Production and Cost Review for AP Economics (page 2)
Review questions for this study guide can be found at:
Main Topics: Short-Run Production Functions, Law of Diminishing Returns, Short-Run Costs, Connecting Production and Cost, Long-Run Costs, Economies of Scale
Short-Run Production Functions
How do economic resources like labor, capital, natural resources, and entrepreneurial talent become a cup of lemonade, or a ton of copper, or a 30-second television commercial? A production function is the mechanism for combining production resources, with existing technology, into finished goods and services. In other words, a production function takes inputs and creates output. In a production function that uses only labor (L) and capital (K):
Fixed and Variable Inputs
The short run is a period of time too brief to change the plant capacity. This implies that some production inputs cannot be changed in the short run. These are fixed inputs. During the short run, firms can adjust production to meet changes in demand for their output. This implies that some inputs are variable inputs. Using only labor and capital, we assume that labor can be changed in the short run, but capital (i.e., the plant capacity) is fixed.
Short-Run Production Measures
By its very nature, production lends itself to be quantified and as a result you need to study these three production measures. To keep it simple, capital is assumed to be fixed while labor can be changed to produce more or less output.
- Total Product (TPL) of Labor is the total quantity, or total output, of a good produced at each quantity of labor employed.
- Marginal Product (MPL) of Labor is the change in total product resulting from a change in the labor input. MPL = ΔTPL/ΔL. If labor is changing one unit at time, MPL = ΔTPL.
- Average Product (APL) of Labor is also a measure of average labor productivity and is total product divided by the amount of labor employed. APL = TPL/L.
As you can see, MPL and APL are both derived from TPL. It is useful to see how these three measures are related with a numerical example.
In the production period of a month, Molly's lemonade stand combines variable inputs of her labor (and the raw materials) to the fixed inputs of her table and her license to operate. Molly adds employees to her plant and forecasts the change in production (cups per day) in Table 8.2
As Molly employs more workers to the fixed plant capacity (the table on the corner), total product increases, eventually peaks, and then begins to fall. This production function can be seen in Figure 8.1
Law of Diminishing Marginal Returns
Imagine what happens to the lemonade stand as Molly adds more and more workers. At first, tasks are divided. (For example, Josh squeezes the lemons; Molly adds the sugar; Kelli stirs.) Specialization occurs. The marginal productivity of successive workers is rising in the early stage of production, but at some point, adding more workers increases the total product by a lesser amount. Maybe the fourth worker is pouring the lemonade and stocking while the fifth is taking money and making change. Beyond the fifth worker, the table is too crowded with employees, cups are spilled, product is wasted, and total production actually falls. The marginal contribution of these workers is negative. This illustrates one of the most important production concepts in the short run, the Law of Diminishing Marginal Returns, which states that as successive units of a variable resource are added to a fixed resource, beyond some point the marginal product falls.
Marginal product is the incremental change in total product as one more unit of labor is added. Marginal product is the geometric slope of total product. In Figure 8.1, the total product curve is initially getting steeper as more labor is added. This is seen in Figure 8.2 as increasing marginal product. From the third to the fifth worker, the slope of total product is still positive, but is becoming less steep. In Figure 8.2 marginal product from workers 3 to 5 is still positive but is falling. Beyond the fifth worker, total product is falling and thus has a negative slope. This turn of events is seen below when marginal product becomes negative.
Average product, also plotted below, initially rises, reaches a peak, and then begins to fall. So long as the marginal (next) worker adds production that is above the current average, they are pulling the average up. This is why we see APL rising so long as MPL is above APL. If the marginal worker adds production that is below the current average, the worker pulls the average down. Thus when MPL is below APL, you see that APL is falling. Logically then, MPL intersects APL at the peak of APL. Average product cannot be negative.
It is important to note that we have discussed production theory without including the nagging necessity of paying for our hired inputs. For every employed input, fixed or variable, a cost is incurred.
In the short run, there is at least one input that is fixed and so these costs are also fixed. All inputs that are variable incur variable costs.
- Total Fixed Costs (TFC) are those costs that do not vary with changes in short-run output. They must be paid even when output is zero. These include rent on building or equipment, insurance or licenses.
- Total Variable Costs (TVC) are those costs that change with the level of output. If output is zero, so are total variable costs. They include payment for materials, fuel, power, transportation services, most labor, and similar costs.
- Total Cost (TC) is the sum of total fixed and total variable costs at each level of output.
TC = TVC + TFC
Table 8.3 summarizes Molly's costs of producing cups of lemonade per minute. Her total fixed costs are assumed to be $6 per minute and total variable costs increase as production increases.
Figure 8.3 illustrates the three total cost functions. Total fixed cost is a constant at all levels of output. Total variable cost quickly rises at first, briefly slows, and then proceeds to increase at an increasing rate. Total cost is simply the sum of TFC and TVC at every level of output and so it lies parallel to TVC. Thus the vertical distance between TC and TVC is equal to TFC.
Marginal and Average Costs
Similar to our discussion of production, we can derive marginal and per unit measures of cost from the total cost functions. These are in Table 8.4.
- Marginal Cost is the additional cost of producing one more unit of output MC = ΔTC/ΔQ. Since TVC are the only costs that change with the level of output, marginal cost is also calculated as MC = ΔTVC/ΔQ. If quantity is changing one unit at a time, MC = ΔTC = ΔTVC.
- Average Fixed Cost (AFC) is total fixed cost divided by output. AFC = TFC/Q. It continuously falls as output rises.
- Average Variable Cost (AVC) is total variable cost divided by output. AVC = TVC/Q.
- Average Total Cost (ATC) is total cost divided by output ATC = TC/Q. Note that ATC = AFC + AVC.