Theory Of The Firm Produces And Sells Goods And

theory of the firm produces and sells goods and services objective to maximize profits where profits defined as total revenue minus tot

Theory of the Firm
Produces and sells goods and services
Objective to maximize profits where profits defined as total revenue
minus total costs
Constraints
Technological Constraint – incur costs during production and sales
Market Constraint – revenues limited by consumer demand and competitor
market share
Overview of Market Constraint – Industrial Organization
At one extreme perfect competition, so many competitors that the
individual firm has no control over price
Other extreme is monopoly, a single firm that can influence price
subject to consumer demand
In between are monopolistically competitive and oligopolistic models.
Overview of Technological Constraint
Two time frames – short run, where at least one input’s level remains
fixed, think of day- to-day operations- two inputs, variable and fixed
Long run, where all inputs are variable. This is more of a planning
horizon.
Start with short-run:
Production function with two inputs, labor and capital.
Q = f(L,K) where K is constant. We can only change Q by changing labor
L.
The amount Q changes with an incremental change in L is defined as the
marginal physical product of labor (MPl). MPl = ΔQ / ΔL, holding K
constant.
The following graph shows the relationship between the total product
(production function) and labor’s marginal product. Note that the
horizontal axis measures the amount of labor, while the vertical
measures the amount of output. The shape of the Total Product curve,
the mapping of the production function holding capital constant, shows
output initially increasing at an increasing rate, then hits an
inflection point, increases at a decreasing rate and finally turns
negative. This is as a result of Diminishing Returns which is
demonstrated in the second graph. Marginal product of labor will
initially rise, peak, and then decrease. This phenomenon drives all
the results in the short-run.

The short-run technological constraint is made up of three cost
curves: Average Total Cost (ATC), Average Variable Cost (AVC) and
Marginal Costs (MC). We need to do two things; first we need to define
and derive these curves, and second show their connection to
productivity and diminishing returns.
Define total cost (TC) as the sum of variable and fixed costs (VC,
FC), payments to variable and fixed inputs, respectively.
TC = VC + FC
As noted above, these costs are driven by diminishing returns relating
the productivity of combining variable input to a given amount of
fixed input.
Fixed costs in the following diagram is portrayed as a horizontal
line, in essence these costs are the same regardless of quantity. The
shape of the variable cost curve takes into account diminishing
returns. It rises at a decreasing rate and then increases at an
increasing rate.

Now define marginal costs as the change in total costs due to an
incremental change in output.
MC = Δ TC / ΔQ = (ΔVC + ΔFC)/ΔQ = ΔVC / ΔQ, since ΔFC equals zero.
If we examine ΔVC more closely, VC can change due to two factors.
Assuming Labor (L) as the variable input then payments to variable
input can change if we change the amount of labor or if the wage rate
changes. We will assume the wage remains constant so the following
holds:
ΔVC = w ΔL.
Substituting back into the MC equation we get:
MC = ΔVC / ΔQ = (w ΔL) / ΔQ. Note that ΔL / ΔQ is the inverse of the
MPl. Therefore MC are inversely related to productivity. MC = w / MPl.
The higher the marginal product of labor, i.e., the more productive
labor is, the lower the marginal costs of producing output. This
should make perfect sense.
Average costs
Average costs as the name suggests are costs per unit output. This is
easily derived from the total cost concepts, simply divide by quantity
output. Average total costs (ATC) are then equal to the sum of average
variable (AVC) and average fixed costs (AFC).
TC/Q = VC/Q + FC/Q, or ATC = AVC + AFC
What we will show is that the shape of both AVC and ATC result from,
you guessed it, diminishing returns. First, we need to return to
marginal cost and its inverse relationship with the marginal product
of labor. Recall initially that MPl increases, peaks, and then falls,
this would suggest that marginal cost, as the inverse, would first
fall, bottom out and then increase. In other words, because of
diminishing returns marginal costs are U- shaped. At first, as a
result of increasing MPl the costs of producing more output falls,
after which diminishing returns takes hold and MPl declines, marginal
cost increase.
Before we can derive the average costs curves we need to understand
the relationship between marginals and averages. The best explanation
by example lays close and dear to students’ hearts, their GPA. If your
grade in this class is higher than your GPA, then your GPA will rise.
That is to say that if the marginal is greater than the average, the
average will rise. Of course, the opposite also applies. If the
marginal is below the average then average will fall. Not a good
situation with GPAs but perhaps a good thing if dealing with costs.
As we first begin to combine labor with a given amount of capital, we
become more productive in using capital and MPl increases. Marginal
costs fall, laying below average variable costs, which in turn causes
AVC to fall. As long as MC is below AVC, AVC will continue to fall.
Once MPl peaks, MC turn upwards. MC eventually intersects AVC at the
minimum of AVC. AVC then turns upward as MC now lies above it.

