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Ch. 7 – Costs and Cost Minimization
Ch. 6 discussed the shape of a firm’s isoquants just as Ch. 3 discussed the shape of a
consumer’s preferences. Now Ch. 7 will add a output constraint (just as Ch. 4 added a budget
constraint), and the firm will choose a level of inputs given input prices and the production
constraint to minimize the costs of producing a fixed amount of output.
Self-checkouts, ATM machines, computerized phone directories, etc. replaced many low-skilled
workers in the last 20 years.thhe Economist estimated that one transaction handled through a
self-checkout kiosk cost 1/10 as much as a transaction handled by an employee. Firms have
substituted K for L. Why?
The answer is that the costs of hourly labour inputs has risen relative to the costs of capital
inputs; so firms have substituted more K for L. We will see in the following model of production
theory that if isoquants are convex and downward-sloping, this outcome can be predicted by the
theory of production.
Basic Production Theory: Cost-minimization
Firm chooses K and L to minimize TC= wL+rK subject to a target level of output Qo.
r= cost of capital; w = wage rate
LR v. SR
Long- Run (all inputs variable)
A firm chooses inputs (K,L) to minimize the costs of producing a FIXED level of output Q.
Exogenous variables: r,w,Q
Endogenous variables : L,K P a g e | 2
Short-run (some inputs are fixed)- usually K fixed and L variable
A firm chooses variable inputs (L) given a fixed level of K, the prices of inputs, and the
level of output it desires to produce. Because some costs are fixed in the SR, total costs
have a variable costs component and a fixed cost component TC = VC + FC = wL + r
K where VC = wL and FC = r K .
Min LL + r Ḱ
Subject to f(L, = Q
SR: Some costs are fixed.
Variable costs – vary with production (Ex: labour hours)
Fixed costs – do not, same regardless of production level (Ex: Rent for an office)
SR: Fixed costs may be either sunk or nonsunk.
Sunk costs- cannot be avoided regardless of the firm’s production decision
Nonsunk costs – are avoidable
Basic Cost Concepts
Cost = value of sacrificed opportunities.
Ex: Cost of flying a plane includes fuel, etc.(explicit costs) as well as the cost of not
renting the plane to other companies (implicit cost).
Explicit costs – Costs that involve a monetary outlay (fuel)
Implicit costs – costs that do not involve outlays of cash.
-Current market price of an input if sold
-Foregone interest if the money had been invested elsewhere. P a g e | 3
Opportunity cost – value of the best foregone alternative.
If choosing among different mutually exclusive alternatives, then the opportunity cost of
a particular alternative is the payoff associated with the best of the alternatives that had to
be foregone by making your choice.
The opportunity cost of an input to a firm is represented by the price of the input.
If the firm chooses not to use the input, then it saves the cost of the input or it can
resell the unused services of the input in the market and gain the market price of the
input when it does so.
Opportunity cost depends on the decision being made.
Ex: Auto firm uses steel to make cars.
1. Buy or not buy the $1million of steel. Opp cost is $1 million because the firm
cannot use this money for something else if it buys the steel.
2. The market price of the steel rises to $1.2 million. Should the firm use this
steel to make cars or not? The opportunity cost of using the steel to make
cars is now $1.2 million because it could resell the steel for this price in the
Ex: Kaisar smelting.
Electricity is a large input into smelting ore. In 1996, Kaisar bought electricity for
$23/megawatt hour under a long-term contract with BPA when the spot price was low. In
2001, spot price for electricity increased to $1000/ megawatt hour. Kaisar had the opportunity
to resell its electricity at the new higher price.What has happened to Kaisar’s opportunity
cost of using electricity? Kaisar decided to close the smelters and sell the electricity back to
Economic costs v. Accounting costs
Economic costs – current opportunity costs (explicit and implicit).
