Lecture 7 · Week 9 · Besanko & Braeutigam ch. 7 · about 45 min

Costs and Cost Minimization

Economic cost versus accounting cost, and the firm's mirror image of consumer choice: choosing the cheapest combination of labour and capital to produce a target output, using the isocost line and the tangency condition.

By the end you can

Distinguish economic cost (explicit plus implicit) from accounting cost
Write the isocost line and identify its slope
Apply the cost-minimization tangency condition to find the optimal input mix
Solve for the minimum cost of producing a target output with a Cobb-Douglas production function

Economic cost versus accounting cost

Economic costDefinitionFormula sheet →

\text{Economic cost} = \text{explicit cost} + \text{implicit cost}

$explicit cost$: actual cash payments (wages, rent, materials)
$implicit cost$: opportunity cost of resources the firm already owns

Use it when you need to compute true economic cost or economic profit, not just the accounting figure — the same distinction opened this course in Week 2.

The most common implicit cost is the opportunity cost of capital: if an owner has 1 million TL of their own money tied up in the business rather than earning a return elsewhere, that forgone return is a real economic cost, even though no invoice records it.

The isocost line

Just as a consumer’s budget line shows affordable bundles of two goods, a firm’s isocost line shows every combination of labour and capital available for a given total expenditure.

Isocost lineKey formulaFormula sheet →

wL + rK = C \quad\Longrightarrow\quad K = \frac{C}{r} - \frac{w}{r}L

$w$: wage rate
$r$: rental rate of capital
$C$: total expenditure on inputs

Use it when you need the set of input combinations available at a given cost, or the isocost line's slope, -w/r.

Cost-minimizing input choice

A firm minimizing the cost of producing a given target output $\bar Q$ chooses the input bundle where the isocost line is tangent to the $\bar Q$ isoquant — the exact mirror image of the consumer’s tangency condition from Lesson 4.

Cost-minimization tangency conditionKey formulaFormula sheet →

MRTS_{LK} = \frac{w}{r} \quad\Longleftrightarrow\quad \frac{MP_L}{MP_K} = \frac{w}{r} \quad\Longleftrightarrow\quad \frac{MP_L}{w} = \frac{MP_K}{r}

$MP_L/w$: MP_K/r = output per lira spent, equalised across both inputs at the cost-minimising bundle

Use it when you are finding the cheapest way to produce a given output level, given input prices.

Deriving a cost function

Repeating the cost-minimization problem at every possible output level $Q$ traces out the firm’s total cost function $C(Q)$ — exactly analogous to tracing a demand curve by repeating consumer choice at every price.

Exam practice

Summary and review

Economic cost = explicit cost + implicit cost (including the opportunity cost of capital).
Isocost line: $wL + rK = C$ ; slope $-w/r$ .
Cost-minimization tangency: $MRTS_{LK} = w/r$ , equivalently $MP_L/w = MP_K/r$ .
Solving requires both the tangency ratio and the output constraint together.
Repeating cost minimization at every output level traces out the firm’s total cost function $C(Q)$ .