Transcript Lecture 1(b) Models - Southern Methodist University

Lecture 3 Production
and Costs
Outline







Production Theory: Basics
Cost Theory: Basics
Economies and Diseconomies of Scale
Production With Multiple Inputs
Time and Costs: Observations on Fixed Costs
Ideas That Matter
Complications
Production Theory: Basics

Production Function: The relationship describing the
most output possible with a given quantity of an input.





(Or the least amount inputs necessary to produce some given
level of output.)
Marginal Product: The change in total product when one
of the inputs is changed.
Approximation: MPx =Change in output/change in
input
Exact (calculus): MPx =dq/dx
Average Product: Output per unit of input
APx =Q/X
Example
Hours of Labor
Quantity of Output
Marginal Product
Average Product
0
0
1
1
1
1
2
3
2
1.5
3
6
3
2
4
8
2
2
5
9
1
1.8
EXTRA Q
PER EXTRA L
The Graph
4
Max AC
occurs when
MC=AC
MP increase
and then
decreases
3
2
1
0
0
1
2
3
Labor
4
5
6
Useful Stuff

MP increases and then decreases


Think about what an odd world it would be if MP did not
decrease.
 (This is commonly defined as diminishing marginal returns).
AP begins to decrease only when MP<AP

Techies can prove this using about two lines of calculus, but it
has a common sense explanation as well
Application: Optimal Choice of
Input
Hours of Labor
Quantity of Output
Marginal Product
0
0
1
5
5
2
9
4
3
12
3
4
14
2
5
15
1
Suppose that the output is worth $10 per unit and labor costs $15 per hour.
Total value (value of output – cost of inputs) is as follows.
Hours of
Labor
Quantity of
Output
Marginal
Product
Total Value
0
0
1
5
5
$35
2
9
4
$60
3
12
3
$75
4
14
2
$80
5
15
1
$75
$
-
More Marginals

Marginal revenue product: the revenue obtained
from the extra output produced when another
unit of the input is employed. Formally,

MRP = Marginal Product x Price of output
Output price=$10
Input price =$15
Hours of
Labor
Quantity of
Output
Marginal
Product
If MRP > Input
price, buy more input
MRP
MRP=10*MP
0
0
1
5
5
$50
2
9
4
$40
3
12
3
$30
4
14
2
$20
5
15
1
$10
Cost Function: Basics


Cost Function: The relationship describing the least expensive way
producing a given quantity of output. (Or, equivalently, the most
output that can be produced for a given level of expenditure.)
“Costs” are simply of way of expressing economically important
information about what the firm does. As such, when we
describe costs, we are really summarizing two kinds of things



The production technology (e.g., what sorts of inputs are able to produce
what sorts of outputs)
The cost of the inputs
Thus, if we have described the technology by writing out the
production function, we need only to know the price of the
inputs before we can describe costs.
Example: Given the production function suppose that cost
of the fixed input=$10 and wage rate=$5)
Cost Function
Hours of
Labor
Quantity of
Output
0
1
2
3
0
1
3
6
$
$
$
$
4
5
8
9
Total Cost
MC
AC
10
15
20
25
5
2.5
1.67
15
6.7
4.17
$ 30
$ 35
2.5
5.0
3.75
3.89
Economies and diseconomies of
scale

Economies of scale the tendency for AC to
decrease when output increases


MC<AC
Diseconomies of Scale: The tendency for AC to
increase when output increases

MC>AC
Why Economies of Scale?




Learning by doing/gains from specialization
The presence of fixed costs
Pure technological factors
Pecuniary Economies: Reduction in input prices
by purchasing in volume.
Why Diseconomies of Scale?


Managerial complexities
Pecuniary diseconomies
Production with multiple inputs

There is more than one way to do most things.
(Think of examples where this is and isn’t the
case.) Thus, the essential problem is how to find
the optimal mix of inputs. This can be stated
formally in either of two ways.
Minimize the cost of producing a given quantity of
output
 Maximize the output from a given level of
expenditures.

Isoquant: various combinations of inputs that will
produce a given level of output. (equivalent to an
indifference curve)
Ways of Producing Q=5
Method
Capital
Labor
A
11
1
B
7
2
C
4
3
D
2
4
E
1
5
Marginal Rate of Technical Substitution: The rate at which
one input can be substituted for another without any change
in output
Capital
Labor
Capital
MRTS
11
1
11
7
2
7
-4
4
3
4
-3
2
4
2
-2
1
5
1
-1
Optimal Input Mix (Price of labor = $10, Price of Labor =$25)
Q=5
Capital
Labor
TC
MRTS
11
1
135
7
2
120
What is the
Marginal Condition
That Makes This
Optimal
-4
4
3
115
-3
2
4
120
-2
1
5
135
-1



MRTS measures the relative productivity of the
two inputs
The ratio of their prices measures their relative
costs
If an input’s relative productivity is greater than
its relative cost, buy more of that input and less
of the other
Time and Costs: Observations on
Fixed Costs

“Long run”, “short run” and fixed costs
Long Run: Period of time sufficiently long to vary all
costs.
 Short Run: Any period less than the long run.
 Fixed Costs: Those costs that cannot be varied in the
short run.

