The Firms Decision Horizon

1
The Firms Decision Horizon Short Run At least
one input is fixed in quantity ?
Entry/Exit? Long Run All inputs are variable
? Entry/Exit? Time that distinguishes SR and LR
is different in different industries (e.g.,
lemonade vs. cars)
2
Firms Behavior Begin with technology Production
Function - gives the (maximum) amount of
output(s) attainable from given inputs (so,
assumes technological efficiency) Example one
output, Q, and two inputs, capital, K, and labor,
L Q f(K, L) Q Ditches K Shovels L
Workers
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• Relationship between increase in input
  and increase in output
• Marginal Product (MP)
• - Increase in total product (output) from a
  one-unit increase in an input, other things equal
• Total product Output from all input units
• Marginal product Output from last input unit
• Average product Average output per input unit
  from all input units

4
Total Product, Marginal Product, and Average
Product
Total Marginal Average Labor product
product product (workers (sweaters
(sweaters per (sweaters per day) per
day) additional worker) per
worker) A 0 0 B 1 4
4.00 C 2 10 5.00 D 3 13
4.33 E 4 15 3.75 F 5
16 3.20
4 6 3 2 1
5
Law of Diminishing Marginal Returns - As use
more and more of an input, with other things
constant, marginal product eventually
diminishes Examples - Studying for an exam (more
time) - Painting a house (more paint, more
time) - Digging a ditch (more workers, more
shovels)
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Total Product, Marginal Product, and Average
Product
Time Total Marginal Average
studying score product product (hours)
on test (per hour) (per hour) A
0 0 B 1 45 45.0 C 2
60 30.0 D 3 70 23.3 E 4
78 19.5 F 5 85 17.0
45 15 10 8 7
7
How to Maximize Profit? - To maximize profit,
must produce given output level at minimum cost -
Also, must product right level of output How to
Minimize Cost? - Must produce at minimum cost in
order to maximize profit (why?) ? Cost
minimization is a necessary condition for profit
maximization
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Cost Minimization Output is produced with L and
K Suppose reduce L just enough to produce one
less Q, holding K constant Q ? by 1
? cost ? by w/MPL
? L ? by 1/MPL
Now, buy just enough extra K to produce one more
Q Q ? by 1
? cost ? by r/MPK
? K ? by 1/MPK
Thus, unless w/MPL r/MPK can produce given Q at
a lower cost by swapping between inputs
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w/MPL is cost of producing one more Q from hiring
labor r/MPK is cost of producing one more Q from
hiring capital w/MPL r/MPK means that the cost
of producing one more unit of output is the same
across all inputs Note w/MPL r/MPK ?
MPL/w MPK/r so that marginal products per
dollar spent are equal across inputs
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Example Q K ? L MPL K and MPK L Fix Q
120 How to produce at minimum
cost? Combinations of L and K that produce Q
120 L K L K L K 2 60 10 12 40
3 3 40 12 10 60 2 4 30 15 8 120 1
5 24 20 6 1 120 6 20 24 5
8 15 30 4
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a) r 10, w 3 ? K 6, L 20 b) r 6, w
5 ? K 10, L 12 c) r 5, w 6 ? K 12,
L 10 d) r 3, w 10 ? K 20, L 6
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Cost per unit of output Average Cost (ATC) cost
per unit of output averaged over all units
produced Marginal Cost (MC) cost of the last
unit produced Note MC w/MPL r/MPK The
relationship between ATC and MC is if MC lt ATC
then ATC must be falling if MC gt ATC then ATC
must be rising (why?) Thus, marginal cost (MC)
equals average cost (ATC) at the minimum of
average cost
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Relationship between Marginal Cost and Average
Cost
12
Marginal cost equals average cost at the minimum
of average cost
9
Average product and marginal product
6
3
Marginal cost above average cost means average
cost is rising
Marginal cost below average cost means average
cost is falling
0 6.5 10
Labor
14
Long-Run Average Cost Curve
15
Returns to Scale

• Returns to scale are the increases in output
  that result from increasing all inputs by the
  same percentage.
• Three possibilities
• Constant returns to scale
• Increasing returns to scale
• Decreasing returns to scale