Download COSTS OF PRODUCTION

CHAPTER 6. PRODUCTION
Part A. © 2009, Kwan Choi
In Part A, we first consider a firm’s production. Cost information is needed to
make optimal production decisions of a firm and will be considered in Part B.
Firm and Entreprenuer
Where do entrepreneurs
come from?
A firm is an entity that organizes production activity
and sells the output in the market. Firms use inputs
like capital (K) and labor (L), and convert them into a
marketable output. Entreprenuers form firms by
combining capital inputs and laborers who are willing
to be passive and sell their labor.
Individuals have two choices:
They can sell their labor in competitive markets
and earn wage.
Alternatively, they can organize a production
activity by combining inputs to produce a marketable
product, which is then sold in the market. Input prices
are more or less fixed in factor markets.
Are entrepreneurs risk
takers?
In western countries, creativity and entrepreneurship
are encouraged. Accordingly, there are more
entrepreneurs than in command economies (e.g.,
former Soviet Union)
Right.
The choice between wage earners and entrepreneurs
are decisions under uncertainty.
Although a salary man gets laid off occasionally
during the economic downturn, their income is more
predictable and safer than that of entrepreneurs. When
employed, they earn fixed incomes, which are
generally less risky than the profits of entrepreneurs.
Accordingly, expected earnings in the labor market
are lower.
Are you saying that the
owner of the firm or the
entrepreneur takes a risk
by organizing a
Profits are uncertain. Moreover, profits can be
negative!
production activity?
In return, he will earn
random profits, rather
than fixed wage.
Thus, whether to work
for someone else for a
fixed wage or to become
an entrepreneur is really
a choice between risky
prospects.
Even though Option B
has expected value of
$75,000, most people
prefer Option A
Because they are risk
averse.
Why does an
entrepreneur need
capital?
If he guesses correctly, he earns profits. If not, he
incurs a loss.
Under no circumstances, wage earners are required to
pay for the right to work. Thus, wage earners cut the
downside risk (of negative wage).
For instance, an individual may be faced with two
options:
Option A: fixed wage W = $50,000
Option B: random income w: 50% chance of earning
$200,000 and 50% chance of losing $50,000.
Moreover, those without capital (i.e., money to lose or
borrow) can only be a wage earner.
According to Kenneth Arrow, individuals show
diminishing absolute risk aversion (DARA), which
means individuals become less risk averse as
income/wealth increases.
Farmers must plant corn in the spring without really
knowing what the market price will be six months
later at the harvest time. Even before planting corn,
the farmer must also dedicate or rent some land and
adds nitro fertilizer in late fall before observing
market price.
Perfect Foresight: The entrepreneur knows all output
and input prices before making production decisions.
That is, the firm has perfect foresight.
Let us take a look at the downside risk.
A firm’s revenue = pQ.
In the worst case, a producer may not
receive any revenue.
But some production costs may
Production costs are incurred because
have been incurred already in order inputs are used to produce something and
to produce outputs.
these inputs are scarce and could have been
used elsewhere.
How do we calculate costs?
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Explicit Cost: the cost of inputs that
involves direct money outlays. It is the cost
of purchasing inputs not owned by the firm.
Implicit Cost: is the highest income
foregone the firm could have earned by
selling its own resources to others. The cost
of resources owned by the entrepreneur.
Your notion of profits would then
be different from the accounting
profits which we use for tax
purposes.
Example: rent for land and buildings owned
by the firm.
Normal profits are the payment required to
keep the entrepreneur in the business. This
is the amount of income the entrepreneur
could have earned elsewhere. This is an
implicit cost of doing business.
Economic Profit = total revenue opportunity cost of all inputs.
= total revenue - (implicit cost + explicit
cost)
Then, it is possible for a firm to
show accounting profits but still
shut down subsequently.
This could happen when the firm
does not earn enough to cover the
cost of the owner’s resources, or
implicit costs.
Right.
If an entrepreneur has a job offer of say,
$100,000 from another company, this
should be taken into account. If accounting
profits are only $50,000, then the
entrepreneur will quit.
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Production Function
To estimate the total cost of producing a given quantity of a good, one must
understand the relationship between inputs and output. Output refers to the goods
produced by a firm. Inputs refer to the resources used by the firm to produce the
output.
To calculate the total cost of a given output, the firm must know precisely what
inputs must be employed in what quantities. This relationship between inputs and
the output is called the production function. For instance, the relationship
between the total output and inputs may be given by
Y  F ( K , X ),
where Y denotes the total output and K and X denote capital input and a variable
input, respectively.
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SR VERSUS LR AND FIXED VERSUS VARIABLE INPUTS
In the short run (SR), the firm's ability to alter
input combinations is limited. If General
Motors (GM) wants to increase its production
of automobiles, it can order more steel and
engine components, hire more workers, use
three rather than two shifts in all plants. But
at some point, the existing plant will reach its
full capacity. In the SR, there is a limit to
how many automobiles can roll off the GM
assembly lines each day. This is because
some inputs are fixed in the short run.
