Q = F(K, L | given Tech)
Or
Output = F(Inputs | Chosen Tech)

Q = F(K, L |T)
◦ But K = K0 (Fixed at level K0 and can’t be changed)
 Short-run -> size of the plant; machinery can’t be
increased/decreased immediately
 -> fixed in the SR
 long-run it can be increased or decreased
 -> variable in the LR
 Look at the short-run for the time being
◦ However L (labor) can be changed very quickly
 Layoffs/hiring
 So it is variable in both the SR and LR
Production Functions: Total Product, Marginal Product, and
Average Product
production function or total product function A numerical or
mathematical expression of a relationship between inputs and outputs.
It shows units of total product as a function of units of inputs.
TABLE 7.2 Production Function
(1)
Labor Units
(Employees)
(2)
Total Product
(Sandwiches per Hour)
(3)
Marginal Product
of Labor
(4)
Average Product of Labor
(Total Product ÷ Labor Units)
0
1
2
3
4
5
6
0
10
25
35
40
42
42
10
15
10
5
2
0
10.0
12.5
11.7
10.0
8.4
7.0
FIGURE 7.3 Production Function for Sandwiches
production function is of the relationship between inputs and outputs.
marginal product of labor is the additional output that one additional unit of labor
produces.
Able to increase the amount of output each laborer can
produce
•Increases Total Product at all levels of employment
Isoquants (q1, q2, q3) represent lines of equal
(iso) production – or of the same height (product
output) from the 3D graph

2 Input Production Function
◦ Q = F(K, L | T)
◦ Cost
 Depend on the quantity of the inputs used
 K = # of units of K
 L = # of employees (units of L)
 Pk , PL = per unit price of Kapital and Labor (wage rate)
 Costs of production for a given level of output
 C(Q) = PkK + PLL
Choice of Technology
TABLE 7.3 Inputs Required to Produce 100 Diapers Using Alternative Technologies
Technology
Units of Capital (K)
Units of Labor (L)
A
B
C
D
E
2
3
4
6
10
10
6
4
3
2
TABLE 7.4 Cost-Minimizing Choice among Alternative Technologies (100 Diapers)
(1)
Technology
A
B
C
D
E
(2)
Units of Capital (K)
2
3
4
6
10
(3)
Units of Labor (L)
10
6
4
3
2
Cost = (L X PL) + (K X PK)
(4)
(5)
PL = $1
PL = $5
PK = $1
PK = $1
$12
9
8
9
12
$52
33
24
21
20
Two things determine the cost of production: (1) technologies that are available and (2)
input prices. Profit-maximizing firms will choose the technology that minimizes the cost of
production given current market input prices.
Factor Prices and Input Combinations: Isocosts
FIGURE 7A.3 Isocost Lines Showing the
Combinations of Capital and Labor Available
for $5, $6, and $7
An isocost line shows all the
combinations of capital and labor that
are available for a given total cost.
(PK  K) + (PL  L) = TC
Substituting our data for the lowest
isocost line into this general
equation, we get
isocost line A graph that shows all the combinations of capital and
labor available for a given total cost.
Factor Prices and Input Combinations: Isocosts
FIGURE 7A.4 Isocost Line Showing All
Combinations of Capital and Labor Available
for $25
One way to draw an isocost line is to
determine the endpoints of that line
and draw a line connecting them.
Slope of isocost
line:
Finding the Least-Cost Technology with Isoquants and
Isocosts
Finding the Least-Cost Combination of
Capital and Labor to Produce 50 Units of
Output
1. Find the least cost “iso-cost”
line that will produce the desired
level of output. That is, the least
cost (IC) line that touches the 50
output Production isoquant
2. Profit-maximizing firms will
minimize costs by producing their
chosen level of output where the
isoquant is tangent to an isocost
line.
3. Here the cost-minimizing
technology—3 units of capital and 3
units of labor—is represented by
point C.
Note: Could produce 50 units at TC
= $7; but it would cost more. Could
not produce 50 units if your “cost
budget” is $5
Finding the minimum cost inputs (quantities)
for different levels of output
FIGURE 7A.6 Minimizing Cost of
Production for qX = 50, qX = 100,
and qX = 150
FIGURE 7A.7 A Cost Curve Shows the
Minimum Cost of Producing Each Level of
Output
Plotting a series of cost-minimizing combinations of inputs—shown in this graph as
points A, B, and C— on a separate graph results in a cost curve like the one shown in
Figure 7A.7.
The Cost-Minimizing Equilibrium Condition
At the point where a line is just tangent to a curve, the two have the
same slope. At each point of tangency, the following must be true:
slope of isoquant  -
MPL
P
 slope of isocost  - L
MPK
PK
Thus,
MPL PL

MPK PK
Dividing both sides by PL and multiplying
both sides by MPK, we get
MPL MPK

PL
PK
APPENDIX REVIEW TERMS AND CONCEPTS
isocost line
isoquant
marginal rate of technical substitution
1.
Slope of isoquant:
K
MPL
L
MPK
2.
Slope of isocost line: