Production Function (MKM
In symbolic logic the
production function of
a firm is:
(7) Q = g (L, K, N)
Q = output
= some function reflecting ‘know-how’ in combining inputs to
produce output, a.k.a., technology
L = labour
K = capital
N = natural resources that
can be enabled to serve human purpose.
The production function is time sensitive.
However, the short- and long-run in economics is measured not in
chronological time but in functional time, e.g., how long it
takes to build a new plant. Thus the long-run in the restaurant
industry is chronologically shorter than in the steel or nuclear
industries but both are functionally the long-run in their
respective industries. There are three types of time periods.
We will graph only in two dimensional space with K and L considered.
i - Very Short-Run
In the very short run, or what Marshall called
‘the market period’, output is fixed. All factors of production are
fixed – labour, capital and natural resources. The very short-run
supply curve is vertical and does not change with price. An example
is the farmers’ market where produce is brought into the city from
the farm for sale. No more produce is available. What is on hand
is all that can be sold, no matter price.
(8) Q = g (L, K)
K, L & Q are all fixed
ii - Short-Run
In the short-run at least one factor of
production is fixed, generally capital plant and equipment (MBB Fig.
7.2). More or
less labour and natural resources can be employed and output
increased or decreased.
(9) Q = g (L, K)
L is variable
K is fixed
Q is variable
With capital fixed and labour
variable in the short run we can graph the production function as an
'S' shaped curve (MKM
Initially as labour is added its
marginal product increases up to about 2.5 units in the graph
(increasing MPL) and then it begins to decrease from 2.5
up to 6.5 units (diminishing MPL) becoming zero at the
peak of the curve and then turns negative (negative MPL).
No profit maximizing firm will expand by hiring more labour if total
output is decreased, i.e., beyond the peak of the production
curve. There are, of course, some firms such as
State owned companies in China that are not profit maximizers but
rather employment maximizers.
Why does MPL eventually decline and become negative.
The simple answer is that capital is being spread thinner and
thinner among more and more workers reducing their marginal product.
In addition more and more workers means increased congestion and
complexity. This is called the law of eventually diminishing
which has significant implications for the costs of a firm as output
rises. It parallels the law of eventually diminishing
marginal utility in Consumer Theory, i.e., eventually the marginal
utility of a good declines and becomes negative, too much of a good
thing makes you sick. The marginal product of labour, i.e., the
additional output generated by employing one more unit of labour is
measured by the slope of the production function. The average
product of labour, or the average output of all workers, is measured
by the slope of a ray, i.e., straight line, from the origin
where it intersects the production function. It should be
noted that some rays will intersect the production function at two
points. At each of these two points average product is the
same. As will be seen this has significant implications for
the shape of the marginal and variable costs curves of a firm,
specifically their 'U' shape. As will be seen, if we know the
cost of labour we can calculate the marginal cost of an additional
unit of output and the average variable cost of any given level of
iii - Long-Run
In the long-run all factors of production are
variable – capital plant & equipment, labour and natural resources.
(10) Q = g (L, K)
L is variable
K is variable
Q is variable
As noted previously modern
microeconomic theory began with demand and the constrained
maximization of utility by the consumer demonstrated using
indifference curves and budget constraint. Initial attempts to
explain production adopted the same basic mechanism with one
important change: measurement of output is cardinal. That is we
can, unlike utiles, count the exact number of units being produced.
The firm thus wants to maximize output
The firm, however, faces a constraint: the cost
of inputs or factors of production. In symbolic logic, this cost
(11) C = PLL
L = labour
K = capital
PK = price of
PL = price of
Assuming all factors are infinitely divisible
then different levels of Q can be produced using different factor
combinations. This generates an isoquant a curve representing a
constant level of output all along its run (R&L
8A-1; M&Y 10th
Fig. 8.2). The slope
of the isoquant is the
marginal rate of technical substitution
of capital for labour maintaining the same Q. In symbolic logic it
(12) MRTS = MPL/MPK where
MPK = marginal product of capital
MPL = marginal product of labour
There are theoretically an infinite number of
isoquants rising to higher and higher levels of output (R&L
8A-2). They are
convex to the origin (opening away) due to the Law of Diminishing
Marginal Product which states that as one factor is given up in favour of another eventually marginal product of the increasing
factor will decrease.