Distinguishing fixed and sunk costs

Fixed costs: Costs that don’t vary with output



an airplane
Sunk costs: Costs that can’t be recovered
a railroad track
what must be given up to get
something (which is often more than
the measured monetary cost)
Economic profit: Revenues-Opportunity Cost
 As distinguished from accounting cost: The dollars that
must be given up to get something else. and accounting
profit: Revenues-accounting cost
 Examples of Opportunity Cost




Retained earnings (was Coca Cola’s great cash flow free?)
Make vs buy (Was Valuejet really wrong to outsource
maintenance?)
Time (Who gets the keys to the company jet?)
Ideas That Matter: Relevant Costs

When do fixed costs matter? As we’ve already seen,
certainly not in any decision involving production levels,
or pricing. Consider these examples




R&D: “We’ve come too far to stop now.
Buildings: “We built in the wrong location, but we’re there now
Eternal problem: Managers who are given the power to
make fixed investments need to be held accountable for
those decisions. But how do you get them to ignore the
investment once it’s made?
Ideas That Matter: Defining and
measuring efficiency



Pure Waste: not obtaining maximum output
from a given amount of inputs
Allocative Efficiency: Employing the wrong mix
of inputs
Caution: Is waste really waste if it would cost
more to eliminate than would be saved by
eliminating
Ideas That Matter: Comparative
Advantage

Suppose:




Attilla can produce 4 units of clean room or 2 units of clean dog per
hour
Godzilla can produce 1 unit of clean room or 1 unit of clean dog per
hour.
Note: Godzilla is, by one measure, less productive.
Can It Ever Be Efficient to Use a Less Productive Asset? Sure :


Suppose both kids spent 1 hour on each chore (4 hours of total work),
producing 5 units of clean room and 3 units of clean dog.
They could produce the same output with less effort. Godzilla could spend
2 hours on dog (producing 2 units of clean dog). Attilla could spend 1.25
hours on room (producing 5 units of clean room) and 0.5 hours on dog
(producing 1 unit of clean dog). They get the same output with only 3.75
hours of labor

Conclusion: The Value of Comparative Advantage





An input is said to have a comparative advantage over another input if
the relative cost of producing one good is lower (Godzilla has a
comparative advantage in the production of clean dog since she only has
to give up one unit of clean room to get an extra unit of clean dog.)
As long as there is a comparative advantage, specialization increases
output
Implications of Comparative Advantage
What do “menial” workers really produce?
Trade is good: the U.S. might benefit from trade with developing
countries that are not as absolutely productive but that have a
comparative advantage in the production of some goods
Complications:Multiple Outputs

Most production processes produce more than one
output




Cars and SUV’s. Consulting services and audits. Finance
majors and marketing majors
Economies of Scope are said to exist when it is less
expensive to produce more than one output jointly than
separately.
Why economies of scope?
The most likely source of economies of scope is
common overhead
Complications: Multiple Plants

: Some firms have several plants that produce
the same output. This raises two kinds of
issues.


Why?
If it is efficient to have more than one plant,
how much output should be assigned to each
plant
Transfer Pricing




Many firms use a separate division to produce some intermediate input. What “price’ should the
division charge for its input.?
The “customer” would like to have a low price (zero is nice) but this creates incentives to produce
too much .
The “seller” would like to have a high price (it is in the position of being a monopolist with a
captive customer) but this creates incentives to produce too little
Principle: transferring at marginal cost requires the end user to recognize the true cost of the
good.
Complications
How do you measure marginal cost (especially when the manager of the intermediate division has
incentives to inflate costs).
What if marginal costs are below average costs meaning that the intermediate division operates at
a loss (Certainly a possibility and if so, how do you assure the manager of the intermediate
division that its good to run a losing operation.)
What if the intermediate good can also be sold on an open market
Actually a blessing since the cost of transfering the intermediate good to the final producer is
really just the price at which it could be sold on the market
But this may create real hard feelings if the outside customers of the intermediate good compete
with the final manufacturer.
Complications




How do you measure marginal cost (especially when the manager of the intermediate
division has incentives to inflate costs).
What if marginal costs are below average costs meaning that the intermediate division
operates at a loss (Certainly a possibility and if so, how do you assure the manager of
the intermediate division that its good to run a losing operation.)
What if the intermediate good can also be sold on an open market
 Actually a blessing since the cost of transfering the intermediate good to the final
producer is really just the price at which it could be sold on the market
But this may create real hard feelings if the outside customers of the intermediate
good compete with the final manufacturer.