Chapter 17 — The Costs of Production

How Firms Think About Costs

Parts I through III of this book looked at markets from the outside: what happens when buyers and sellers meet, what prices emerge, what happens when the market fails. Part IV goes inside the firm. The next five chapters ask: how does a firm decide how much to produce, what price to charge, and whether to enter or exit a market?

The answer, in every case, starts with costs. A firm that doesn't understand its own cost structure — what's fixed, what's variable, what happens to costs as output changes — can't make good decisions about anything. This chapter builds the cost framework that Chapters 18–21 will use.

The running example is the Riverside Foods plant in Millbrook. We've seen Riverside before (Chapters 3, 5, 9). Now we go inside the plant and look at its actual cost structure — what it pays for, how those payments change as it produces more or less frozen food, and what the cost curves look like.

17.1 What firms pay for: fixed costs and variable costs

Every firm pays for two kinds of things.

Fixed costs don't change with output. Riverside Foods pays about $180,000 per month for its building lease, $95,000 per month in property taxes and insurance, $120,000 per month for salaried managers and administrative staff, and about $60,000 per month in loan payments on its processing equipment. These payments are the same whether the plant produces 1 million pounds of frozen vegetables this month or 2 million. They are fixed in the short run.

Fixed cost (FC): costs that do not change with the quantity of output produced. Examples: rent, property taxes, insurance, salaried personnel, loan payments on equipment.

Variable costs change with output. Riverside pays its production workers (about 800 hourly employees) roughly $22/hour. It pays for raw vegetables from farmers — the more it produces, the more vegetables it buys. It pays for packaging materials, electricity to run the freezers, water for the washing lines, and natural gas for the blanching process. Each of these rises as output rises and falls as output falls.

Variable cost (VC): costs that change with the quantity of output produced. Examples: hourly labor, raw materials, packaging, electricity, shipping.

Total cost is the sum:

$$TC = FC + VC$$

At zero output, total cost equals fixed cost (the plant still pays rent and managers even if it produces nothing). As output rises, variable cost rises, and total cost rises with it.

A numerical example

Suppose Riverside's monthly costs look like this:

| Output (thousands of lbs) | Fixed cost ($K) | Variable cost ($K) | Total cost ($K) | |---|---|---|---| | 0 | 455 | 0 | 455 | | 200 | 455 | 180 | 635 | | 400 | 455 | 320 | 775 | | 600 | 455 | 430 | 885 | | 800 | 455 | 520 | 975 | | 1,000 | 455 | 600 | 1,055 | | 1,200 | 455 | 700 | 1,155 | | 1,400 | 455 | 840 | 1,295 | | 1,600 | 455 | 1,040 | 1,495 | | 1,800 | 455 | 1,320 | 1,775 |

Notice: variable cost rises with output, but it rises unevenly. At low output levels, each additional 200,000 pounds costs about $160K–$180K in variable costs. At high output levels, each additional 200,000 pounds costs $200K–$280K. The variable cost is rising at an increasing rate. This is the key pattern that drives the marginal cost curve.

17.2 Average costs

To compare firms of different sizes, or to evaluate whether a firm is making money on each unit, we compute average costs.

Average total cost (ATC) = TC / Q

Average fixed cost (AFC) = FC / Q

Average variable cost (AVC) = VC / Q

Note that ATC = AFC + AVC (because TC = FC + VC, and dividing both sides by Q gives ATC = AFC + AVC).

The shape of average cost curves

AFC always declines. Fixed cost is constant; dividing a constant by a larger and larger Q produces a smaller and smaller number. This is spreading the overhead — the more you produce, the less fixed cost per unit. At 200K lbs, AFC = $455K/200K = $2.28/lb. At 1,000K lbs, AFC = $455K/1,000K = $0.46/lb. At 1,800K lbs, AFC = $455K/1,800K = $0.25/lb.