While the firm wants to maximize Q it faces a
cost constraint. For a given cost a maximum amount of capital or
labour can be bought illustrated by the intercepts of the x- and
y-axis. Its slope is the relative cost of the two factors or in
symbolic logic is:
(13) Cost Ratio = CL/CK
As with the budget constraint price ratio by
convention the cost ratio is the inverse of the slope of the
resulting cost constraint curve. The curve shows all combinations
of K and L that can be bought for a specific cost (R&L
8A-3; M&Y 10th
Fig. 8.2). Maximum Q
for a specific cost is achieved where the cost constraint just
touches or is tangent to the highest attainable isoquant. At that
point, the slope of the cost constraint equals the slope or MRTS of
MRTS = MPL/MPK
= - (CL/CK)
dollar-for dollar the
marginal product of an additional unit of L is equal
dollar-for-dollar to the marginal product of an additional unit of K
iv - Expansion Path
As with consumption and the Income Consumption
Curve, if we relax the cost constraint while holding factor prices
constant, a new cost constraint with the same slope (CL/CK)
is created and a new equilibrium established. Repeating this
process a locus of point is created all of which satisfy the
equilibrium conditions (MPK/CK
= MPL/CL) forming the expansion path
for the firm
This initial attempt to plot the supply curve of
the firm was judged inadequate for the simple reason that factors of
production especially capital are not infinitely divisible but
rather ‘lumpy’ particularly in the short-run. A new approach was
required that focused on the short-run behavior of the firm.
i - Opportunity Cost
choice involves how to satisfy infinite human wants, needs and
desires with scarce resources. It requires a choice between
alternatives, e.g., a
pensioner choosing food or medicine. The choice of the best alternative
means the next best alternative is not chosen. Put another way, the
cost of choosing one possibility is the next best alternative foregone.
This is called ‘opportunity cost’. All economic costs are opportunity
costs even those not expressed by market prices.
for convenience one usually measures opportunity cost in dollars it
actually involves real alternatives foregone. Thus for a firm,
the opportunity cost of producing (OCP) a good (and therefore opportunity
cost of employing factors of production) is the next best alternative action.
There are two components to a firm’s OCP : explicit and implicit costs
Explicit costs are paid directly in money; implicit costs or opportunities foregone
are not paid directly in money (even though
measured that way). Explicit costs include direct payment for factors of
production, e.g. in the case of labour,
money cost or wages are generally equal to their OC. Implicit costs include
the implicit cost of physical capital, inventories and the owner’s resources.
(MKM Fig. 13.1)
Fixed, Variable &Total
Assuming one factor of
production is fixed (usually capital) then we are in the short-run
and can identify three types of costs measured in three different
ways. In the short-run a firm can produce different levels of output but
only by varying variable inputs. Accordingly the firm has three
distinct types of costs:
a) fixed costs associated with the
fixed factor of production - usually K but in the knowledge
industries often L or 'the talent'. Fixed costs must be paid no
matter the level of output, i.e. even if the firm shuts down
fixed costs still have to be paid;
b) variable costs associated with
variable factors of production - usually L. Variable costs rise and
fall according to how much of the variable factors are employed.
The higher the level of production, all things being equal, the
higher the variable costs; and,
c) total costs that include all
fixed and variable costs or TC = TFC + TVC (MKM
Average, Marginal & Total
In turn, for each type of cost at every level of production, average
costs can be calculated:
a) Average Fixed Cost (AFC) =
fixed cost per unit output.
AFC will decline as output increases as the fixed cost is spread
over a larger and larger level of output;
b) Average Variable Cost (AVC)
= variable cost per unit output.
The distance between the AVC curve and the TC curve will tend to
narrow as output increases because AFC declines as output increases;
c) Average Total Cost (ATC) = fixed
(AFC) + variable (AVC) cost per unit output.
In turn, for each level of production, marginal cost can be
calculated from the cost associated with one additional
unit of output (M&Y 10th
Fig. 8.10). Average total
and marginal cost can also be calculated from the total cost curve.
Average total cost can be derived from the slope of a straight line
or 'ray' drawn from the origin to any point on the total cost curve.
Marginal cost can be derived from the changing slope of the total
cost curve itself.
