23.01.08 · economics / firm-theory

Costs of Production

draft3 tiersLean: none

Anchor (Master): Mas-Colell, Whinston & Green, Microeconomic Theory; relevant academic sources

Intuition [Beginner]

Every business has costs. A bakery pays for flour, sugar, and eggs (these change depending on how much bread is baked). It also pays rent for the shop (this stays the same whether it bakes 10 loaves or 1,000). Understanding how costs behave as production changes is essential for making good business decisions.

Fixed costs do not change with the level of output. Rent, insurance, and loan payments are fixed -- you pay them regardless of how much you produce. Variable costs do change with output. Raw materials, hourly labor, and electricity for machinery all increase as you produce more.

Total cost is simply fixed cost plus variable cost. But the most important cost concept is marginal cost: the cost of producing one additional unit. If producing 100 loaves costs $200 an d p r o d u c in g 101 l o a v escos t s$ 203, the marginal cost of the 101st loaf is $3.

Marginal cost matters because it drives decision-making. A firm should produce an additional unit only if the revenue from that unit exceeds its marginal cost. As production increases, marginal cost typically rises at some point -- the bakery runs out of oven space, workers get in each other's way, or equipment is stretched to capacity. This is the principle of diminishing marginal returns: adding more of a variable input to a fixed input eventually yields smaller and smaller increases in output.

In the long run, everything is variable. The bakery can sign a new lease on a bigger shop or buy more ovens. This allows the firm to achieve economies of scale -- lower average cost as production increases -- up to a point. Beyond that point, the firm may face diseconomies of scale as coordination costs grow.

Visual [Beginner]

Cost Curves (Short Run)

Cost |
  |            MC
  |           /
  |          /
  |    ATC  /     AVC
  |    / \ /
  |   /   X
  |  /  / \  /
  | / /    \/
  |//        AFC (declining)
  |_____________________ Quantity

MC crosses AVC at its minimum.
MC crosses ATC at its minimum.
AFC declines continuously.

Cost Type	Formula	Behavior
Fixed cost (FC)	Costs independent of Q	Constant
Variable cost (VC)	Costs that depend on Q	Increases with Q
Total cost (TC)	FC + VC	Increases with Q
Marginal cost (MC)	Change in TC per unit change in Q	Typically U-shaped
Average fixed cost (AFC)	FC / Q	Declines as Q rises
Average variable cost (AVC)	VC / Q	U-shaped
Average total cost (ATC)	TC / Q	U-shaped

Worked Example [Beginner]

A firm produces widgets. Its costs are:

Fixed cost: $500 per month (rent on the factory).

Variable costs by output level:

Output (Q)	Variable Cost	Total Cost	Marginal Cost	ATC
0	$0	$500	--	--
10	$200	$700	$20	$70
20	$380	$880	$18	$44
30	$550	$1,050	$17	$35
40	$740	$1,240	$19	$31
50	$950	$1,450	$21	$29
60	$1,200	$1,700	$25	$28.33
70	$1,500	$2,000	$30	$28.57
80	$1,880	$2,380	$38	$29.75
90	$2,340	$2,840	$46	$31.56

Key observations:

Marginal cost initially falls (as workers specialize and machines operate efficiently) then rises (as congestion and resource constraints set in). The minimum MC is at Q = 30.
Average total cost falls until Q = 60 ($28.33), then rises. The minimum ATC occurs where MC = ATC.
Average fixed cost falls continuously: at Q = 10, AFC = $50; a tQ = 90, A F C =$ 5.56.

If the market price is $30 p er w i d g e t, t h e f i r mma x imi z es p r o f i tw h er e$ P = MC $. R e a d in g f r o m t h e t ab l e, M C r e a c h es$ 30 at approximately Q = 70. The firm should produce 70 widgets.

Profit = Total Revenue - Total Cost = ( $30 x 70) -$ 2,000 = $2, 100 -$ 2,000 = $100.

