Production and Cost Review for AP Economics

Graphically Speaking

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 AP_L rising so long as MP_L is above AP_L. If the marginal worker adds production that is below the current average, the worker pulls the average down. Thus when MP_L is below AP_L, you see that AP_L is falling. Logically then, MP_L intersects AP_L at the peak of AP_L. Average product cannot be negative.

Short-Run Costs

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.

Total Costs

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.

1. 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.
2. 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.
3. 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.

1. 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.
2. Average Fixed Cost (AFC) is total fixed cost divided by output. AFC = TFC/Q. It continuously falls as output rises.
3. Average Variable Cost (AVC) is total variable cost divided by output. AVC = TVC/Q.
4. Average Total Cost (ATC) is total cost divided by output ATC = TC/Q. Note that ATC = AFC + AVC.

Graphically Speaking

If marginal product is the slope of total product, it should be no surprise that marginal cost is the slope of total cost, or total variable cost. We can see that marginal cost initially falls due to specialization, but soon begins to rise as more output is produced. This is the Law of Increasing Costs and is a direct result of the Law of Diminishing Marginal Returns to production. Both being U-shaped curves, average variable and average total costs initially fall, hit a minimum point, and begin to rise. Average Total Cost is vertically above AVC by the amount of AFC. Figure 8.4 illustrates this.

Marginal cost and average variable and average total cost are related in much the same way as marginal product is related to average product of labor. When the marginal cost of producing another cup of lemonade exceeds the current average cost the average is rising. When the marginal cost of producing another cup of lemonade falls below the current average cost the average is falling. Therefore, marginal cost equals average total cost at the minimum of ATC and equals average variable cost at the minimum of AVC.

Bridge over (Troubling) Economic Waters

Many students think that production and cost concepts are two sets of theoretical topics. This separation creates the impression that "there's twice as much to remember." These students are surprised to find out that production and cost are closely connected.

Think about it from Molly's point of view. If the next worker employed has a high marginal product, then the marginal cost of producing that increased product must be quite low. When things are going well with production, they must be going well with cost. Try to see the concepts of production and cost not as two isolated bodies of theory, but as two related sets of concepts that just need to be bridged. Let us try to build this bridge with a little algebra.

Marginal Product and Marginal Cost

MC = ΔTVC/ΔQ and since the only variable input is labor being paid a fixed wage w,

MC = wΔL/ΔQ which can be modified as,

MC = w/(ΔQ/ΔL) = w/MP_L. MC and MP_L are inverses of each other!

Average Product and Average Variable Cost

AVC = TVC/Q and with the only variable input being labor paid a fixed wage w,

AVC = wL/Q which can be modified as,

AVC = w/(Q/L) = w/AP_L. AVC and AP_L are inverses of each other!

If we put smoother versions of our production and cost figures together, we can see these relationships in Figures 8.5 and 8.6. The output q₁ where MP_L is at a maximum is the same as the output where MC is at a minimum. Likewise, the output q₂ where AP_L is at a maximum is the same as the output where AVC is at a minimum.

Long-Run Costs

Since all inputs are variable in the long run, discussion of production levels isn't so much about output per hour or day; it's more a question of plant size or capacity. In the short run, the firm asks, "With our current plant size, how much must we produce today?" The long run is long enough to adjust the plant capacity so the issue is really one of scale. The firm might ask itself, "At what scale do we want to operate?"

Long-Run Average Cost

I like to think of the firm's short-run average costs as a snapshot of the firm's ability to produce efficiently at the fixed plant size. Over time, the firm may grow and expand the plant size and begin to produce efficiently, but at the larger fixed plant size, giving us another snapshot. This process repeats itself as the firm expands or contracts and each time we receive another short-run snapshot of average cost. If we could put these short-run snapshots together into a kind of motion picture, we would see a more continuous long-run home movie of the firm's average costs. The example and Figure 8.7 illustrate the connection between short- and long-run average costs.

Example:

• In year one, Molly's firm operates at a "small" scale, producing on SRAC₁.
• In year two, Molly could expand and operate at a "medium" scale, producing on SRAC₂, but only if she can sell more than 100 gallons of lemonade. At quantities below 100, SRAC₁ < SRAC₂, so expansion would not be wise.
• In year three, Molly might expand to operate at a "large" scale and move to SRAC₃, but only if she can sell more than 250 gallons.
• Beyond the "large" scale exists a "grande" scale, but very quickly SRAC₄ > SRAC₃ and so this plant capacity actually begins to pay rising per unit costs.

Each of these four short-run snapshots of average costs can be smoothed out into the home movie long-run average cost curve, which is composed of sections of each short-run average cost curve at each of the four plant sizes that Molly might choose for her firm. In Figure 8.7, the long-run average cost curve would lie along the segments a→b→c→d→e.

Economies of Scale

Construction of a smoother version of Figure 8.7 allows us to see more easily some important stages of the long-run average cost curves (Figure 8.8).

1. Economies of scale are advantages of increased plant size and are seen on the downward part of the LRAC curve. LRAC falls as plant size rises.
   1. Labor and managerial specialization is one reason for this.
   2. Ability to purchase and use more efficient capital goods also can explain economies of scale.
2. Constant returns to scale can occur when LRAC is constant over a variety of plant sizes.



3. Diseconomies of scale are illustrated by the rising part of the LRAC curve and can occur if a firm becomes too large.
   1. Some reasons for this include distant management, worker alienation, and problems with communication and coordination.

   

Review questions for this study guide can be found at:

The Firm, Profit, and the Costs of Production Review Questions for AP Economics