ECONOMICS 304 SECTION SIX (6) LESSON

Intermediate Microeconomics is divided into two: Consumer behavior and firm behavior.

In consumer behavior/theory, learners were taught about how individuals make choices
subject to how much income they have available to spend and the prices of goods and
services in order to maximize their utility. That is, individuals have the freedom to choose
between different bundles of goods and services for their satisfaction subject to their
income. Utility maximization, nonsatiation, and the notion of diminishing marginal utility
were concept discussed.

In this course, we will focus our attentions on the behavior of the firm or theory of the firm.
We shall discuss the firm in term of its characteristics in production, how firms are grouped
in different productive activities to form market structure, and game theory. We begin with
production of the firm.
WHAT IS A FIRM

The firm is an organizational activity that transforms factors of production, or productive

inputs, into outputs of goods and services. Economics itself is the study of how society
chooses to satisfy virtually unlimited human wants subject to scarce productive resources.
In fact, this economic problem can be viewed as a constrained optimization problem in
which the objective is to maximize some index of human happiness, which is assumed to
be a function of the consumption of limited, or scarce, amounts of goods and services.

Productive resources, or inputs, or factors of production are used by firms to produce goods
and services. These productive resources may conceptually be divided into two broad
categories—human and nonhuman resources. Nonhuman resources may be further
classified as land, raw materials, and capital. While these classifications are arbitrary, they
are conceptually convenient.

Land (e.g., arable land for farming, or the land under buildings and roads) may be
described as a “gift of nature.” Raw materials include such natural resources as coal, oil,
copper, sand, and trees.

In an economic sense, “capital” does not refer to such financial assets as money, corporate
equities, savings accounts, and U.S. Treasury securities. There is a loose conceptual
connection between the economic and financial definitions of the term in that firms that
wish to acquire capital equipment will do so only if the additional return from an investment
in capital goods is sufficient to cover the opportunity cost of the interest that might have
been earned by investing in a financial asset.

Human resources, on the other hand, might be classified as labor and entrepreneurial
ability. Labor consists of the physical and mental talents of individuals engaged in the
production process. Labor services are similar to services derived from nonhuman resources
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
in that the rental value of labor services (wages, salaries, health benefits, etc.) is determined
by the interaction of supply and demand conditions in the market for factors of production.
Labor is unique among the other factors of production, however, in that in a free society,
labor decides for itself how intensively its services will be made available in the production
process.

Entrepreneurial ability is a special subset of human resources because without the

entrepreneur, all other factors of production cannot be combined. In other words, the
services of land, labor, and capital are “rented” to the highest bidder through the
interaction of supply and demand.

THE PRODUCTION FUNCTION

The technological relationship that describes the process whereby factors of production
are efficiently transformed into goods and services is called the production function.
Mathematically, a production function utilizing capital, labor, and land inputs may be
written as
Q = f(K, L, M), where K is capital, L is labor, and M is land.

For the sake of pedagogical, theoretical, and graphical convenience, let us assume that
all productive inputs may be classified as either labor (L) or capital goods (K). Equation (5.1)
may therefore be rewritten as
Q = f (K, L).

THE COBB–DOUGLAS PRODUCTION FUNCTION

Perhaps the most widely used functional form of the production process for empirical and
instructional purposes is the Cobb–Douglas production function. The appeal of the Cobb–
Douglas production function stems from certain desirable mathematical properties. The
general form of the Cobb–Douglas production function for the two-input case may be
written as

where A, α and β are known parameters and K and L represent the explanatory variables
capital and labor, respectively. It is further assumed that α+β=1.

Consider, for example, the following empirical Cobb–Douglas production function:

The Cobb–Douglas production function has the following features:

Substitutability, returns to scale, and the law of diminishing marginal product.

Substitutability
When a given level of output is generated, factors of production may or may not be
substitutable for each other. See table 1 below. It can be seen, for example, that to
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
produce 122 units of output, labor and capital may be combined in (row, column)
combinations of (3, 8), (4, 6), (6, 4), and (8, 3).

The Cobb–Douglas production function also illustrates the fundamental economic problem
of constrained optimization. Although there are theoretically an infinite number of output
levels possible, the firm is typically subject to a predetermined operating budget that limits
the amount of productive resources that can be acquired by the firm. Because of this
restriction, an increase in the use of one factor of production requires that less of some
other factor be employed. The degree of substitutability of inputs is important because it
suggests that managers are able to alter the input mix required to produce a given level
of output in response to changes in input prices.

