Short-Run Costs: AFC, AVC, ATC and Marginal Cost

At a pizzeria, going from 10 to 20 pizzas a night, each extra pizza adds $2 to costs. Going from 40 to 60, each one adds $40. Same oven, same recipe. So why does a later pizza cost twenty times as much? This is Module 3.2, short-run production costs.

In the short run, the pizzeria is stuck with its one oven. Rent is $480 a night. Rent is a fixed cost: total fixed cost, TFC, stays $480 whether the shop bakes 60 pizzas or none. Cooks, paid $20 an hour, are the only variable input. Their wages are total variable cost, TVC: zero at zero pizzas, rising with output. Total cost adds the two: TC = TFC + TVC. At 40 pizzas, $480 plus $520 is $1,000. At zero pizzas, TC is still $480.

On a graph of totals, TFC is a flat line at $480, and TC runs $480 above the climbing TVC curve.

So what just happened? One: TFC is $480 at every output, even zero. Two: TVC, the wages, changes with output. Three: TC is TFC plus TVC: $1,000 at 40 pizzas.

Marginal cost, MC, is the extra cost of one more unit of output. The formula: the change in total cost divided by the change in output. This table jumps 10 pizzas at a time. From 10 to 20 pizzas, total cost rises from $560 to $580: $20 more. Now divide by the change in output, 10 pizzas. $20 over 10 is $2 per pizza. That's the marginal cost. Exam trap: $20 is the cost of 10 more pizzas, not the marginal cost. Don't divide by 1 out of habit. On a recent AP exam, fewer than one student in ten earned this point.

The last step jumps 20 pizzas, from 40 to 60. Total cost rises $800, from $1,000 to $1,800. $800 over 20 is $40 per pizza. TVC works too. Fixed cost never changes, so TVC also rises $800, from $520 to $1,320.

So what just happened? One: MC is the change in total cost over the change in output. Two: 10 to 20 pizzas: $20 over 10 is $2. Three: 40 to 60: $800 over 20 is $40.

Quick refresher from Module 3.1: marginal product is the extra output from one more unit of labor. Here, that's one more cook-hour.

From 10 to 20 pizzas, wages rose $20: at $20 an hour, one extra hour made 10 more pizzas. $20 over 10 is $2 each. From 30 to 40, wages rose $280: fourteen more hours for the same 10 pizzas, because cooks wait their turn at one oven. $280 over 10 is $28 each. That's diminishing marginal returns. Marginal product falls, so each pizza takes more labor, and MC slopes upward. At the start, though, MC fell from $8 to $2. With more cooks, one stretches dough while another tops and bakes. That specialization, or division of labor, gets more pizzas per hour, so MC falls.

So why does a later pizza cost twenty times as much? One: specialization made early pizzas cheaper: MC fell to $2. Two: then cooks crowded one oven, and marginal product fell. Three: so MC climbed to $28, then $40.

Quick refresher: an average is a total divided by the number of units. For costs, that means units of output: pizzas.

Average fixed cost, AFC, is TFC over quantity. Average variable cost, AVC, is TVC over quantity. Average total cost, ATC, is TC over quantity. At 40 pizzas: AFC is $480 over 40, $12. AVC is $520 over 40, $13. ATC is $1,000 over 40, $25. And $12 plus $13 is $25: ATC is AFC plus AVC. So AFC is ATC minus AVC.

So what just happened at 40 pizzas? One: AFC, $480 over 40, is $12. Two: AVC, $520 over 40, is $13. Three: ATC, $1,000 over 40, is $25: AFC plus AVC.

Exam trap: divide by output, never by workers, even when a table lists workers first. On a recent AP exam, only about three in ten got average fixed cost right.

Now graph the averages. AFC falls the whole way: the same $480 spread over more pizzas. AVC and ATC are U-shaped, and the vertical gap between them is AFC. At 40 pizzas, ATC is $25 and AVC is $13: a $12 gap. As output grows, AFC falls, so the gap narrows: at 60 pizzas, $30 minus $22 is just $8. An average times quantity gives back the total: $12 times 40 is $480. So TFC equals ATC minus AVC, times quantity.

