Production and Cost
Chapter 5
Productivity => Cost => Profitability
Today’s agenda
• Collect Assignment 1
• Status of first half of applied managerial economics
• How much to produce?
– Marginal analysis applied to choice of price and quantity
• How to produce? – Output maximization and cost minimization
• What to produce? – Competitive Strategy Ch. 8
• For whom to produce – Consumer behavior and Ch. 7 pricing
• Production & Cost concepts
– “short run”
• Returns to an input & cost functions
• Profit maximization
• Marginal product and marginal revenue product
– “long run”
• Optimal input mix – output maximization and cost minimization
• Economies of scale
General Ideas
• Production functions
– show how output varies as input usage varies
• Cost functions
– show different cost measures & how they vary
as output varies
• What can you do to improve productivity?
Lower costs?
• Link to profits
Short run production & cost
• Short run
some inputs held fixed while other(s) vary
• Production
Returns to an input x is sensitivity of output to the input x
Total product TP = output (Q) produced per period
Average Product AP = output per unit of input x = TP / x
Marginal Product MP
= change in output per unit increase in input x = D TP / D x
• Cost
– Fixed cost and variable cost per period shown as functions of output
– TFC + TVC = TC which varies with output (Q)
– Per unit costs – each total cost measure per unit of output
• e.g. AVC = TVC/Q
• AVC + AFC = ATC
– Marginal cost
= change in TC per unit increase in output = D TC/ D Q
Production functions
Isoquants
• An isoquant map is a method to display
production functions in graphical form
• Short and long run applications
• Definition: An isoquant shows the set of all
input combinations that produce the same
level of output.
The Soprano Garbage Company
Short Run Costs using isoquant data
• The Soprano Garbage Company
hires labor and capital to produce
dumpsters. The price of labor is $3.
The rental rate of capital is $2 per
unit. In the short run, the Sopranos
have 5 units of capital.
• Given the isoquant map shown,
calculate & draw this firm’s shortrun total cost curve, short-run
average cost curve, short-run
average variable cost curve, shortrun average fixed cost curve, and
marginal cost curve.
The Soprano Garbage Company
Quantity
L K Pl
0
5
12
21
28
33
36
37
0
1
2
3
4
5
6
7
5
5
5
5
5
5
5
5
$3
$3
$3
$3
$3
$3
$3
$3
Short Run
Pk Fixed Cost Variabl Total Cost
e Cost
$
$
$
$
$
$
$
$
2
2
2
2
2
2
2
2
10
10
10
10
10
10
10
10
0
3
6
9
12
15
18
21
10
13
16
19
22
25
28
31
Average
Fixed Cost
-----$
$
$
$
$
$
$
2.00
0.83
0.48
0.36
0.30
0.28
0.27
Average
Variable Cost
---$
$
$
$
$
$
$
0.60
0.50
0.43
0.43
0.45
0.50
0.57
Average
Total Cost
----$
$
$
$
$
$
$
Marginal Marginal Cost
Product of
Labor
2.60
1.33
0.90
0.79
0.76
0.78
0.84
5
7
9
7
5
3
1
0.60
0.43
0.33
0.43
0.60
1.00
3.00
Average and marginal costs
Variable Cost
Total Cost
35
30
20
$
$
25
15
10
5
0
0
10
20
30
quantity produced
40
3.5
3
2.5
2
1.5
1
0.5
0
Average
Fixed Cost
Average
Variable
Cost
Average
Total Cost
5
15
25
quantity produced
35
45
Marginal
Cost
Short run production & cost – classic case
Average and marginal costs
45
Marginal
Cost
3
2.5
Average Variable
Cost
Marginal Cost
2
1.5
1
0.5
36
33
28
0
21
If MC rises above AVC, it pulls
AVC up
35
3.5
12
Bad game pulls batting
average down
25
quantity produced
5
•
–
15
If MP falls below AP, it pulls
AP down
y
–
Average
Variable
Cost
Average
Total Cost
5
Marginals influence averages
ua
nt
it
•
Concave TP curve
Diminishing MP curve
Increasing MC curve (if single
variable input)
Average
Fixed Cost
0
–
–
–
$
Diminishing returns to the
variable input
Q
•
3.5
3
2.5
2
1.5
1
0.5
0
Short Run Production & Cost – Classic case
Short run production & cost: discussion
• What causes diminishing returns to a variable
input?