Accounting costs – explicit costs that have been incurred in the past. Must be
Ex: Mark-to-market accounting
Financial crisis of 2009. Mark-to market represents the true opportunity cost of holding
a mortgage.Subprime mortgage crisis burst the housing bubble in the U.S. Value of
houses fell by 1/3 or more. The value of mortgages and mortgage-based assets held by the
banks had to valued at current market prices (mark-to-market), i.e. current opportunity cost.
Value of the banks’ capital (net worth) fell, and the banks had to cut lending or call in loans to
meet their capital requirements. Resulted in credit crisis and deep recession. As part of
the rescue package, banks were allowed to scrap mark-to-market accounting and report the P a g e | 4
original accounting values, not the lower economic values that reflected the true value of
the mortgage assets.
Sunk v. Nonsunk costs (SR concept)
Sunk costs – costs that have been incurred and cannot be recovered (unavoidable)
Nonsunk costs – costs that are incurred only if a particular decision is made and are
avoided if the decision is not made. (avoidable)
When making a decision, a rational firm only considers nonsunk costs and ignores
Whether a cost is sunk or not depends on the decision being made.
Variable Costs v. Fixed Costs (SR concept)
Variable costs – costs that change with production (output) are nonsunk.
Fixed costs – costs that are fixed in the short run and do not vary with production, such
as a lease payment on office space, may be sunk or nonsunk. For ex, If the firm decides to
shut down, it may be possible to recover some fixed costs by subletting the office space to
another company and recovering some of the lease payment.
Not all fixed costs are sunk. In some cases the firm can recover its fixed costs by:
1) renting its capital (ex: airline may rent its planes or airport gates to other
2) reselling its capital secondhand
The book assumes that all fixed costs are sunk to make the short-run cost-minimization
problem easier. P a g e | 5
The accounting costs are simply the sum: 25,000 + 75,000 + 80,000 + 6,000 = $186,000
and the shop’s accounting profit is $64,000 which means that Mr. Moore’s total gain from this
venture is 80,000 + 64,000 = $144,000.
The economic costs also include the opportunity cost of the land rental ($100,000) and of
Mr. Moore’s next best alternative, which in this case is $95,000. That is, Mr. Moore loses
$15,000 by not choosing his next best alternative. Therefore Mr. Moore’s total economic costs
are 186,000 + 100,000 + 15,000 = $301,000, which exceeds his revenues by $51,000.
Should he shut down?
Yes. If he were to shut down the shop, Mr. Moore would earn 100,000 + 95,000 =
$195,000 which is more than the $144,000 he currently earns (by precisely the $51,000 figure
from above). Therefore he should shut down the shop.
The cost min decision differs depending on whether the firm is in the LR or the SR.
A) Long-run = all inputs are variable
We DO NOT maximize isoquants with respect to an isocost line as we did when
we maximized utility subject to a budget constraint!
Instead, we minimize the isocost line subject to a fixed isoquant output constraint.
This was like the expenditure minimization problem of the consumer in Ch. 5.
Graph: P a g e | 6
Cost minimization problem: The firm chooses inputs (K,L) to minimize the costs of
producing a FIXED level of output Q.
r = cost of capital and w = wage rate, f(K,L) is the production function for a fixed level of
1. Isocost curve like a budget constraint.
The isocost line shows you the combinations of K and L that have the
same total cost TC= wL + rK.
K = TC/r – (w/r)L is the point-slope form of the equation of isocost line.
-w/r = slope of isocost line
y-intercept = TC/r
x-intercept = TC/w
2. Isoquant (from production function) like a utility curve. P a g e | 7
4 types of production function yield 4 different types of isoquants (list in
Slope of isoquant=MRTS = MPL/MPK.
Example 2: What does an MRTS of 0.4 mean?
If the MRTS = 0.4, then ΔK/ΔL = 0.4/1. This means that the firm can substitute .4
machine hours for 1 less labour hour and still produce the same amount of output Q.
3. In figure 7.2 graph above, at the point E
-MRTS < - w/r
MPL/MPK > w/r