3. The Production Function
A Production Function is the maximum quantity from any amounts of inputs
If L is labor and K is capital, one popular functional form is known as the Cobb-
Douglas Production Function.
The number of inputs is often large. But economists
simplify by suggesting some, like materials or labor,
is variable, whereas plant and equipment is fairly
fixed in the short run.
4. Average Product
output per labor
Marginal Product
output attributable to last unit of labor
applied.
Similar to profit functions, the Peak of
MP occurs before the Peak of average
product.
5. Short Run Production Function
Numerical Example
L Q MP AP
0 0 --- ---
1 20 20 20
2 46 26 23
3
4
5
70
92
110
24
22
18
23.33
23
22
Marginal Product
L
1 2 3 4 5
Average
Product
Labor Elasticity is greater then one,
for labor use up through L = 3 units
6. When MP > AP, then AP is RISING
IF YOUR MARGINAL GRADE IN THIS CLASS IS HIGHER
THAN YOUR GRADE POINT AVERAGE, THEN YOUR
G.P.A. IS RISING
When MP < AP, then AP is FALLING
IF YOUR MARGINAL BATTING AVERAGE IS LESS THAN
THAT OF THE NEW YORK YANKEES, YOUR ADDITION
TO THE TEAM WOULD LOWER THE YANKEE’S TEAM
BATTING AVERAGE
When MP = AP, then AP is at its MAX
IF THE NEW HIRE IS JUST AS EFFICIENT AS THE
AVERAGE EMPLOYEE, THEN AVERAGE PRODUCTIVITY
DOESN’T CHANGE
7. Law of Diminishing Returns
INCREASES IN ONE FACTOR OF PRODUCTION,
HOLDING ONE OR OTHER FACTORS FIXED,
AFTER SOME POINT,
MARGINAL PRODUCT DIMINISHES.
A SHORT
RUN LAW
point of
diminishing
returns
Variable input
MP
8. Figure 7.4 on Page 306
Three stages of production
Stage 1: average
product rising.
Stage 2: average
product declining (but
marginal product
positive).
Stage 3: marginal
product is negative, or
total product is
declining. L
Total Output
Stage 1
Stage 2
Stage 3
9. Isoquants & LR Production Functions
In the LONG RUN, ALL
factors are variable
Q = f ( K, L )
ISOQUANTS -- locus of
input combinations which
produces the same output
(A & B or on the same
isoquant)
SLOPE of ISOQUANT is
ratio of Marginal
Products, called the
MRTS, the marginal rate
of technical substitution
ISOQUANT MAP
B
A
C
Q1
Q2
Q3
K
L
10. Cobb-Douglas Production Functions
Q = A • Kα
• Lβ
is a Cobb-Douglas Production Function
IMPLIES:
Can be CRS, DRS, or IRS
if α + β = 1, then constant returns to scale
if α + β < 1, then decreasing returns to scale
if α + β > 1, then increasing returns to scale
Coefficients are elasticities
α is the capital elasticity of output, often about .67
β is the labor elasticity of output, often about .33
which are EK and EL
Most firms have some slight increasing returns to scale