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CHAPTER 7: PRODUCTION THEORY
Production Theory:
 managers must decide:
 what to produce for the market
 how to produce it in the most efficient/ least cost manner

Basic Production Theory:
An application of the constrained optimization = the firm attempts either to minimize the
cost of producing a given level of output or to maximize the output attainable with a given
level of cost
Production:
Production Function:
is a table, graph or an equation showing the highest output that a firm can
produce from every specified combination of inputs given the state of technology
Average & Marginal Product of an Input:

Average Prod of an Input:
Total Product
Total Units of Input
 Marginal Product:
∆Total Product
∆ Units of Input
= the addition to Total Output resulting from the
addition of the last unit of the input
holding constant the amount of other inputs
Relationship:
 MProd > AProd
AProd Increasing
 MProd < AProd
AProd Decreasing
 MProd = AProd
AProd @ Max
Calculation:
 MProd =
∆Q/∆x
 AProd =
Q/x
= ∆(Q/x)/ dx = [x(∆Q/∆x) – Q(∆x/∆x]/x
2
1/x[(∆Q/∆x) – (Q/x)] (recall ch 2)
 AProd max when ∆(Q/x)/ ∆x = 0, then
∆(Q/x)/ ∆x = 1/x[(∆Q/∆x) – (Q/x)] = 0
This means that ∆Q/∆x MUST = Q/x, when AProd is a maximum
when AProd (Q/x) is a maximum MProd (∆Q/∆x) = ApProd
Total, Average & Marginal Product:
 Marginal Prod = slope of Total Prod
 Max/Min Function
1
st
derivative & set = 0
 @ pt A Total Prod = highest = MProd highest
 @ pt C Total Prod = max
MProd/ Slope = 0
MProd intersects horizontal axis
30
90
130
161
184
196
Total Product
∆
Q
from hiring fourth worker
∆
Q
from hiring third worker
∆
Q
from hiring second worker
∆
Q
from hiring first worker
L { ± ‚“ @
L { ± ‚“ @
L { ± ‚“ @
L { ± ‚“ @
² ²
diminishing
marginal
returns
Units of
Number of
6
2
3
4
5
1
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This note was uploaded on 04/18/2008 for the course MGCR 293 taught by Professor Salmasi during the Fall '08 term at McGill.
 Fall '08
 Salmasi

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