The Costs of Production Highlighted Sections Production Functions Cost Functions Short and Long-Run Costs Production Functions - (Back to Top) Remember that a production function is a relationship between resources used (like land, labor or capital) and output produced (like Twinkies). The table below is a sample production function for the production of Twinkies. Assume that the company producing Twinkies has a factory and capital in place, and has to hire a work force (therefore, the variable input is labor, the fixed input is capital). Table #1 Production Function for Twinkies   Labor   Twinkies Marginal Product 0 0 --- 1 100 100 2 180 80 3 240 60 4 280 40 5 300 20 6 300 0 In the table above, we see the relationship between workers hired and Twinkies produced. The last column gives the marginal product, which is defined as the increase in output produced from an additional input (one more worker). When the first worker is hired, twinkie output rises from 0 to 100 units - therefore, the marginal product of the first worker is 100 Twinkies. The second worker increases output from 100 units to 180 units - therefore, the marginal product of the second worker is 80 Twinkies.   Notice that marginal product gets smaller and smaller as the number of workers hired increases. Diminishing marginal product is also reflected in the graph below. This figure depicts the production function from table #1.   Q: What is the relationship between the slope of the production function and marginal product? A: Marginal product IS the slope of the production function. Note that the axes are output produced and inputs used. Marginal product is defined as (paraphrasing from the definition in your text) the change in output divided by the change in inputs used. Cost Functions - (Back to Top) For economists, having the information given by a production function is important. However, since economists want to understand the production decisions made by various types of firms (the subject of the next 4 chapter in the text) it is better to translate the information given in the production function into a cost function. A cost function relates different levels of output (number of Twinkies produced) to the cost of producing that output.   Suppose that a firm producing Twinkies has the following cost structure: the fixed cost of operating the plant is $500 the variable cost of labor is $25/worker Click here to get a blank table of cost information for your practice.   Click here to check your answers.   The information you solved in the previous table is graphed below. The first figure shows total cost on the vertical axis, and the number of Twinkies produced on the horizontal axis. The second figure depicts marginal cost, average fixed cost, average variable cost and average total cost.   Short and Long-Run Costs - (Back to Top) Short and long-run costs are the subject of the java exercise in this chapter. Before you move on to that exercise, you should review the following terminology and concepts: For economists, the difference between the short-run and the long-run is determined by whether or not firms can change their use of ALL productive resources. For example, if you operate a restaurant that has a one-year lease, any decisions with less than a one-year time horizon are short-run decisions. The reason is that your monthly lease payment is fixed for the next year, and you cannot change it. Therefore, firms have fixed costs in the short-run.   If you, as owner of a restaurant, decide to move to a larger location after one-year (when your lease has expired), you are making a long-run decision. This points out the important distinction for economists between the short and long-run - in the long-run all costs are variable.   Firms can change everything about their operations in the long-run - even the size of their production facilities. When firms change their use of land, labor AND capital, there are three possibilities:   economies of scale - firms experience economies of scale if their average cost per unit in production falls as the firm expands in size   diseconomies of scale - firms experience diseconomies of scale if their average cost per unit in production rises as the firm expands in size   constant returns to scale - firms experience constant returns to scale if their average cost per unit in production is constant as the firm expands in size The figure below shows the relationship between economies of scale, constant returns to scale and diseconomies of scale and a typical firm's Long-Run Average Cost curve. At levels of output less than Q1, this firm experiences economies of scale (average cost falls as firm size rises). Between Q1 and Q2, this firm experiences constant returns to scale (average cost is constant as firm size rises). At levels of output larger than Q2, this firm experiences diseconomies of scale (average cost rises as firm size rises). *The relationship between short-run and long-run average cost will be explored in this chapter's java exercise. (Back to top)