Production & Costs
Short-run production, marginal product, fixed/variable costs, ATC, AVC, MC, and economies of scale
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Production and Costs
Behind every supply curve lies a firm's cost structure. Microeconomic firm theory begins with the production function — the relationship between inputs (labor, capital) and output (Q) — and translates that physical relationship into the dollar costs that drive supply decisions.
Short Run vs Long Run
In the short run, at least one input (usually capital — plant, machinery) is fixed. The firm can only vary labor and other variable inputs. In the long run, all inputs are variable; the firm can change plant size, exit, or enter.
The Law of Diminishing Marginal Returns
In the short run, as more units of a variable input (labor) are added to a fixed input, the marginal product (MP) of additional units eventually FALLS. This is purely physical — the third worker sharing one machine adds less output than the second. Diminishing returns is the reason short-run marginal cost () eventually rises.
Short-Run Cost Concepts
| Cost | Meaning |
|---|---|
| TFC | Total fixed cost — does not change with output |
| TVC | Total variable cost — rises with output |
| TC | |
| AFC | — falls continuously |
| AVC | — U-shaped |
| ATC | — U-shaped (sum of AFC and AVC) |
| MC | — U-shaped |
A critical relationship: the marginal cost curve crosses both AVC and ATC at their MINIMUM points. This is a pure mathematical property of averages — when marginal is below average, it pulls the average down; when above, it pushes it up.
Long-Run Average Total Cost (LRATC)
In the long run, the firm picks the most efficient plant size for each output level. The LRATC curve is the lower envelope of all possible short-run ATC curves. Its shape reveals:
- Economies of scale: LRATC falls as output rises (specialization, bulk discounts).
- Constant returns to scale: LRATC flat.
- Diseconomies of scale: LRATC rises (coordination/management problems).
Profit Concepts
- Accounting profit = .
- Economic profit = (including the opportunity cost of the owner's resources).
A firm earning ZERO economic profit is doing JUST as well as in its next-best alternative — it is breaking even in economic terms even while earning a positive accounting profit.
📚 Practice Problems
1Problem 1easy
❓ Question:
A firm's TFC = $200 and TVC at Q = 50 is $300. Compute (a) TC, (b) AFC, (c) AVC, and (d) ATC at Q = 50.
💡 Show Solution
(a) TC = TFC + TVC = 200 + 300 = \boxed{\500}$.
(b) AFC = TFC/Q = 200/50 = \boxed{\4}$.
(c) AVC = TVC/Q = 300/50 = \boxed{\6}$.
(d) ATC = TC/Q = 500/50 = \boxed{\10}ATC = AFC + AVC = 4 + 6 = 10$.)
2Problem 2easy
❓ Question:
Total cost when Q = 20 is $300. When Q rises to 25, total cost is $340. Compute the marginal cost over this range.
💡 Show Solution
MC = \dfrac{\Delta TC}{\Delta Q} = \dfrac{340 - 300}{25 - 20} = \dfrac{40}{5} = \boxed{\8}$ per unit.
3Problem 3medium
❓ Question:
Explain why MC must cross both AVC and ATC at their minimum points. Use the analogy of test scores.
💡 Show Solution
It's a pure mathematical property of averages and marginals.
If the next test score (marginal) is BELOW your current average, your average must FALL. If the next score is ABOVE your average, the average must RISE. The average is unchanged only when the marginal equals the current average — and that's exactly the minimum of the average curve.
Translating to costs: when MC < AVC, AVC is falling. When MC > AVC, AVC is rising. Therefore MC = AVC exactly at AVC's minimum. Same logic for ATC. (MC need not be at its own minimum at this point — the minimum of MC occurs earlier.)
4Problem 4medium
❓ Question:
A firm earns total revenue of $80,000 per year. Explicit costs are $50,000. The owner could have earned $40,000 working elsewhere. Compute (a) accounting profit and (b) economic profit. (c) Is the firm earning profit "in the economic sense"?
💡 Show Solution
(a) Accounting profit = TR - \text{explicit costs} = 80{,}000 - 50{,}000 = \boxed{\30{,}000}$.
(b) The implicit (opportunity) cost of the owner's time is $40,000. Economic profit = TR - \text{explicit} - \text{implicit} = 80{,}000 - 50{,}000 - 40{,}000 = \boxed{-\10{,}000}$.
(c) No. Economic profit is negative — the owner would be $10,000 better off in the next-best alternative. Even though accounting books look healthy, the firm is destroying value relative to the owner's opportunity cost.
5Problem 5hard
❓ Question:
A firm in the short run has the following cost structure: TFC = $100. At Q = 10, TVC = $60; at Q = 11, TVC = $72; at Q = 12, TVC = $88. (a) Compute MC for the 11th and 12th units. (b) What does the rising MC tell you about marginal product of the variable input? (c) The firm faces a market price of $15 per unit. Should it produce the 11th and 12th units?
💡 Show Solution
(a) MC_{11} = 72 - 60 = \boxed{\12}MC_{12} = 88 - 72 = \boxed{$16}$.
(b) MC is rising ⇒ each additional unit takes MORE variable input than the last ⇒ the marginal product of the variable input is falling. This is the law of diminishing marginal returns at work.
(c) Compare price (= MR for a price-taker) to MC.
- 11th unit: ⇒ produce (adds $3 to profit).
- 12th unit: ⇒ do not produce (would lose $1).
Optimal short-run output stops where — i.e., the 11th unit is the last profitable one.
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