Module 72 – Cost-Minimizing Input Combination
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Alternative Input Combinations
 Firms employ an input up to a point where the MR gained = marginal factor cost of that input
 Ex. Hiring up until it is not profitable, buying land until not profitable
 What do you do when there are different ways to produce the same output?
 Construction company, hire more workers with hammers, or invest in nail guns?
Substitutes and complements
 Substitutes  2 factors that can do essentially the same work
 ATM and bank teller; backhoe and team of men with shovels; American computer programmer
and Korean programmer
 Complements  2 factors that must be combined to produce output. Presence of 1 increases marginal
output of the other.
 Backhoe and its driver; pilots and jets; big rig and driver
Determining the optimal input mix
 Cost minimization
 Dora’s Ditch Diggers has been hired to dig a 100-foot drainage ditch.
 Combination 1: rented backhoe and skilled driver
 Combination 2: 10 unskilled workers with shovel
1
2
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Cost of labor
Cost of capital
$500
$100 * 10 = $1000
$2500
$25 * 10 = $250
Total cost per 100 feet
of ditch
$3000
$1250
 Low-tech is preferred, and combination 2 will be chosen. But what if the backhoe turned out to
be more productive, and could dig 3 times faster (300 feet in time it takes the team of 10 to dig
100 feet)
 Combination 1 still costs $3000
 Combination 2 costs $1250 * 3 = $3750
 Firms should consider more than price of labor and capital. Should consider productivity.
Cost-minimization rule
 Utility is maximized when ratio of marginal utility per dollar is equal for each good
 MUX/PX = MUY/PY
 Similarly, firms want to minimize cost of inputs to produce as much output as possible.
 MPL/W = MPK/r
 W = wage; r = rental rate; l = labor; k = capital (?)
 Marginal product per dollar is equal for labor and capital
 Activity: What if it isn’t?
 Assume wages $1; rental rate $2
 Firm hired labor to point where MPL=50, capital to point where MPK=40
a. Using formula, MPL/W=MPK/R
i. 50/1 = 40/2  50=20
ii. MPL/W > MPK/R
iii. If firm spends $2 less on capital, it could hire 2 more units of labor
iv. Lost production from 1 less unit of capital = 20 units
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v. Gained production from 2 more units of labor = 50 units
vi. Firm sees more production at same cost
Firm hired labor to point where MPL=10, capital to point where MPK=60
a. Using formula
i. 10/1 = 60/2  10=30
ii. MPL/W<MPK/R
iii. If firm spend $2 less on hiring 2 units of labor, it could hire 1 more unit
of capital.
iv. Lost production from 2 less units of labor = 10 units
v. Gained production from 1 more unit of capital = 30 units
vi. More production at same cost