Marginal cost (MC) will initially decline as output increases but
eventually, assuming at least one fixed factor of production, the
Law of Eventually Diminishing Marginal Product/Return sets in and marginal cost begins to
rise. The MC curve will cut the average cost curve (AC) at its
lowest point. Thus as long as MC < AC then AC falls; when MC = AC
then AC will be at its minimum; when MC > AC then AC will increase
Using the one fixed factor cost function, the long-run cost or
expansion path of a firm is considered to be the sequence of
short-run (SR) scenarios for varying scale of plant and equipment
In each SR scenario the scale of plant and equipment increases but
during that period plant and equipment are consider to be fixed.
The result is a set of average cost curve for each scale of
production. An envelop curve can then be drawn representing the
long-run (LR) minimum average cost at each level of output (M&Y 10th
The question remains as to when this series of SR scenarios
becomes the LR.
3. Supply Curve (MKM
The question remains: How much output will a firm be willing to
supply given its cost constraints? Put another way: What is the
firm's supply curve? This depends on how much the firm can get for
its output, i.e. the price or revenue it receives per unit (P&B 7th
Fig. 12.5; R&L
CP TGQ #1,
MKM Fig. 14.4).
Shut Down (MKM
If a firm cannot earn at least enough to cover all of its variable
costs then in the short run it will shut down. This occurs at point
B where marginal cost is equal to minimum average variable cost.
This is called the 'shut down point'. If a firm earns a price
higher than B it can cover all of its variable costs and some of its
fixed costs and it will stay in business. Put another way, the firm
will maximize profits by minimizing losses.
In the long run, however, a firm must cover all costs - fixed and
variable - or it will go out of business (M&Y 10th
Fig. 9.3). This occurs at point D
where marginal cost is equal to minimum average total cost. This is
called the break-even point. At this point all factors of
production - including entrepreneurship - are fully paid their
opportunity cost. If the firm receives a price higher than the
break-even point then it will earn economic or excess profits. Thus
the supply curve of a firm is the marginal cost curve above minimum AVC (shut down point) in the short-run and above minimum ATC
(break-even point) in the long-run.
It is important to appreciate that the price or revenue a firm
receives applies to each and every unit of output it sells.
Accordingly it will produce to the point at which the cost of the
next unit of output (MC) equals the price or marginal revenue (MR)
it receives for that last unit. In effect, a firm earns a profit on
each previous unit (if the price or revenue is greater than minimum
AVC or minimum ATC in the short- and long-run, respectively). A
firm thus maximizes profits (or minimizing losses) by producing at
the point where price or marginal revenue equals marginal cost of
the last unit of output.
(16) MR = MC
From the resulting cost
function we can determine
the supply curve of the firm,
i.e., how much it is willing to produce at each price. The
supply curve is the marginal cost curve of the firm above the
shut-down point in the short-run. If the firm cannot earn enough to
cover all its variable costs, it shuts down. The curve will in the
short-run be upward sloping reflecting the Law of Supply: the higher
the price, the greater the supply; the lower the price the smaller
In the long-run, firms can adjust
the size of their plants
13.6) creating a series of short-run average and marginal cost curves.
The long-run average cost curve is made up of an envelope of the
minimum points of the short-run average cost curves. In the case of
increasing return to scale industries at some point the most
efficient plant size is achieved where long-run average cost is
lowest. At this point optimal scale is attained and the short-run
marginal cost curve, in effect, becomes the long-run marginal cost
Elasticity refers to the
sensitivity of one variable to a one percentage change in another.
Price elasticity of supply
refers to the percentage
change in the quantity of a commodity supplied compared to a one
percentage change in its price
MKM Fig. 5.6). The amount supplied can increase:
a) more than
proportionately, i.e. elasticity is greater than one - at the
extreme a horizontal supply curve is perfectly elastic - a small
increase in price results in a large change in the quantity
b) proportionately, i.e.
elasticity is equal to one (unitary elasticity); or,
c) less than
proportionately. i.e. elasticity is less than one (inelastic)
- at the extreme, a vertical supply curve is perfectly inelastic -
any change in price results in no change in the amount of the
commodity demanded or supplied.
Symbolic Summary of Supply
(8) Q = g (L, K)
L, K & Q are fixed in the
L & Q variable, K fixed in the short-run
K, L & Q all variable in the long-run
(11) C = PLL
+ PKK where
L = labour
K = capital
PK = price of
PL = price of
(16) Profit Maximization
MR = MC