# Chapter 5: Production and Cost Analysis in the Short Run Economics for Managers

```Economics for Managers
by
y Paul Farnham
Chapter 5:
Production and Cost Analysis
in the Short Run
5.1
Defining the
P d ti
Production
Function
F
ti
The formula can be read as “quantity
quantity of
output is a function of the inputs
listed inside the parentheses”
Q = f (L, K, M…)
where
Q = quantity of output
L = quantity of labor input
K = quantity
y of capital input
M = quantity of materials input
5.2
Fixed Inputs Versus
V i bl Inputs
Variable
I
t
 Fixed input: quantity a manager
cannot change
g during
g a given
g
time
 Variable input: quantity a manager
can change during a given time
 Amount of output would vary as
regarding amounts of input
5.3
Short-run Versus
L
Long-run
P d ti
Production
 Not expressed in terms of
calendar time,, but in terms of
fixed and variable inputs
 Short
Short-run
run production function:
involves at least one fixed input
 Long-run
Long run production function:
production process in which all
inputs are variable
5.4
Managerial Rule of Thumb:
Short-run
Short
run Production and
Long-run Planning
 Managers operate in the short
run, but must have long-run
vision
i i
 They need to be aware that the
currentt amountt off fixed
fi d inputs
i
t
may not be appropriate as market
conditions change
 Managers make more long run
economic decisions
5.5
Model of the Short-run
P d ti
Production
Function
F
ti
Total product: total quantity of output
produced with a given quantity of
fixed and variable inputs
TP or Q = f (L, K)
where
TP or Q = total p
product or quantity
q
y
of output
L = quantity of labor input
K = quantity of capital input
5.6
Average Product
Average product:
A
d t amountt off
output per unit of variable input
AP = TP / L or Q / L
where
AP = The average product of labor
5.7
Marginal Product
Marginal
M
i l product:
d t the
dditi
l
output produced with an
MP = ΔTP / ΔL = ΔQ / ΔL
where
MP = The marginal product of labor
5.8
Total Product: Short-run
Production Function
Figure 5.1a
Law of diminishing
returns where marginal
product eventually
decreases
TP
0
L1
L2
L3
L
5.9
TP: Short-run
P d ti
Production
Function
F
ti
 TP increases rapidly up to level of
labor input L1 then increases at a
slower rate as labor input increases
 TP curve becomes flatter and flatter
until it reaches maximum output
level at L3
 Curve implies that marginal product
of labor first increases rapidly then
decreases, eventually becoming
zero or less
5.10
AP and MP: Short-run
Production Function
Figure 5.1b
MP
AP
0
L1
L2
L3
L
5.11
AP and MP: Short-run
Production Function
 Between zero and L2, MP curve
lies above AP curve, causing AP
curve to increase
 Below L2, MP curve is below AP
curve, causing AP curve to
decrease
 Therefore, MP curve must
intersect AP curve at maximum
point
i t off AP curve
5.12
Economic Explanation
 Increasing marginal returns:
region where MP curve is positive
and
d increasing
i
i
 Law of diminishing returns:
region
i where
h
marginal
i l product
d t
curve is positive but decreasing
 Negative
N
ti marginal
i l returns:
t
region
i
where product curve is negative
so that TP is decreasing
5.13
Law of Diminishing
R t
Returns
p
(MP) is decreasing
 Occurs because capital input and
technologies are held constant
5.14
Productivity Changes
A
Across
I
Industries
d t i
Q = f (K, L, E, M, t)
where
Q = industry output
K = capital services
L = labor services
E = energy use
M = materials use
t = level of technology
5.15
Model of Short-run
C t Functions
Costs
F
ti
 Cost function: shows relationship
between cost of p
production and
level of output
 Opportunity cost: reflects use of
