Advanced Microeconomics/Production

Properties of Production SetsEdit

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 maximizationEdit

ExampleEdit


Single OutputEdit

where

marginal revenue productEdit

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 substitutionEdit

Properties of profit functions and supplyEdit

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

Cost MinimizationEdit

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

ExampleEdit

 

  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 FunctionsEdit

  •   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