• Pick a good/service your org. produces. Could
you double production next month? If so would
your marginal costs increase?
• How do the Soprano's cost functions compare with
classic case? What can you infer about differences
in productivity patterns?
Profit maximization / Loss-Minimization
in the short run
• Total profit = TR - TC
• To maximize total profit or minimize total loss
– A firm should increase output as long as marginal
revenue exceeds marginal cost
– A firm should not increase output if marginal cost
would exceed marginal revenue
• At the profit-maximizing level of output, (approx)
MR=MC
• Fixed costs are irrelevant for determining this level of
output
Loss-Minimization:
Short run shut-down case
• “Shutting down production”
– producing zero output while continuing to pay fixed
cost
• Minimize loss by shutting down if
TR < TVC
e.g. $50 < $60 with TFC = $10
if operate then loss is $20
if shut down then loss is $10 – why?
Equivalently, shut down if P < AVC.
Where is Sopranos shut down point?
• What is the Sopranos’ output if competitive
market price is $1? $3? Resulting profit?
“Long-run” production and cost
In future a manager could
• Change levels of fixed inputs
– Substitute capital for labor
– Increase the entire scale of operations
We will look at three ways to possibly reduce costs
• Substituting one input for another (optimal input
mix)
• Increasing scale (extra capital & other inputs)
• Increasing scope (additional related products)
• Increasing learning (feedback from more output)
Long run: Optimal input mix
Many inputs have some degree of substitutability
•
•
•
•
•
Degree of automation – people vs. machines
Different metals in automobile parts
Different types of labor – e.g. skilled vs. unskilled
Great hitting versus taking walks
Blazing fastball versus deceptive ball movements
Cost Minimization Problem
• Choice variables – levels of inputs
• Objective – minimize total cost of producing a target
output level
Dual Problem: Output maximization for a given
level of cost
• Objective –maximize output for a given target level of
expenditures
Optimal input mix
Isoquants
•Each isoquant shows different
combinations of inputs (metals)
that will produce a given amount
of output (auto parts)
•Isoquants portray technical
combination of inputs to produce
a given level of output
•Slope = marginal rate of
technical substitution of one
input for the other = ratio of
marginal products of the two
inputs
MRTS x , y
dQ
MPx

 dx
MPy dQ
dy
Optimal input mix example
Isoquants: differing input substitutability
• Curvature of isoquants reflects degree of substitutability of
inputs
• In our example, steel & aluminum have substitute AND
complement characteristics
• Perfect substitutes would have straight-line isoquants
Cost Minimization Problem
Many inputs have some degree of substitutability
•
•
•
•
•
Degree of automation – man vs. machine
Different metals in automobile parts
Different types of labor – e.g. skilled vs. unskilled
Great hitting versus taking walks
Blazing fastball versus deceptive ball movements
Cost Minimization Problem
• Choice variables – levels of inputs
• Objective – minimize total cost of producing a target
output level
• Mr. Burn’s Principle
Dual Problem: Output maximization for a given
level of cost
• Objective –maximize output for a given target
level of expenditures
Cost Minimization Problem
Isocost lines
• Isocost lines portray
combinations of inputs that
entail the same cost
• Isocost lines change as input
prices change
• TC = PXX + PYY
Slope of isocost is 
Px
Py
Isocost lines
changes in input prices
The optimal choice of inputs is where
Slope of the isoquant = Slope of isocost line
"optimal input mix" rule
MPX MPY

PX
PY
Input Y
per week
TC1
TC2
Excellent!
TC3
MRTS=Relative
Price of Inputs
Y*
q1
0
X*
Input X
per week
Optimal Input Mix
Change in input prices
If price of steel rises then Ps/Pa goes up and
isocosts get steeper
=> Change cost minimizing input mix to more
aluminum, less steel
Discussion:
The Oakland A’s and Cost minimization
• How did the A’s produce more at a lower
cost???
