PAC - The Production Function Lesson

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The Production Function Lesson

Before exploring production and costs at the firm, it is important to review the basic types of business organizations in an economy. There are three main business organizations - sole proprietorship, partnership, and corporation. The chart below highlights the strengths and weaknesses of each.

Strengths Weaknesses

Sole Proprietorship: A business owned and run by one person

 Easy to start; Easy to manage because there are no other owners to consult; Profits do not have to be shared with other owners; No special business taxes because the owner and business are one legal entity; the psychological benefit of "being your own boss"; The business is easy to dissolve Unlimited liability (owner is solely responsible for business debts); Due to small size, raising financial capital is difficult; Inefficient due to small size; Usually the owner has limited experience operating a business; Difficult (because of expense) to hire the best employees; Limited life (when the owner dies or sells the business, it ceases to exist)

Partnership: A business owned jointly by two or more people

 Easy to establish (just need Articles of Partnership); Easy to manage (each owner can specialize in the area they are best at); Few special taxes; Easier to attract financial capital; Slightly larger size makes it more efficient; Greater available financial capital allows the business to attract more qualified employees Unlimited liability (owners equally share in debts unless it is a limited partnership); Limited life (as partners join and leave the business); Conflict between partners

Corporation: A business organization recognized as a separate legal entity that has the rights of an individual

 Very easy to raise financial capital (through selling stocks); Greater financial capital allows for best employees to be hired; Owners have limited liability (the business and not the individuals are responsible for debt); Unlimited life (continues to exist even when ownership changes); Easy to transfer ownership Expensive to start (requires charter); Owners have little input in the daily operations of the business; Must pay separate income taxes; Subject to a great deal of government regulation

No matter the type of business organization, or the type of market structure in which a firm operates, the production and cost functions for all firms will operate similarly.  

To begin the analysis of production and costs, we will assume a perfectly competitive firm operating in a perfectly competitive market. There are several key characteristics to perfect competition and they are listed below. 

Perfect Competition A perfectly competitive market has a large number of sellers producing identical products in a market with no barriers to entry/exit. Because of this, no individual seller has control over the market price. It is easy to enter the market when profit exists and it is easy to exit the market when losses occur.

The Production Schedule and Production Function

Production is a function of capital and labor. That is, Q = f(K, L), with Q representing total output or total product, K representing capital, and L representing labor. A short run production function typically assumes that K is fixed. By holding K constant, the production function shows how changes in L impact the total product. Labor is considered a variable resource because the firm can easily manipulate the number of workers it employs. Capital is considered a fixed resource because firms are not able to manipulate the amounts of capital they employ in the short run.

Production Schedule

Labor

Total Product

(or Quantity)

Average Physical Product (AAP)

Marginal Physical Product (MPP)

1

10

10

10

2

25

12.5

15

3

45

15

20

4

57

14.25

12

5

65

13

8

6

66

11

1

7

62

8.86

-4

 

Total Product or Total Output (Q) = total number of units produced by a firm with a given quantity of labor and capital.

Average Product (AP or APP) = total output divided by a given quantity of labor; AP = Q/L

Marginal Product (MP or MPP) = the additional product created by an additional unit of labor; MP = ΔQ/ΔL

Remember this general rule: If the margin is greater than the average, the average will rise or if the margin is less than the average, the average will decrease. This will help as you graph the curves.  

Production Function

Production Function X-axis – Labor Y-axis – Quantity There are three curves on this graph. Total product curve has 3 stages. The other curves are APP and MPP. As MPP is increasing total product is rapidly increasing. As MPP begins to decline, the increase in total product begins to slow down. MPP reflects the slope of the total product curve. MPP also influences APP. MPP>APP then APP increases MPP<APP then APP decreases The changes in MPP and APP will have great implications on costs at the firm.

The Stages of Production Video

View the following video to get an introduction to the stages of production. To make the video full screen, click the double arrows at the bottom right corner of the object.

The stages of production are characterized by marginal product and the impact marginal product has on total product. Remember, marginal product is the change in total product due to a one unit change in labor. That is, MP = ΔTP/ΔL.  

Stage I - Increasing Returns:  ↑MP and ↑TP   With each successive worker added, marginal product is larger than the previous marginal product. This causes total product to increase at an increasing rate.  

Stage II - Diminishing Returns:   ↓MP and ↑TP   With each successive worker added, marginal product is less than the previous marginal product (but still positive). This causes total product to increase at a decreasing rate.

Stage III - Negative Returns:   -MP and ↓TP   With each successive worker added, marginal product is negative. This causes total product to decrease.

As you can see in the graph above, marginal product is the slope of the total product curve.

Perfect Picture Palace Activity

Complete the activity below.

Producer Theory Video

Please view the video below for more explanation on the production function. To make the video full screen, click the double arrows at the bottom right corner of the object.

What Causes Increasing, Diminishing, and Negative Returns?

Specialization: Initially, as more units of labor are added to the firm, those units of labor are able to specialize in production and result in greater gains (increasing marginal product) in total product.  

Fixed Capital: As the firm continues to add labor, the law of diminishing returns sets in because of a fixed amount of capital in the short run. This happens because there are so many workers trying to make use of a limited amount of capital. As diminishing returns set in, marginal product is still positive, but it is getting smaller and smaller with every additional unit of labor added by the firm. Eventually, if the firm continues to hire additional labor, negative returns will occur. This means marginal product becomes negative and total product will actually decrease. In the long run, when firms are able to manipulate levels of capital, the onset of diminishing and negative returns can be delayed.  

What does the production schedule/function reveal? By itself, it reveals very little. However, it will reveal how costs change at the firm as variable inputs (like labor) are added.

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