Average fixed costs are a rectangular hyperbola that asymptotes with
both axes. Actually, AFC are very simple. Recall AFC = FC/Q. FC are
constant, so AFC changes as Q changes. Because Q is in the
denominator, as Q becomes increasingly large AFC goes to zero. As the
denominator of a fraction goes to infinity the fraction gets closer
and closer to zero, AFC asymptotes with the horizontal axis. The
reverse also holds true, in that if Q approaches zero, AFC becomes
infinite.
Average total costs are the sum of AVC and AFC. At each Q we add the
heights of the AFC and AVC curves. So at the qith unit of output the
sum of the heights of the blue and red lines equals the height of the
green line. ATC is equal to the sums of AFC and AVC.
We generally do not include the AFC curve in the firm’s short-run
technological constraint since that information is already present at
the vertical distance between ATC and AVC. In other words since ATC =
AVC + AFC, then AFC = ATC – AVC. So in the graph the difference in
heights between the green and red lines is equal to the height of the
blue line.
One last parting shot with the short-run, note that MC intersects ATC
and AVC at their minimums. This relates back to the relationship
between marginals and averages. When they are equal, then it must be
either a maximum or a minimum (excepting inflections) for the average.
Long-Run Technological Constraint
The long-run is a time period where all input levels are variable. In
other words, the oxymoron of a variable fixed input holds. Here the
decision makers not only choose the amount of labor, more importantly
they are choosing the size of the factory. The choice of scale of
operation (factory size) depends on a variety of issues not least of
which is expected demand and technology. The main point to be made is
that the long-run can be thought of as a planning horizon where all
factory sizes are possible. However, once a choice of capital is made
and implemented, then the situation reverts back to the short-run so
at each level of capital there is a family of short-run costs.
There is a concept called long-run average costs (LRAC) where costs
per unit are calculated for each level of capital.

In the graph we have eight short-run ATC curves labeled one through
eight, each with an progressively increasing amount of capital, i.e.,
K1 below. It shows the lowest average cost possible for each level of
output. Note that it is either below or in the case of tangencies,
equal to the height of the corresponding short-run curve. The long run
by definition is one where there is no constraining fixed input,
therefore, the firm has greater flexibility in production and
consequently lower average costs.
The LRAC curve also has a characteristic U-shape. The downward sloping
section of the LRAC is called economies of scale. This can be
interpreted by ”bigger being better” with regards to the scale of
operations and average costs. As we move to the right the amount of
capital increases, in other words the size of the factory is larger,
the lower the average costs, the lower the cost per unit output.
Usually these efficiency gains arise from specialization of inputs.
Large scale operations have large production runs. In these cases
inputs can become highly specialized and with high quantities of
output average costs can be low.
The second region of the LRAC is one where LRAC are at a minimum
suggesting all gains from specialization having been exploited. This
is called constant returns to scale. The part of the LRAC that is
upward sloping is called diseconomies of scale, suggesting that the
firm has gotten too big. Increasing the firm’s size results in higher
average costs, hence it would be more efficient on the cost side to
reduce the scale of operations. Note that long-run and short-run costs
are both U-shaped, but for very different reasons: returns to scale in
the long-run and diminishing returns in the short run.