The document discusses production functions and their key components. It defines a production function as showing the maximum output that can be produced from given quantities of inputs. It then discusses total product curves, marginal product curves, and the law of diminishing returns. Specifically, it provides an example total product curve for tax return production as a function of labor input. It shows how the marginal product is calculated and how the marginal product curve depicts this relationship. Finally, it briefly introduces the Cobb-Douglas production function.

1. Production slide 1
PRODUCTION
PRODUCTION FUNCTION: The term
economists use to describe the technology of
production, i.e., the relationship between
inputs and the output of a good or service.

2. Production slide 2
There is a production function for every good that
shows the maximum output you can get from any
quantities of inputs.
The production function is the description of the
current best technology for making a good.
Production functions apply to firms. E.g., MSU has a
production function for producing Sweet. GM has a
production function for producing cars.

3. Production slide 3
TOTAL PRODUCT CURVE
The total product curve shows output as a function of
a single variable input, holding all other inputs
constant.

4. Production slide 4
The production function for tax returns in a small
accounting firm can be written like this:
Q(returns) = f(office space, accountants,
computers, furniture, supervisors, office
supplies, etc.)
The dependent variable is quantity of output
(number of returns filed in this case).
The independent variables are quantities of
inputs.

5. Production slide 5
Here’s a table of values for tax return production
as a function of a single variable input,
LABOR:
Labor
Total
Product
0 0
1 3
2 15
3 36
4 48
5 56
6 62
7 66
8 68

6. Production slide 6
Total product curve for tax returns
as a function of the amount of labor
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8 9 10
Plot the remaining points
Q
LABOR
Hidden slide

7. Production slide 8
Marginal product of an input: The change in output per
unit change in input.
Marginal product is the slope of the total product curve:
Q/ L
Marginal product is a measure of input productivity.

8. Labor
Total
Product
Marginal
Product
0 0
1 3 3
2 15 12
3 36 21
4 48 12
5 56
6 62
7 66
8 68
(48-36)/
(4-3)

9. Production slide 10
The marginal product curve shows the marginal
product as a function of the quantity of labor used.
The independent variable is the amount of the input
(labor).
The dependent variable is the marginal product of labor.

10. Production slide 11
0
2
4
6
8
10
12
14
16
18
20
22
0 2 4 6 8 10
Hidden slide
Plot the remaining points showing
MP here, and connect them.
Label the axes correctly.

11. Production slide 13
Law of Diminishing Returns
As the amount of an input increases, all other inputs
being held constant, the marginal product of the
input will eventually decline.

12. Production slide 14
0
2
4
6
8
10
12
14
16
18
20
22
0 2 4 6 8 10
Total Product Curve
Marginal Product Curve
The Law of Diminishing
Returns says the the total
product curve eventually
gets flatter as the amount of
the variable input increases.
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6 7 8 9 10
Q
TP
L
MP
MP
L

13. Cobb-Douglas Production Function
Q = F(K,L)
The maximum amount of output that can be
produced with K units of capital and L units
of labor.
Production slide 15

14. Production slide 16
Example: Q = F(K,L) = K.5 L.5
K is fixed at 16 units.
Short run production function:
Q = (16).5 L.5 = 4 L.5
Production when 100 units of labor are used?
Q = 4 (100).5 = 4(10) = 40 units