Production and costs

Behind every supply curve are firms deciding how much to produce. Those decisions depend on costs, and costs depend on how inputs are turned into outputs. This lesson develops the economist's theory of production and cost, which underlies the analysis of market structures in lessons 9 to 11. It introduces the distinction between the short run and the long run, the law of diminishing returns, the family of cost curves that economists use, and the idea of economies of scale. BUS-110 lesson 3 used fixed and variable costs to calculate break-even points for a business; here we look at how costs change with output and why, and we define costs in the economist's way, including opportunity costs.

Economic profit and accounting profit

Accountants measure profit as total revenue minus explicit costs, the payments a firm actually makes for wages, materials, rent and interest. Economists measure economic profit as total revenue minus all costs, including implicit costs, the opportunity costs of resources the firm uses without paying for them directly. The main implicit costs are the owner's time, which could have earned a salary elsewhere, and the owner's capital, which could have earned a return elsewhere. Economic profit is therefore smaller than accounting profit. A firm earning zero economic profit is earning a normal profit: just enough to keep its resources in their current use, because it covers all opportunity costs.

The short run and the long run

Economists distinguish two time horizons. In the short run, at least one input is fixed. A factory's building and major machinery cannot be changed quickly, so in the short run the firm varies output by changing variable inputs such as labor, materials and energy. In the long run, all inputs are variable: the firm can build a new plant, close an existing one, or enter or leave the industry. The length of the short run varies by industry: a food truck can double its capacity in weeks, while a pulp mill or an oil sands project may take years.

Production and diminishing returns

A production function shows the relationship between the quantities of inputs used and the maximum output that can be produced. In the short run, with capital fixed, we can ask how output changes as more workers are added. The marginal product of labor is the extra output produced by one more worker. At first, marginal product may rise, as workers specialize and use the equipment more fully. Eventually, however, the law of diminishing marginal returns sets in: as more and more of a variable input is added to a fixed input, the marginal product of the variable input eventually declines. Picture a small kitchen with two ovens. The second and third cooks greatly increase output; the sixth and seventh mostly get in each other's way.

Diminishing returns is a short-run concept; it arises because one input is fixed. It is not the same as decreasing returns to scale, a long-run concept discussed below. Diminishing returns is one of the most reliable regularities in economics and is the reason short-run cost curves eventually slope upward.

Costs in the short run

Short-run costs divide into fixed costs (FC), which do not vary with output, such as rent, insurance and the cost of equipment, and variable costs (VC), which do, such as wages, ingredients and energy. Total cost (TC) is their sum. Dividing by output gives average fixed cost (AFC), average variable cost (AVC) and average total cost (ATC). Marginal cost (MC) is the change in total cost from producing one more unit, which equals the change in variable cost because fixed cost does not change.

Marginal cost is closely linked to marginal product. If each worker costs the same wage, then when marginal product is rising, each extra pizza requires less extra labor, so marginal cost falls; when marginal product is falling, each extra pizza requires more labor, so marginal cost rises. Diminishing marginal returns therefore produces rising marginal cost.

# Short-run cost table for the pizza kitchen: fixed cost $400/day, wage $160/day per worker
fixed, wage = 400, 160
output = [0, 40, 100, 150, 185, 210, 225, 230]
print("workers   Q    VC    TC    AFC    AVC    ATC     MC")
for w, q in enumerate(output):
    vc = wage * w
    tc = fixed + vc
    if q == 0:
        print(f"{w:7} {q:4} {vc:5} {tc:5}")
        continue
    mc = (tc - (fixed + wage * (w - 1))) / (q - output[w - 1])
    print(f"{w:7} {q:4} {vc:5} {tc:5} {fixed / q:6.2f} {vc / q:6.2f} {tc / q:6.2f} {mc:6.2f}")

workers   Q    VC    TC    AFC    AVC    ATC     MC
      0    0     0   400
      1   40   160   560  10.00   4.00  14.00   4.00
      2  100   320   720   4.00   3.20   7.20   2.67
      3  150   480   880   2.67   3.20   5.87   3.20
      4  185   640  1040   2.16   3.46   5.62   4.57
      5  210   800  1200   1.90   3.81   5.71   6.40
      6  225   960  1360   1.78   4.27   6.04  10.67
      7  230  1120  1520   1.74   4.87   6.61  32.00

The table shows the typical patterns. Average fixed cost falls continuously as the fixed cost is spread over more output. Marginal cost falls at first, as the second worker adds 60 pizzas, and then rises steadily as diminishing returns set in, reaching $32 per pizza for the seventh worker. Average variable cost and average total cost are U-shaped. And a key relationship holds: marginal cost cuts through the minimum points of both AVC and ATC. When the cost of the next unit is below the average, it pulls the average down; when it is above, it pulls the average up. The same logic applies to grades: if your next test score is below your average, your average falls.

Costs in the long run

In the long run, a firm can choose the size of its plant. For each plant size there is a short-run ATC curve; the long-run average cost (LRAC) curve traces the lowest cost of producing each level of output when the firm can choose any plant size. Its shape reflects returns to scale. Over a range of outputs, many industries experience economies of scale: long-run average cost falls as output rises. Sources include specialization of workers and equipment, spreading large fixed costs such as research, design and advertising over more units, bulk purchasing of inputs, and engineering relationships (a pipeline's capacity rises faster than the steel needed to build it). At some point, average costs may level off (constant returns to scale) and eventually rise (diseconomies of scale), as large organizations become harder to coordinate, communication slows and workers feel less connected to results.

The output at which long-run average cost stops falling is called the minimum efficient scale. It helps explain market structure. If minimum efficient scale is small relative to market demand, as for hair salons or restaurants, many firms can operate at low cost and markets tend to be competitive. If minimum efficient scale is large relative to demand, as for commercial aircraft, freight railways or electricity transmission, only a few firms, or even one, can produce at low cost, and markets tend to be concentrated. Software and digital platforms are an extreme case: the cost of developing the product is large but the marginal cost of serving one more user is close to zero, so average cost falls over an enormous range of output.

Other cost concepts

Economies of scope exist when producing several products together is cheaper than producing them separately, because they share inputs such as distribution networks, brand names or technology. A bank that offers deposit accounts, mortgages and credit cards through the same branches and app benefits from economies of scope. Learning curves describe the tendency for unit costs to fall as cumulative output rises, because workers and managers learn better methods. The cost of solar panels has fallen by roughly 20 % for each doubling of cumulative global production over several decades, one of the best-documented learning curves.

Finally, recall from lesson 1 that sunk costs are irrelevant to forward-looking decisions. In the short run, a firm's fixed costs are often sunk: the rent must be paid whether or not the firm produces. This means that a firm deciding whether to operate in the short run should compare revenue with variable costs only, a principle that leads to the shutdown rule in lesson 9.

Costs and business decisions

Cost curves are not merely textbook constructs. Managers use marginal cost to decide whether to accept a special order at a discounted price: if the price exceeds the marginal cost and the order does not undermine regular sales, it adds to profit even if the price is below average total cost. Airlines, hotels and electricity generators price aggressively at off-peak times for exactly this reason. Managers use average cost to decide whether to expand or build a new plant, and the concept of minimum efficient scale to judge whether a market can support a new entrant. And understanding economies of scale helps explain mergers: firms often justify mergers by claiming cost savings from greater scale, a claim competition authorities examine carefully, as lesson 11 discusses.