1. Production Functions
Ap Econ 10/4

2. Warm Up
Making Links-I need two volunteers to work in my factory  ***Keep this worksheet, continue to work on it, you will turn it in on Monday

3. Production Function
Production function is the relationship between a firm’s quantity of output which depends on the quantity of inputs
Fixed input: quantity fixed for period of time – cannot be varied
Variable input: quantity can be varied at any time – depends on the level of output
Example – wheat farm
Fixed inputs: Land
Variable inputs: Workers

4. Short Run Vs. Long Run
***Whether an input is fixed or not depends on time “Long run vs. Short run”
Short Run (fixed plant): the period of time too brief for a firm to alter its plant capacity, yet long enough to permit a change in the degree to which the fixed plant is used (output can vary)
Long run (variable plant): the period of time long enough for a firm to adjust the quantities of all the resources it employs including plant capacity
Also includes enough time for firms to enter or leave the industry

5. Production Function
Land: fixed input
Labor: variable input
Marginal Product of Labor (MP) shows the change in quantity of output generated by adding one more worker
MP= ∆𝑄 ∆𝐿
Average Product (AP), also called labor productivity, is the output per unit of labor input
AP = 𝑇𝑃 𝑄𝐿
Quantity of Labor
Quantity of Wheat (total product)
Marginal Product (MP) of Labor
Average Product (AP) -- 1 19 2 36 17 18 3 51 15 4 64 13 16 5 75 11 6 84 9 14 7 91 8 96 12

6. Total Product Curve
Quantity of wheat (bushels)
Quantity of labor L
Quantity
of wheat Q
MP of labor
MPL =  Q /  L
(worker)
(bushels)
(bushels per worker)
Adding a 7th worker leads to an increase in output of only 7 bushels 19 1 19 17 2 36 15
Total product, TP 3 51
100
Adding a 2nd worker leads to an increase in output of 17 bushels 13 4 64 11 80 5 75 9 6 84 7 60 7 91 5 8 96 40 20 1 2 3 4 5 6 7 8
Quantity of labor (workers)
Although the total product curve in the figure slopes upward along its entire length, the slope isn’t constant: as you move up the curve to the right, it flattens out due to changing marginal product of labor.

7. Marginal Product of Labor Curve
Marginal product of labor falls as the number of workers increases
Diminishing returns to an input (labor): Adding more workers adds to TP, but TP increases at a decreasing rate – decreasing returns to labor
Negative returns: MP of labor is negative – bad!
Marginal product of labor (bushels per worker)
There are diminishing returns to labor. 19 17 15 13 11 9 7 5
Marginal product of labor, MPL 1 2 3 4 5 6 7 8
Quantity of labor (workers)

8. MP and AP

9. Diminishing Returns to Inputs
Why? If they continue to add more and more workers without being able to increase their land, they get to a point where more workers are not efficiently being used

10. Land Increases from 10 Acres to 20
Quantity of wheat
(bushels)
Marginal product of labor
(bushels per worker)
160 30 TP
140 20 25
120
100 20 TP 10 80 15 60 10 40
MPL 5 20 20
MPL 10 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Quantity of labor (workers)
Quantity of labor (workers)
(a) Total Product Curves
(b) Marginal Product Curves
With more land, each worker can produce more wheat. So an increase in the fixed input shifts the total product curve up from TP10 to TP20.
This shift also implies that the marginal product of each worker is higher when the farm is larger. As a result, an increase in acreage also shifts the marginal product of labor curve up from MPL10 to MPL20.