TOP2_08 - Topic 2 Physical Properties of Single Variable...

Topic 2: Physical Properties of Single Variable Factor Production Functions
I.
Output is measured in physical rather then money terms and is referred to as total
physical product (TPP). We will use y to represent TPP.
A. y = f(x
1
|x
2
,...,x
n
)
1. Called explicit form of the function
2. If converted to F(x
1
,y)=0, then would be in implicit form.
3. y is output or total physical product
4. x
1
is variable factor of production
5. x
2
,...,x
n
are the fixed factors held constant
6. | means given
7. Simplify notation to y = f(x) for a fixed production period and a given plant with a
single-variable factor of production
B. Classical three-stage production function is cubic equation. In explicit form we will
use example: y = 24x + 2.4x
2
- 0.1x
3
II.
The average physical product (APP) function is the ratio of physical output to
physical input.
A.
x
)
x
( f
=
x
y
= APP
i
i
i
B. APP = 24 + 2.4x - 0.1x
2
III. The marginal physical productivity (MPP) function is the rate of change of the total
physical product function for an infinitesimal change in the factor. It is the slope
of the total physical product function at a particular level of the variable input.
Beattie and Taylor make point of the technical difference between the marginal
physical productivity and the marginal physical product.
A.
) ( =
) (
= =
(TPP)
= MPP x f
dx
x df
dx
dy
dx
d
′
B. MPP = 24 + 4.8x - 0.3x
2
C. Beattie and Taylor define marginal physical product as
dx x f dy ) ( ′ =
D. Local maximum at
0 and MPP 0 (x) f (x) f <
′ ′
= =
′
E. 24 + 4.8 x - 0.3x 2 = 0
⇒
(implies) x = 20 or - 4
F.
0