AVC typically falls, then rises. At low output, adding workers to the plant improves productivity (each worker has more equipment, more space, more specialization). AVC falls. At high output, the plant gets crowded — workers get in each other's way, machines are running at capacity, overtime kicks in, errors increase. AVC rises. The turning point is the output level where the plant is running at its most efficient operating point.

ATC is U-shaped. At low output, ATC is high because AFC is spread over few units. At intermediate output, ATC falls as AFC spreads and AVC is in its efficient range. At high output, ATC rises because AVC is rising faster than AFC is falling. The bottom of the U — the minimum ATC — is the firm's most efficient scale of production.

              AVERAGE COST CURVES — Riverside Foods

   Cost
   per lb
    $3.00 |
          |    ATC
    $2.50 |     ╲
          |      ╲
    $2.00 |       ╲         AVC
          |        ╲        ╱
    $1.50 |         ╲      ╱
          |          ╲    ╱
    $1.00 |           ╲  ╱     ← ATC minimum (most efficient scale)
          |            ╲╱
    $0.75 |             ╱╲
          |            ╱  ╲
    $0.50 |           ╱    ╲      AFC
          |   AFC    ╱      ╲___________
    $0.25 |    ╲    ╱
          |     ╲__╱ ____________
          |_____________________________________________
          0     500    1000    1500    2000       Output (K lbs)

Figure 17.1 — Average cost curves for Riverside Foods. AFC declines continuously as fixed costs spread over more output. AVC is U-shaped (falls then rises). ATC = AFC + AVC is also U-shaped, reaching its minimum at the plant's most efficient operating level.

17.3 Marginal cost: the most important curve

Marginal cost (MC) is the additional cost of producing one more unit of output.

MC = ΔTC / ΔQ

Marginal cost is what firms actually use when they decide whether to produce one more unit. If the price they can sell for exceeds the marginal cost, the additional unit is profitable. If the price is below marginal cost, the additional unit loses money.

Why marginal cost curves are U-shaped

The marginal cost curve falls at first (when the plant is below capacity, adding output is cheap) and then rises (when the plant approaches and exceeds its designed capacity, each additional unit is increasingly expensive).

The reason for the rising portion is diminishing returns — one of the most fundamental ideas in production economics.

Diminishing returns (also called diminishing marginal product): holding some inputs fixed (the plant, the equipment), adding more of a variable input (workers) eventually produces smaller and smaller increments of additional output.

The first 10 workers added to a production line at Riverside are very productive — each one fills a role the line needs. The 100th worker is still productive but adds less than the 10th (the line is designed for about 90 workers; the 100th is doubling up on a task). The 150th worker barely adds anything — the line is so crowded that adding one more person actually slows things down (workers bumping into each other, waiting for equipment, making errors because they're rushing).

Diminishing returns means that at high output levels, each additional unit of output requires more and more additional variable input (labor, materials, energy). This means the marginal cost of each additional unit rises. The marginal cost curve slopes upward once diminishing returns kick in.

The relationship between marginal cost and average cost

There is a mathematical relationship between marginal cost and average total cost that is both intuitive and useful:

• When MC < ATC, ATC is falling. If the cost of the next unit is below the current average, producing it pulls the average down.
• When MC > ATC, ATC is rising. If the cost of the next unit is above the current average, producing it pulls the average up.
• MC crosses ATC at ATC's minimum. At the exact bottom of the U-shaped ATC curve, MC = ATC.

The same relationship holds for MC and AVC.

The analogy: if your GPA is 3.5 and you earn a 4.0 this semester (the "marginal" grade is above the "average"), your GPA goes up. If you earn a 3.0 this semester (the marginal is below the average), your GPA goes down. The marginal pulls the average in its direction.