Exam trap: that $480 is already the total. Multiply by quantity once, not twice. On a recent AP exam, fewer than half got total fixed cost right.

So what just happened? One: the gap between ATC and AVC is AFC: $12 at 40 pizzas. Two: the gap narrows as output rises. Three: gap times quantity, once, is TFC: $480.

Now add MC. The rule: MC crosses AVC and ATC at their lowest points. Every released AP exam from 2023 to 2026 scored MC through the minimum of ATC. Here's why. From 20 to 30 pizzas, MC is $14, below ATC's $29. Pizzas that cost less than the average pull it down, to $24. From 30 to 40, MC is $28, above $24, so it pulls the average up, to $25. ATC bottoms out where MC crosses it. Same for AVC: MC of $2 pulls it down to its low of $5 at 20 pizzas, then MC of $14 pulls it back up.

Exam trap: draw ATC as a clear U with one lowest point, and run a rising MC right through it. A flat bottom, or an MC that misses it, loses the point.

So what just happened? One: MC below an average pulls it down. Two: MC above an average pulls it up. Three: so MC crosses AVC and ATC at their lowest points: $5 at 20 pizzas, $24 at 30.

Last, cost curves shift when input costs or productivity change. Say the wage rises from $20 to $30 an hour. At 30 pizzas, the shop uses 12 cook-hours, which now cost $360 instead of $240. AVC rises from $8 to $12, and ATC from $24 to $28. From 20 to 30 pizzas, 7 more hours now cost $210, so MC is $210 over 10: $21, up from $14. MC, AVC and ATC shift up. AFC doesn't move. If rent rises instead, to $660, AFC and ATC shift up: at 30 pizzas, to $22 and $30. MC and AVC stay put: wages didn't change, so an extra pizza costs no more to make.

And if cooks get faster, each pizza takes less labor, so MC, AVC and ATC shift down.

So what just happened? One: a higher wage shifted MC, AVC and ATC up. Two: higher rent shifted AFC and ATC up, but not MC. Three: faster cooks shift MC, AVC and ATC down.

Exam moment: two questions the way the AP exam asks them, then one free-response part.

On a firm's cost graph, at 25 units, ATC is $34 and AVC is $27. What is the firm's total fixed cost? A) $7 B) $175 C) $675 D) $850 E) $4,375

The answer is B. The gap, $34 minus $27, is AFC: $7 a unit. Times 25 units is $175. A stops at AFC, a per-unit number. C is AVC times 25: total variable cost. D is ATC times 25: total cost. E multiplies by 25 twice.

A firm with fixed costs reaches its lowest short-run average total cost at 240 units. Which of the following is true at 240 units? A) MC is at its lowest point. B) MC is below ATC. C) MC equals ATC. D) MC equals AVC. E) AFC is at its lowest point.

The answer is C. A rising MC crosses ATC at ATC's lowest point, so there the two are equal. A flips the rule: it's ATC's bottom, not MC's. B is true only while ATC is still falling. D happens at AVC's lowest point, a smaller output. E can't be: AFC keeps falling.

Free response. A laundry service's only variable input is labor, at $96 per worker per day. With 3 workers it washes 42 loads a day; with 4 workers, 48. Calculate the marginal cost when output rises from 42 to 48 loads. Show your work.

What earns the point: formula, numbers, answer. MC equals the change in total cost over the change in output. The fourth worker adds $96 of cost and 6 loads: $96 over 6 is $16 per load. The costly mistake: stopping at $96, the change in cost, as if output rose by one load. On a recent AP exam, fewer than one student in ten earned this point.

So what just happened in that answer? One: write the formula first. Two: find both changes: $96 more in wages, 6 more loads. Three: divide: $96 over 6 is $16 per load.

Recap: total cost is fixed plus variable cost, and fixed cost stays put, even at zero. MC is the change in total cost over the change in output, whatever the step. And MC crosses AVC and ATC at their lowest points. Next: Module 3.3, Long-Run Production Costs.