resources in one activity while
foregoing
g g another
5.16
Model of Short-run
C t Functions
Costs
F
ti
 Explicit cost: payment to an
individual that is recorded in an
accounting system
 Implicit costs: value of using a
resource that is not explicitly paid
out,, is often difficult to measure,,
and not recorded in an accounting
system
5.17
Measuring
O
Opportunity
t it Cost
C t
 Prices that a firm pays for input
reflects opportunity cost
 If managers do not recognize
opportunity costs, they may have
t
too
much
h invested
i
t d in
i buildings
b ildi
or
other assets
 Historic
Hi t i cost:
t amountt off money a
firm paid for an input when it was
purchased
5.18
Accounting Profit and
E
Economic
i Profit
P fit
 Profit: difference between total
revenue and total cost of
production
d ti
 Accounting profit: difference
b t
between
total
t t l revenue and
d total
t t l
explicit cost
 Economic
E
i profit:
fit difference
diff
between total revenue and total
costs, both implicit and explicit
5.19
Managerial Rule of Thumb:
I
Importance
t
off Opportunity
O
t it Costs
C t
 Measuring opportunity costs can
be difficult because accountants
are trained to examine explicit
costs
 Managers need to take into
account both types
yp of costs
(explicit and opportunity costs)
5.20
Short-run
Short
run Cost Functions
 Short-run cost function: shows
relationship
p between output
p and
costs based on underlying shortrun production function
 It is a cost function for short-run
production process
p
p
in which there
is at least one fixed unit of
production
5.21
Costs
 Total fixed cost: cost of using
fixed input
p
 Total variable cost: price per unit
of labor times quantity of labor
input
 Total cost: sum of total fixed cost
plus total variable costs
5.22
Costs
 Average
A
fi
fixed
d cost: totall fixed
fi d cost
per unit of output
 Average variable cost: total variable
cost per unit of output
 Average total cost: total cost per
unit of output plus average variable
cost
 Marginal cost: additional cost of
5.23
Total, Average, and
M
Marginal
i l Cost
C t
 AFC decreases continuously as
more output
p is produced
p
 Since TFC is constant, AFC must
decline as output increases
 AVC and ATC first decrease then
increase
 ATC always equals AFC plus AVC
5.24
TC, TCV, TFC Functions
Figure 5.2a
TC
TVC
TFC
0
Q1
Q2
Q3
Q
5.25
MC, ATC, AVC,
and
d AFC Functions
F
ti
Figure 5.2b
MC
ATC
AVC
0
Q1
Q2 Q3
AFC
Q
5.26
Short-run
P d ti
Production
and
d Cost
C t
MC
AVC
AP
0
MP
L1
L2
L
0
Q1 Q2
Q
5.27
Managerial Rule of Thumb:
U d
Understanding
t di
Your
Y
Costs
C t
M
Managers
need
d to
t understand
d t d
• Technology and prices paid for
iinputs
t off production
d ti
• Difference between variable and fixed
costs
t
• Difference between average costs
(costs per unit of output) and
producing
p
p )
5.28
Econometric Estimation
off C
Costt F
Functions
ti
 Dean’s
D
’ studies
t di off a furniture
f
it
factory,
f t
a leather belt shop, 1976
 Johnston’s
J h t ’ study
t d off British
B iti h electric
l ti
transport and food processing firm,
transport,
firm
1960
 Hall,
Hall 1986
 Blinder, et al, 1990s
5.29
Summary of Key Terms
 Accounting profit
 Explicit cost
 Average
g fixed
 Fixed input
p





cost
Average product
Average total cost
Average variable
costt
Cost function
Economic profit
 Historic cost
 Implicit cost
 Marginal returns
 Diminishing returns
 Long-run production
functions
5.30
Summary of Key Terms
 Marginal cost
 Total
T t l costt
 Marginal product
 Total fixed cost
 Negative
N
ti marginal
i l
 Total product
returns
pp
y
 Production function  Opportunity
cost
 Short-run
production function  Total variable
cost
 Short-run cost
function
 Variable input
p