              MARGINAL AND AVERAGE COST CURVES

   Cost
   per lb
    $2.00 |
          |       MC
    $1.75 |         ╱
          |        ╱
    $1.50 |       ╱         ATC
          |      ╱           ╱
    $1.25 |     ╱           ╱
          |    ╱       ★  ╱   ← MC crosses ATC at ATC's minimum
    $1.00 |   ╱      ★  ╱
          |  ╱    ★    ╱
    $0.75 | ╱   ★     ╱
          |╱  ★      ╱
    $0.50 |  ★ AVC  ╱
          |★    ╲  ╱
          |  ★   ╲╱
          |    ★__★
          |_____________________________________________
          0     500    1000    1500    2000       Output (K lbs)

Figure 17.2 — MC, ATC, and AVC. MC crosses both AVC and ATC at their respective minimums. When MC is below ATC, ATC is falling; when MC is above ATC, ATC is rising.

17.4 The short run vs. the long run

Everything above has been short-run cost analysis — the analysis that holds some inputs (the plant, the equipment, the building) fixed and varies others (labor, materials). In the short run, Riverside Foods can't build a new plant or buy new equipment. It can only adjust the variable inputs.

In the long run, all inputs are variable. The firm can build a bigger plant, buy new equipment, move to a different location, adopt new technology, or exit the industry entirely. In the long run, there are no fixed costs — everything is a choice.

Economies and diseconomies of scale

In the long run, the firm's average cost depends on its scale — how big it is.

Economies of scale: average cost falls as the firm gets larger. Larger firms can spread fixed costs over more units, negotiate better input prices (bulk discounts), use more specialized equipment, and exploit the division of labor more fully.

Diseconomies of scale: average cost rises as the firm gets too large. Very large firms face coordination problems (communication across thousands of employees), bureaucracy, difficulty monitoring quality, and reduced flexibility.

The long-run average total cost (LRATC) curve is U-shaped (or, more often, L-shaped): it falls as the firm grows from small to medium (economies of scale), reaches a minimum at the efficient scale, and then either stays flat or rises as the firm grows from large to very large (constant returns or diseconomies of scale).

For many industries, the LRATC curve is relatively flat over a wide range of firm sizes. A medium-sized frozen-food processor like Riverside Foods is not dramatically more or less efficient per unit than a large one. This is why many industries have firms of many different sizes coexisting — the cost advantage of being bigger is real but modest once you're past the minimum efficient scale.

For some industries — particularly those with very large fixed costs (automobile manufacturing, semiconductor fabrication, airline operations) — the LRATC continues to decline over a wide range, meaning that a few very large firms are much more efficient than many small ones. This is one source of natural monopoly (Chapter 19).

17.5 Sunk costs in the context of firm decisions

Chapter 1 introduced sunk costs: costs that have already been paid and cannot be recovered. In the context of firm decisions, sunk costs show up constantly — and the mistake of factoring them into forward-looking decisions is just as common for firms as for individuals.

Riverside Foods paid $8 million for its processing equipment ten years ago. The equipment is now worth about $1 million on the used market. The $7 million difference is sunk. Should the manager consider the $8 million when deciding whether to continue operating? No. The only relevant costs are the forward-looking ones: what will it cost to operate from now on, and what revenue will it generate?

A firm should shut down when the revenue from operating is less than the variable cost of operating. Fixed costs are irrelevant to this decision because they're sunk in the short run — the firm pays them whether it operates or not. If revenue exceeds variable cost but doesn't cover total cost, the firm should continue operating in the short run (because operating reduces the total loss relative to shutting down, since operating at least covers some of the fixed cost) but exit in the long run (when the lease expires and the equipment can be sold, those fixed costs become variable).

The shutdown rule: shut down if P < AVC (if the price is below the minimum average variable cost, every unit produced loses money on variable costs alone, and the firm is better off producing nothing).

The exit rule: exit the industry if P < ATC in the long run (if the price doesn't cover total cost including the opportunity cost of capital, the firm's resources would be better used elsewhere).

17.6 Riverside Foods, worked through

Let's apply all of this to Riverside Foods.

**Fixed costs (~$455K/month):** building lease ($180K), property taxes and insurance ($95K), salaried staff ($120K), equipment payments ($60K). These are paid regardless of output.