Check Your Understanding [Beginner]

Formal Definition [Intermediate+]

Short-run cost functions (one input fixed, typically capital $K = \overset{ˉ}{K}$ ):

$T C (Q) = F C + V C (Q) = r \overset{ˉ}{K} + w \cdot L (Q)$

where $r$ is the rental rate of capital, $w$ is the wage rate, and $L (Q)$ is the labor required to produce $Q$ units given the fixed capital stock (from the short-run production function $Q = f (L, \overset{ˉ}{K})$ ).

Marginal cost:

$M C (Q) = \frac{d T C}{d Q} = \frac{d V C}{d Q}$

Average costs:

$A T C (Q) = \frac{T C ( Q )}{Q}, A V C (Q) = \frac{V C ( Q )}{Q}, A F C (Q) = \frac{F C}{Q}$

Relationship between MC and ATC/AVC:

$M C < A T C \Rightarrow A T C$ is falling
$M C > A T C \Rightarrow A T C$ is rising
$M C = A T C$ at the minimum of ATC
$M C = A V C$ at the minimum of AVC

Proof (ATC): $\frac{d ( A T C )}{d Q} = \frac{d}{d Q} (\frac{T C}{Q}) = \frac{M C \cdot Q - T C}{Q ^{2}} = \frac{M C - A T C}{Q}$ . This is zero when $M C = A T C$ , negative when $M C < A T C$ , positive when $M C > A T C$ .

MC and marginal product: With one variable input $L$ :

$M C = \frac{d V C}{d Q} = \frac{d ( w L )}{d Q} = w \cdot \frac{d L}{d Q} = \frac{w}{M P _{L}}$

where $M P_{L} = \frac{d Q}{d L}$ is the marginal product of labor. Diminishing $M P_{L}$ implies rising $M C$ .

Long-run cost function: All inputs variable. The firm chooses $L$ and $K$ to minimize cost for each $Q$ :

$C (Q) = L, K min {w L + r K : Q = f (L, K)}$

Solved via the Lagrangian. The solution gives the expansion path in input space.

Returns to scale and long-run costs:

Increasing returns to scale $\Rightarrow$ declining LRAC (economies of scale)
Constant returns to scale $\Rightarrow$ flat LRAC
Decreasing returns to scale $\Rightarrow$ rising LRAC (diseconomies of scale)

Formally, if the production function is homogeneous of degree $k$ : $f (t L, t K) = t^{k} f (L, K)$ . Then LRAC scales as $t^{k - 1}$ .

Academic Perspectives [Master]

Neoclassical Theory of the Firm

The neoclassical firm is defined by its production function $Q = f (L, K)$ , which maps inputs to output. Cost functions are derived from the dual problem: given input prices and technology, minimize cost for each output level. The resulting cost function $C (Q; w, r)$ is the foundation of the neoclassical theory of supply. Under perfect competition, the firm's supply curve is its marginal cost curve above the minimum of average variable cost (the shutdown condition).

Shephard's Lemma (1953) establishes the duality between cost and production functions: $\frac{\partial C}{\partial w} = L^{*} (Q, w, r)$ , the conditional factor demand. This duality means that the cost function contains all economically relevant information about the technology.

The concept of economies of scale is formalized through the cost function: economies of scale exist when $C (Q) / Q$ is decreasing, or equivalently when the cost elasticity $ε_{C Q} = \frac{d C}{d Q} \cdot \frac{Q}{C} < 1$ .

Keynesian Economics

Keynesian economists emphasize that in practice, firms operate with excess capacity much of the time. Average costs are relatively flat over a wide range of output (the L-shaped cost curve empirically documented by Johnston, 1960). This means firms can increase output without raising marginal cost, supporting the Keynesian argument that aggregate demand drives output and employment rather than cost-based supply constraints.

Post-Keynesian economists such as Kalecki and Eichner argue that firms set prices as a markup over average variable cost (full-cost pricing), not by equating marginal cost to marginal revenue. The markup depends on the degree of market power and the firm's desired profit margin.

