Module 21 The Production Function Module Objectives Students will learn in this module: • The importance of the firm’s production function, the relationship between quantity of inputs and quantity of output. • Why production is often subject to diminishing returns to inputs. Module Outline Opening Example: The example describes why European farmers are more productive than U.S. farmers in producing wheat: European government policies provide incentives for using more inputs, and with more inputs comes increased productivity. I.The Production Function A.Definition: A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces. B.Inputs and outputs 1. Definition: A fixed input is an input whose quantity is fixed for a period and cannot be varied. 2. Definition: A variable input is an input whose quantity the firm can vary at any time. 3. Definition: The long run is the time period in which all inputs can be varied. 4. Definition: The short run is the time period in which at least one input is fixed. 5. Definition: The total product curve shows how the quantity of output depends on the quantity of the variable input, for a given amount of the fixed input. 6. The slope of the total product curve is not constant. The slope of the total product curve is equal to the marginal product of the variable input. a.Definition: The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input. b. Marginal product of labor or 118 = Change in quantity of output Changge in quantity of labor MPL = ∆Q/∆L module 21 the production function 7. Definition: There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input. a.Diminishing returns only holds if the quantity of all other inputs is fixed. Teaching Tips The Production Function Creating Student Interest A good starting point is to talk about the costs of owning a car. Assume that the car is a fixed input while it is in the garage and a variable input when you drive it. Ask students to think about the fixed cost of owning a car (as it sits in the garage) and the variable costs of owning a car (as you drive the car). The fixed costs are depreciation and registration fees, and the variable expenses are gasoline and maintenance. Ask students to brainstorm the fixed and variable inputs used at a fast-food restaurant or at the student bookstore. List them on the board. Presenting the Material Use this example of a fast-food restaurant to illustrate the concept of a production function. Use the size of the store as the fixed input and the number of workers as the variable input. Quantity of labor (workers) 0 1 2 3 4 5 6 Total production of hamburgers per hour Marginal product of labor 0 5555 12065 19070 23040 24010 2455 This example of a production function shows the total output of hamburgers given the addition of workers. Diminishing marginal product occurs after the third worker. The total production function rises at an increasing rate through the third worker and rises at a slower rate after the third worker. Explain that this happens due to crowding. Plot the total product curve and the marginal product curves on two separate graphs. Common Student Pitfalls • What’s a Unit? Students can be confused about how to measure a unit of labor. For example, labor can be measured in hours, days, weeks, or years or as the number of workers. Make sure students understand that the units used to measure labor do not affect the analysis—as long as you are consistent in the units you select. • Marginal versus total product and diminishing returns. Make clear to the students the distinction between declining marginal product and declining total 119 120 module 21 the production function product. Diminishing returns sets in when there is a decrease in the rate at which total product increases (not a decrease in total product). So, total product may continue to rise with diminishing returns. It just rises more slowly. Case Studies in the Text Economics in Action The Mythical Man-Month—The title of this EIA is also the title of a book published in 1975. The book applies the concept of diminishing returns to the writing of computer software. Ask students the following questions: 1. How does the law of diminishing marginal product apply to the writing of software? (It was found that doubling the number of programmers did not proportionately reduce the time necessary to complete a project.) 2. How did the title of the book The Mythical Man-Month originate? (It was found that a project that was possible for one programmer to produce in 12 months could not be accomplished by 12 programmers in one month.) 3. How does the nature of programming lead to diminishing returns? (Programmers must coordinate their work with all the other programmers: A greater quantity of programmers leads to an increase in the time spent communicating with everyone instead of writing code.) Activities Producing Successful College Students (3–5 minutes) Pair students or form into teams of four. Ask them to list all the inputs on a college campus which are used to “produce” successful college students. In the “short run,” which inputs are “fixed”? which inputs are “variable”? (Plant size, such as the number of classrooms, is the fixed input. As the number of registered students increases, the number of instructors needed—a variable input—increases.) Production at a Fast-Food Restaurant (3–5 minutes) Ask students to list the fixed and variable inputs at a typical fast-food restaurant. How has the company attempted to produce efficiently during busy times of the day? What technological changes has the company added to achieve a more efficient production? For a follow-up assignment ask students to interview a manager of a fast-food restaurant and ask what production problems occur. Ask the manager what amount of hamburger production is efficient and what quantity would be highly inefficient to produce. “Grow Rice on a Chalkboard” (10–20 minutes) (Adapted from Classroom Activities by Charles Stull, Dryden Press, 2001.) “Grow Rice on a Chalkboard” is a short simulation that illustrates the principle of diminishing marginal product. On the board, draw two rectangles, 2 × 3 feet each. Select two volunteers to act as farm managers and draw two equal-sized rectangular areas on the chalkboard, approximately 2 × 3 feet. These rectangles are the farm on which they will “grow” rice by writing the word RICE. Before they start producing, they must run to the back of the class to get a slip of paper from you that says LOAN on it. They then run to the board and start writing RICE in the same size, in a 30-second period. In the next module 21 the production function round, the managers can hire one worker from the class. The game is played repeatedly, adding another student each period. Track total output and the quantity of labor on the board as the game proceeds. It becomes increasingly too crowded to produce the rice efficiently. A typical result might be as follows: Labor Total Output 00 13 215 325 432 533 Have the class calculate the marginal product and determine when diminishing marginal product began. 121
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