Variable costs: production labor (~800 workers × $22/hr × 160 hrs/month ≈ $2.8M at full capacity, but scales with output), raw vegetables ($0.35–0.50/lb of output, depending on season), packaging ($0.08/lb), electricity ($45K–$120K depending on output), natural gas ($15K–$40K), shipping ($0.12/lb), and miscellaneous ($30K).

Current output: about 1.2 million lbs/month.

Revenue: Riverside sells its frozen products to grocery chains at an average wholesale price of about $1.10/lb. Monthly revenue: $1.2M × $1.10 = $1,320K.

Is Riverside profitable? - Total cost at 1.2M lbs (from our table, interpolating): about $1,155K - Revenue: $1,320K - Profit: $1,320K − $1,155K = $165K/month

Yes, Riverside is profitable. But notice how thin the margin is: $165K on $1,320K in revenue is a profit margin of about 12.5%. A 10% increase in raw vegetable prices (a bad growing season) or a 5% decrease in wholesale prices (a tough negotiation with a grocery chain) could push the plant into the red.

Should Riverside expand to 1.6M lbs/month?

From the cost table: total cost at 1.6M lbs is $1,495K. Revenue would be 1.6M × $1.10 = $1,760K. Profit: $1,760K − $1,495K = $265K/month. That's higher than at 1.2M lbs. The expansion is profitable.

But the marginal cost of the last 400K lbs (from 1.2M to 1.6M) is $1,495K − $1,155K = $340K. The marginal revenue is 400K × $1.10 = $440K. Since MR > MC, the expansion passes the marginal test.

Should Riverside expand to 1.8M lbs/month?

Total cost at 1.8M lbs: $1,775K. Revenue: 1.8M × $1.10 = $1,980K. Profit: $205K/month. Profit is lower than at 1.6M lbs ($265K).

Marginal cost of the last 200K lbs (from 1.6M to 1.8M): $1,775K − $1,495K = $280K. Marginal revenue: 200K × $1.10 = $220K. Now MC > MR. The expansion to 1.8M destroys value. Riverside should stop at 1.6M.

This is the marginal-cost rule applied to a real firm: produce where MR = MC (or as close as you can get). For Riverside, the optimal output is somewhere around 1.5–1.6 million lbs/month.

17.7 Where this is going

Chapter 17 gave you the cost framework. The next four chapters apply it:

• Chapter 18 — Perfect Competition: many firms, identical products, free entry. The supply curve is the MC curve (above AVC). Long-run equilibrium: economic profit = 0.
• Chapter 19 — Monopoly: one firm. The monopolist produces where MR = MC but charges a price above MC, creating deadweight loss.
• Chapter 20 — Monopolistic Competition and Oligopoly: the messy middle. Product differentiation, game theory, OPEC.
• Chapter 21 — Labor Markets: the most important market for most readers. Wage determination, human capital, the minimum wage (deep treatment), automation.

Each of these chapters will use the cost curves you built here. Take the time to understand them before moving on.

Key terms recap: fixed cost — doesn't change with output (rent, insurance, salaried staff) variable cost — changes with output (hourly labor, raw materials, packaging) total cost = FC + VC average total cost (ATC) = TC/Q (U-shaped) average fixed cost (AFC) = FC/Q (always declining) average variable cost (AVC) = VC/Q (U-shaped) marginal cost (MC) = ΔTC/ΔQ (the cost of one more unit; U-shaped; crosses ATC at ATC minimum) diminishing returns — adding more of a variable input eventually produces smaller increments of output economies of scale — ATC falls as the firm gets larger (in the long run) diseconomies of scale — ATC rises as the firm gets too large shutdown rule — shut down if P < AVC (can't cover variable costs) exit rule — exit if P < ATC in the long run (can't cover total costs)

Themes touched: Tradeoffs (produce more or less?), Incentives (marginal cost drives the decision), Affects daily life (every product you buy reflects a firm's cost structure).