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How long is the short run?
The relationship between inputs
and outputs are similar to that
between consumption and utility.
It depends on the product or industry in
question. In manufacturing industries,
production occurs continuously throughout
the year. The decision to buy and use new
capital equipment can be made within a few
months in one industry, but may take a few
years in another.
In agriculture, land becomes a fixed input in
the short run, because rent decisions are made
annually.
Yes, but with one exception. Production may
reach a peak and decline thereafter as more
inputs are used. In contrast, utility is
monotonically increasing as consumption
increases.
In Figure 1, a short run relationship between
input X and output Y can be examined for
given amount of capital, K = 5. A vertical
cross section of the production function at K
= 5 shows a contour of the total product curve
to be discussed shortly. A horizontal slice or
cross section of the production function
shows what is called an isoquant (iso = equal,
quant = quantity).
What is a fixed input?
Fixed Input: is an input whose quantity
cannot be changed in the short run (when an
immediate change in output is desired).
The cost of increasing the quantity of the
fixed input is too high to accommodate a
quick variation in output. It is not a
technological impossibility, but it is not
economically practical to change the fixed
input in the short run.
What then is a variable input?
Variable Input is an input whose quantity
can be changed instantaneously in response to
a change in demand.
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Workers are then a variable
input?
Yes, in the United States and China.
In other countries, however, labor is a fixed
input.
For instance, in Japan a job is a lifetime
employment, and they do not lay off workers
during an economic downturn.
In France, due to regulations, it is next to
impossible to fire a worker, and hence labor
becomes a fixed input.
When making production decisions, we also
distinguish two time periods: short run and long run.
Short Run is defined to be the period of time in
which some inputs are fixed.
Usually, plants and capital equipment are fixed.
How long is the SR?
Then how long is the long
run?
The SR does not designate a specific period of time.
The length of SR depends on the output produced.
For many manufacturing industries, SR could be a
few months, whereas in public utilities and oil and
natural gas industries, SR could be several years.
Long Run is the period of time in which all inputs
can be varied, including the plant size.
Of course, the time it takes to alter plant capacity
varies from industry to industry. For example, it
would take several years for GM to design and
construct a new factory. A corner drug store may be
able to build a new wing in a few months.
Right.
Production costs will
depend on the time
horizon.
TC = TFC + TVC
Total cost =Total fixed cost + total variable cost
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Law of Diminishing Returns
The relationship between inputs and output
are not generally linear.
So, that must be the Law of
Diminishing Returns (Law of
Diminishing Marginal Product).
But in the SR, you can only
increase some inputs, but while
other inputs are fixed.
Increasing only one input generally increases
output, but beyond a certain point, the
increment declines.
Right.
For most products, inputs must be mixed
together to yield a maximum output.
Right
The following table shows the relationship
between an input and output in a
hypothetical firm.
Notice how MP is calculated. It is the
increment of output attributable to an extra
unit of the input.
Input X
Output Q
Marginal Product (MP)
0
0
-
1
8
8
2
20
12
3
30
10
4
37
7
5
40
3
6
40
0
7
35
-5
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What does point A represent?
It is called the Inflexion point (TP
curve is convex to the left of B and
concave to the right). This is the point
where the curvature changes. (the
second derivative = 0.)
Ray 1 from the origin intersects the TP
curve at points, B and D.
Right
Then the average product (Q/X) must
be the same at both points.
At C, the ray from the origin is just
tangent, that is where MP (marginal
product) and AP (average product) are
equal. That is where AP is highest.
What does point C signify?
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Right.
And when TP falls to zero, TP = AP =
0.
At point D, total product reaches a
maximum. I bet its MP = 0.
If X denotes a variable input (such as
labor), a SR product function is given
by
Q  g ( K , X )  f ( X ),
and is obtained for a specific value of
capital.
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Marginal product (MP) is the
increment of output from a small
increase in the variable input.
MPX 
As in the utility theory, the extra unit
X would depend on the unit of
measurement.
Q
.
X
Right.
It is desirable to obtain marginal
product when X is infinitesimally
small. In mathematics, this marginal
concept is often described as a
derivative. From now on, marginal
product is written as
MPX  f '( X ).
Give me an example.
For instance, if the production function
is written as:
y  ax  bx 2  cx3 . (1)
Right.
The marginal product (MP) is
Average Product is total output divided
by the quantity of the variable input.
dy
 a  2bx  3cx 2 , (2)
dx
APX 
which looks like the MP curve in
Figure 3, provided that c is negative.
TP Q
 . (3)
X
X
Now derive average product for the
example.
Average product of X is
y
 a  bx  cx 2 , (4)
x
which also looks like the AP curve in
Figure 3, provided that c is negative.
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