Marxian Economics

Marx analyzed costs in terms of constant capital (c, investment in means of production -- analogous to fixed costs) and variable capital (v, wages -- the cost of labor power). The key Marxian insight is that the cost of labor power (wages) is not the same as the value labor creates. The organic composition of capital (c/v) tends to rise over time as firms replace labor with machinery, leading to a falling rate of profit.

Marx distinguished between the cost price of a commodity ( $c + v$ , what the capitalist actually spends) and its value ( $c + v + s$ , where $s$ is surplus value). The difference is the unpaid labor of workers. This distinction has no counterpart in neoclassical cost theory, which treats wages as the full cost of labor.

Austrian School

Austrian economists, following Mises and Hayek, emphasize that costs are subjective. The cost of producing a good is the value of the highest-valued alternative use of the resources employed. This is the opportunity cost concept applied to production. The entrepreneur's judgment about future costs is inherently uncertain -- it cannot be read off from a production function because the relevant information does not yet exist.

Kirzner (1973) argued that the neoclassical production function assumes knowledge that entrepreneurs must discover. The cost curves drawn in textbooks are retrospective descriptions of decisions already made, not guides for future action.

Institutional Economics

Institutionalists emphasize that cost structures are shaped by organizational form, contracts, and institutions. Coase (1937) asked why firms exist at all: if markets are efficient, why not organize all production through market contracts? His answer: transaction costs. Firms internalize transactions when the cost of using the market (searching for partners, negotiating contracts, enforcing agreements) exceeds the cost of organizing internally.

Williamson (1985) extended this analysis, showing that asset specificity, uncertainty, and frequency of transactions determine whether activities are organized within firms or through markets. The boundary of the firm -- and thus its cost structure -- depends on institutional arrangements.

Behavioral Economics

Behavioral research on costs focuses on sunk cost fallacy: the tendency of decision-makers to continue investing in projects because of resources already committed, even when marginal cost exceeds marginal benefit. Thaler (1980) documented that individuals and firms systematically fail to ignore sunk costs, violating the neoclassical prescription that only marginal costs should influence forward-looking decisions. This has practical implications for firm behavior: managers may continue unprofitable projects because "we've already invested so much."

Historical Context [Master]

The classical economists (Smith, Ricardo, Marx) analyzed costs primarily in terms of the labor required for production. Ricardo's theory of rent (1817) distinguished between the cost of production on the marginal (least productive) land and the surplus earned on more fertile land -- an early analysis of differential costs.

The marginal revolution (1870s) shifted attention from total costs to marginal costs. Jevons, Menger, and Walras emphasized that decisions are made at the margin: the relevant cost for the next unit of output is the marginal cost, not the average.

The formal theory of cost curves was developed in the 1920s and 1930s. Viner (1931) provided the classic analysis of short-run and long-run cost curves, including the famous (and much-discussed) error in his original article where the draftsman failed to draw the long-run envelope correctly. Viner's analysis remains the standard textbook treatment.

The theory of duality between production and cost functions was formalized by Shephard (1953) and extended by McFadden (1978). This mathematical framework showed that cost functions and production functions contain equivalent information, allowing empirical estimation of production technology from cost data.

Coase's (1937) "The Nature of the Firm" introduced the concept of transaction costs and asked why firms exist -- a question that previous cost theory had ignored. Williamson's $(1975, 1985)$ development of transaction cost economics became a major branch of institutional economics.

Empirical work on cost curves (Johnston, 1960; Walters, 1963) found that many industries have approximately constant marginal costs over a wide range of output, contradicting the textbook U-shaped MC curve.

Bibliography [Master]

Viner, J. (1931). "Cost Curves and Supply Curves." Zeitschrift fur Nationalokonomie, 3, 23-46.
Coase, R. H. (1937). "The Nature of the Firm." Economica, 4(16), 386-405.
Shephard, R. W. (1953). Cost and Production Functions. Princeton University Press.
Williamson, O. E. (1985). The Economic Institutions of Capitalism. Free Press.
Johnston, J. (1960). Statistical Cost Analysis. McGraw-Hill.