• Specifically how did the management
change the A’s mix of inputs?
• What will Beane do if the relative prices of
different types of baseball talent changes?
• Additional questions?
Optimal Input Mix
Derivation of Long run cost curves
The Sopranos
• The Soprano Garbage Company
hires labor and capital to produce
dumpsters. The price of labor is $3.
The rental rate of capital is $2 per
unit. In the long-run, the Sopranos
can vary both the amount of labor
and capital they use.
• The expansion path shows the
tangencies between various isocost
lines and isoquants.
• Calculate & draw this firm’s longrun total cost curve, long-run
average cost curve, and marginal
cost curve.
• How do these costs compare with
the short-run counterparts? Why?
Optimal Input Mix
Derivation of long run cost curves
The Sopranos
Quantiy
0
5
12
21
28
33
36
37
L
K
0
2
2.5
3
3.5
4
4.5
5
Pl
0
3
4
5
5.5
6
6.5
7
$
$
$
$
$
$
$
$
Pk
3
3
3
3
3
3
3
3
$
$
$
$
$
$
$
$
Total
Cost
2
2
2
2
2
2
2
2
$
$
$
$
$
$
$
$
12.00
15.50
19.00
21.50
24.00
26.50
29.00
Average
Total
Cost
----$ 2.40
$ 1.29
$ 0.90
$ 0.77
$ 0.73
$ 0.74
$ 0.78
"Batch" of
additional
output
Marginal
Cost of
Batch
5
7
9
7
5
3
1
$
$
$
$
$
$
$
12.00
3.50
3.50
2.50
2.50
2.50
2.50
Marginal
Cost of
one Unit
2.40
0.50
0.39
0.36
0.50
0.83
2.50
Total Cost
3
$35.000
2.5
Average Total Cost
$30.000
2
$25.000
Marginal Cost of one
Unit
1.5
$20.000
Total Cost
$15.000
1
$10.000
0.5
$5.000
0
$0
10
20
30
40
5
15
25
35
45
Long – Run Supply
Long Run Supply
$3.00
Price per unit
$2.50
$2.00
Average Total Cost
$1.50
Marginal Cost of one
Unit
$1.00
$0.50
$0
10
20
30
Quantity of Output
40
Cost Minimization Problem Example:
Labor substitutability
• Choose high school or college educated
reps?
• Compare relative productivities with
relative wage rates
• Minimize labor cost by choosing most
favorable cost/productivity ratio
• Other considerations?
Cost Minimization Problem - Example
Choose between skilled and unskilled sales workers to minimize total
wage cost of achieving a target level of sales revenue
College grads
HS grads
Average Sales per
worker
$1.88333 mill/year
$1.475 mill/year
Hourly wage
$10.25 / hour
$6.82 / hour
Wage and sales
higher
Wage and sales
lower
Economies of Scale
•Scaling up levels of all
inputs due to higher
production scale can alter
ATC patterns. The fixed
costs are higher but savings
in AVC may offset.
•Economies of scale for
plant sizes 1,2,3 on graph
but diseconomies of scale
thereafter
•Many companies have
constant returns to scale,
which means that lowest
ATC doesn’t vary with
expansion.
The dark, lower envelope of the SR
average cost curves is the “long run
average cost” curve: lowest achievable
unit costs for different scales when you can
vary all inputs.
Looking Forward
•
Assignment 2 – on Blackboard
–
Due on October 14,18, or 19
Read Managerial Economics Chapters 6 and 8
Wal-Mart, p. 221
Going for the Gold and Pineapple Acid Test, WSJ
•
•
•
–
•
•
What are/were the barriers to entry into the premium pineapple market?
What is/will be the market structure of that market? Profitability?
Note on the Structural Analysis of Industries – Michael Porter
Pick a market/industry with which you are familiar. Based on
your text reading, how would you describe its market structure
and why? How narrowly/broadly are you defining the market
(e.g. does Coke compete in all beverages or bottled soft
drinks)? How would you characterize barriers to entry to this
market?