supply[edit]

- Profit functions exhibit homogeneity of degree 1 doubling all prices doubles nominal profit
- supply functions exhibit homogeneity of degree 0

## Cost Minimization[edit]

The optimal CMP gives cost function <align>\funcd{c}{w,q}</align>

### Example[edit]

The ratio of input prices equals the ratio of marginal products

The marginal cost of expansion through $z_1$ equals the marginal cost of expansion through

The solution to the CMP gives factor demands, and the cost function

## Cost Functions[edit]

- gives positive economic profit, short run and long run
- In short run, fixed costs are irrelevant. Shut down if
- minimum efficient scale:

No economic profits in the long run, given free entry for any firms enter, in the long run until