Unit 5.
Production or Manufacturing of
output, revenues, costs, and profits
as functions of input level
GM Labor Issues
GM (General Motors) officials are about to begin
labor contract renewal negotiations with the UAW
(United Auto Workers Union). GM officials are
concerned about lagging worker productivity in their
plants vis-à-vis the competition. For example, Ford
workers produced an average of 33.2 vehicles per
year and were paid an average wage of $43 per hour,
while the corresponding figures for GM were 27.9
cars at $45 per hour. Based on this information, how
much higher are GM’s labor costs per car than
Ford’s? What GM labor output would result in GM’s
labor costs per car being equal to Ford’s with current
wages?
Managing Office Space
Global Technologies is currently leasing the office
space used by staff at corporate headquarters in
Seattle. Other than a change in the price or cost of
office space, what economic factors might explain
management’s decision to increase leased office
space by 10%? Suppose in the geographic area of
Global’s Corporate headquarters (i.e. Seattle)
management has reason to believe that other
companies may be cutting back on their needs for
office space. Based on this information, what advice
do you have for Global Technologies management
regarding the future purchase of office space in
Seattle?
How Many Workers to Hire?
A concession stand owner/operator
hires workers (= L) at a daily wage (=
W) of $40 to sell pop (= q) at $2.00 (= P
= price) per bottle. If q = 200L1/2 and
total fixed costs = $100, how many
workers should be hired? For simplicity,
assume labor costs are the only
variable costs.
Who’s To Blame?
The salaries of professional athletes in
major sports often are above $1 million
per year. Who or what is the main
economic explanation as to why this
happens? Is the main cause the
athletes themselves, the owners,
television networks, sports clothing
companies, and/or the fans?
Production-Related Qs of Interest to
Firm Managers (Examples)
How does output Q change as input Q
changes?
Can output Q be increased w/o increasing
input Q?
To what extent can one input be substituted
for another in the production process?
What input Q would minimize costs?
Maximize profits?
How should inputs be acquired?
Revenues & Costs
(Input side relationships)
1. Graphical
$
Q o f i npu t
2. Mathematical
$ concepts = f(Q of input)
D em and E conom ics:
D factors
C onsu mer u tility
E lasticities o f D
etc.
P xQ
M gm t C oncerns
_ _____________
= R ev enu es
- C o st
============
=
S u pp ly E con omics:
S fa ctors
P rod uction p rocesses
In p u t p rodu ctivity
etc.
P rofits
Firm Decisions that Impact TR
1.
2.
3.
4.
Products to produce
Product prices
Quantity of products
How to market/promote products
Firm Decisions that Impact TC
1.
2.
3.
4.
5.
Quantity of products produced
What inputs to use to produce products
What quantity and combinations of
inputs to use
How to acquire inputs
How to make inputs more productive
Production
= the process by which inputs are
combined and transformed into
outputs
Production Analysis
Production Function
Q = F(K,L)
 The maximum amount of output that can
be produced with K units of capital and L
units of labor.
 Short-Run vs. Long-Run Decisions
 Fixed vs. Variable Inputs

Types (or lengths) of production
periods
1.
Short run (SR) => period of time for
which a firm is stuck with a fixed or
given quantity of at least one input
2.
Long run (LR) => period of time for
which a firm can vary or alter the
quantities of all inputs
Assume q = f( K ,L) = a short-run
production function where:
Q =
K =
L =
r =
w =
physical units of output
physical units of fixed capital
physical units of variable labor
per unit cost (rental rate) of
capital
per unit cost (wage rate) of
labor
Linear Production Function
TP
TP = aL
L
AP
MP
a
AP = MP
L
SR Production Concepts
Concept/Definition
Math Calculation
q=linear fn of L
q=nonlinear fn of L
= q=aL
= q=aL2-bL3 (e.g.)
1.
TP = total product
= total physical units of output
= total quantity of output (=q)
2.
AP = average product
= output per unit of input
= output of ‘average’ input
= slope of line from origin
to TP curve= a
= TP/L
= q/L
= aL/L
MP = marginal product
= additional output per unit
of additional input
= slope of TP curve
= output of last input unit
= TP/L
= TP/L
=a
3.
NOTE:
= TP/L
= q/L
= (aL2-bL3)/L
= aL = bL2
when MP > AP, AP is increasing
when MP < AP, AP is decreasing
when MP = AP is either at a maximum or constant
= TP/L
= TP/L
= 2aL – 3bL2
Nonlinear Production Function
Input Productivity Increase
Total Product
Cobb-Douglas Production Function
Example: Q = F(K,L) = K.5L.5
K is fixed at 16 units.
 Short run production function:
Q = (16).5L.5 = 4L.5
 Production when 100 units of labor are
used?
Q = 4 (100).5 = 4(10) = 40 units

Revenue Concepts that are a fn of
the level of input usage.
1.
Total Revenue Product
2.
Average Revenue Product =
=
=
Marginal Revenue Product =
=
3.
=
=
=
=
TRP
TP x P
paired observations on the S
value of output and physical
units of a variable input
ARP
AP x P
revenue per unit of input
MRP
MP x MR
(note MR=P for price-taking
firms)
add’l revenue per unit of add’l
input
SR Revenue Product Function
Example
Q = K1/2L1/2
where K = 16
 q = 4L1/2 = TP
 AP = TP  4 L 
1/ 2
L
 MP 
 TP
L
L
4
L
1/ 2  1
 (1 / 2 )( 4 ) L

2
L
Revenue Products if P of
output = 50
TRP = P • TP = 50 (4L1/2) = 200L1/2
ARP = P • AP = 50 (
4
MRP = P • MP = 50 (
2
L
L
)=
200
)=
100
L
L
Total ‘Cost’ Concepts as
Functions of Input Level
TVC
TFC
TC
=
=
=
=
=
=
=
total variable costs
wL
total fixed costs
rK
total costs
TVC + TFC
r K + wL
Graphs of Total ‘Cost’ Concepts as
Functions of Input Level
Marginal Factor Cost (MFC)
=
the additional cost per unit of
additional input
= the wage rate (w) if the additional
input is an additional unit of labor
=> MFC = w = the price of labor
$
$
S
MF C=w
D
L
F irm
L
M kt
‘Optimal’ input level (usage)
Profit-maximizing input level
A manager should keep using additional
Qs of an input up to the point where the
additional income equals the additional
cost from the last input unit (sometimes
called MFC = marginal factor cost)
e.g. labor, MRP = W (= MFC)
Profit-maximizing L if
M RP 
100
L
M F C  10
 M RP  M FC

100
 10
L

L  10
 L * 100
SR Profit-Maximizing Input Level
(Solution Procedure)
Given: prod fn, r, w, P
Derive:

product concept equations as fns of L
(e.g. TP, AP, MP)
Derive:




revenue concept equations as fns of L
TRP = TP x P
ARP = AP x P
MRP = MP x MR (MR = P for P taking firm)
Find optimal L*

Set MRP = MFC (=w) and solve for L
Calculate optimal profit at L*
= TRP – TFC – wL*
Profit-Maximizing Input Level
Firm D for Variable Input (e.g. L)
Input D Factors
1.
2.
3.
Input price
Output price
Input productivity

the demand for an input is a
‘derived’ demand
(i.e. derived from factors that determine
the profitability of using that input)
Increased D for Labor (examples)
LR Input P Disequilibrium
LR Equilibrium Competitive Input P