1. ©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.
Production Functions
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

2. Profit Maximization
We assume the objective of the firm is to maximize economic profit.
Profit (π) = Total Revenue - Total Cost
Total Revenue:
determined by the level and nature of competition in your market
Total Cost:
determined by factor market prices and the firm’s technology or production function

3. Production & Cost Structures
There are lots of ways to describe production and cost concepts.
You need to understand them all.
For example, we have:
total, fixed and variable concepts.
total, average and marginal concepts.
long run and short run concepts.
They are all related to each other in important ways, as you will see.

4. Example: The U.S. Apple Market
Core Facts:
About 2,500 known varieties of apples are grown in the United States. More than 7,500 are grown worldwide.
The 2008 apple crop was 233 million 42-pound cartons.
The largest U.S. apple crop on record, of million cartons, was harvested in 1998.
An estimated 7,500 U.S. apple growers managed orchards covering 379,000 acres in 2005, trailing only oranges and grapes in the amount of U.S. acreage committed to fruit production.
In 2005, the average U.S. consumer ate an estimated 16.9 pounds of fresh-market apples, and 29.2 pounds of processed apples, for a total of 46.1 pounds of fresh apples and processed apple products. In 2004, average per-capita consumption was 50.6 pounds of apples and apple products.
Sixty-three percent of the 2005 U.S. apple crop was eaten as fresh fruit, while 36 percent was processed into apple products, and 1 percent was not marketed. Of the 36 percent of the crop that was processed, 18.6 percent was used in juice and cider; 2 percent was dried; 2.5 percent was frozen; 12.2 percent was canned and 0.7 percent was fresh slices. Other uses include the making of baby food, apple butter or jelly, and vinegar.
U.S. apple growers received an average of 27.6 cents per pound for fresh-market apples from the 2005 crop, up from 21.8 cents per pound in 2004.
The United States was the world's second-largest producer of apples in 2005, behind the People's Republic of China. Turkey, Poland, and Italy rounded out the world's top five apple producing countries in 2005.
Exports of fresh-market apples from the 2005 crop totaled an estimated 35.7 million bushels, or 24 percent of the total U.S. fresh-market crop. Imports in that same year totaled an estimated 8.2 million bushels, resulting in a positive balance of fresh-apple trade.
Exports of U.S. apples have increased over the past decade, due to liberalization of export markets, increased disposable income in developing countries, and substantial industry export promotion efforts. Leading markets for U.S. apples include Mexico, Canada, Taiwan, Malaysia, Indonesia, Hong Kong, United Kingdom, India, United Arab Emirates, and Saudi Arabia.

5. Jonathan’s New York State Apple Farm
The farm is a business organized to grow and sell apples.
The owner/proprietor, Jonathan, tries to maximize his profits from the business.

6. Production Functions
The production function shows the input requirements for each level of production.
For some businesses the production function is relatively simple--a few processes with little substitution.
For some businesses the production function involves thousands of different processes and millions of substitution possibilities.
The production function is the economist’s summary of the input requirements for each level of production.

7. Fixed Factors
A fixed factor is one that does not vary as the quantity produced increases or decreases.
The length of time a factor is fixed depends on the nature of the factor and commitments the entrepreneur has made.
Some factors are fixed for only a short period of time (e.g., managerial time).
Others are fixed for a longer time (e.g., cultivated acreage).
No factors are fixed forever.

8. Variable Factors
A variable factor is one that must be increased in order to increase output and can be decreased when output is decreased.
The classic variable factor is labor.
Variable factors are typically assumed to exhibit diminishing marginal productivity – that is, as you add more and more of a variable factor to the production of an output, holding other inputs constant, the marginal contribution of the variable factor eventually declines.

9. The Short Run And The Long Run
The Short Run: A time frame for analysis in which there exists at least one fixed factor of production.
The length of the short run will depend on commitments the entrepreneur has entered into for various factors of production.
The Long Run: A time frame for analysis in which there are no fixed factors present. That is, you are free to vary all the factors of production.
More like a planning phase.

10. Jonathan’s Apple Farm Short Run Production Function
The table describes Jonathan’s inputs for the annual production of apples shown in the first column.

11. Jonathan’s Fixed And Variable Factors
Jonathan has two fixed factors
His cultivated acreage (100 acres)
His own managerial time (1,100 hours)
Jonathan must vary the labor input he hires to increase his production of apples.
At first this variation is modest going from 50 tons/year to 100 tons/year requires an additional 1,200 hours.
Going from 200 to 250 tons/year requires an additional 3,200 hours.

12. Jonathan’s Total Product of Labor
Total product of labor TPL = f(L) given land and Jonathan’s time

13. Jonathan’s Average Product & Marginal Product Of Labor
Average product of labor APL = TPL /L = f(L)/L given land and Jonathan’s time
Marginal product of labor MPL = ΔTPL / Δ L = Δ f(L)/ Δ L given land and Jonathan’s time

14. The Average/Marginal Relation: Grade Point Average Example
For product curves or any other average/marginal pair of curves:
If marginal (product) is above average (product), then the average (product) is rising.
If marginal (product) is below average (product), then the average (product) is falling.
Therefore, marginal (product) equals average (product) when average (product) is at a critical value (in this case, a maximum).
The relation of the marginal to the average is just like the effect of your next grade on your grade point average:
If the next grade you receive is below your current grade point average, then your GPA will fall (margin below average implies average falls).
If the next grade you receive is above your current grade point average, then your GPA will rise (margin above average implies average rises).

15. Locations, Shifts and Movements
The underlying technology along with the levels of the other inputs will determine the location and shape of the total product curve, which in turn determines the shape of the average and marginal product curves.
Using more or less of the variable factor being considered (e.g., labor in this case) moves us along the product curves.
With more “other inputs”, the product curves shift “up”.
When the law of diminishing marginal returns “sets in” the total product curve starts to increase at a decreasing rate.
At this point, the marginal product curve be at its maximum and will start to fall.
Jonathan’s 3 product curves are very typical. Consider variations on what you have seen. For example:
Find the 3 product curves assuming the total product curve is actually linear.
Find the 3 product curves assuming the total product curve increases at a decreasing rate right from the 1st unit of labor used.

16. Next Session….
Using the production information with input price information to get Jonathan’s short run cost structure.