Returns to Scale
Suppose that capital and labor are multiplied by some scalar. If output increases by that
same scalar, the term constant returns to scale (CRTS) applies. If capital and labor are
multiplied by a scalar and output increases by a multiple greater than the scalar, the
condition is referred to as increasing returns to scale (IRTS). Finally, if capital and labor are
multiplied by a scalar and output increases by a multiple less than the scalar, the condition
is referred to as decreasing returns to scale (DRTS).

Law of Diminishing Marginal Product

The law of diminishing marginal product (also referred to as the law of diminishing returns).
This law, sometimes referred to as the second fundamental law of economics, states that
when at least one productive input is held fixed while at least one other productive
resource is increased, output will also increase but by successively smaller increments. The
law of diminishing marginal product is a short-run production concept.

SHORT-RUN PRODUCTION FUNCTION

Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
In the production process, economists distinguish between the short run and the long run.
The short run in production refers to that period of time during which at least one factor of
production is held constant. The law of diminishing marginal product is a short-run
phenomenon. The long run in production occurs when all factors of production are
variable. Denoting K0 as a fixed amount of capital, the short-run production function may
be written

It is the total product of labor, or more simply as TPL.

The decision maker must determine the optimal amount of the variable input (L) given its
price (PL) and the price of the resulting output (P). It is assumed that the state of technology
is captured in the specification of the production function and that production is efficient.

Equivalently, if labor is assumed to be the fixed input, the short-run production function
would be written as

KEY RELATIONSHIPS: TOTAL, AVERAGE, AND MARGINAL PRODUCTS

There is a crucial relationship between any total concept and its related average and
marginal concepts. Since the present discussion deals with production, we will explore the
relationship between the total product of labor and the related average product of labor
(APL) and marginal product of labor (MPL). The reader is advised, however, that the
fundamental relationships established here are perfectly general and may be applied to
any functional relationship.

Total Product of Labor

If we assume that the level of capital usage is fixed, the total product of labor (TPL) of the
short-run production function is defined as the maximum amount of output attainable from
any given level of labor usage.

Average Product of Labor

The average product of labor (APL) is simply the total product per unit of labor usage and
is determined by dividing the total product of labor by the total amount of labor usage.
This relationship is defined as

MARGINAL PRODUCT OF LABOR

The marginal product of labor (MPL) is defined as the incremental change in output
associated with an incremental change in the amount of labor usage. Mathematically,

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
since the amount of capital is constant, this is equivalent to the first partial derivative of the
production function with respect to labor given as:

Find the marginal product of both capital and labor given the Cobb-Douglas production
function:

2. Suppose that you are given the following production function:

Determine the marginal product of capital and the marginal product of labor when K = 25
and L = 100.

Mathematical Relationship between APL and MPL

The mathematical relationship between the average product of labor (or any average
concept) and the marginal product of labor (or any related marginal concept) may be
illustrated by the use of optimization analysis. Consider again the definition of the average
product of labor

By the first order condition (FOC), APL yields:

which implies

When MPL > APL, then ∂APL/∂L > 0, which implies that the average product of labor is rising.
When MPL < APL, then ∂APL/∂L < 0, which says that the average product of labor is falling.
Only when MPL = APL and ∂APL/∂L = 0 will the average product of labor be stationary (either
a maximum or a minimum). The second-order condition for minimum average product is a
negative definite.

Consider again the Cobb–Douglas production function:

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Verify that when the average product of labor is maximized, it is identical to the marginal
product of labor.

The Law of Diminishing Marginal Product

The Cobb–Douglas production function exhibits a number of useful mathematical
properties. One of these properties is the important technological relationship known as the
law of diminishing marginal product (law of diminishing returns). This concept can be
described by this law: that as increasing amounts of a variable input are combined with
one or more fixed inputs, at some point the marginal product of the variable input will begin
to decline.

Numerous empirical studies have attested to the veracity of the law of diminishing marginal
product. As noted earlier, this phenomenon is exhibited mathematically in the Cobb–
Douglas production function. A necessary condition for the law of diminishing returns is that
the first partial derivative of the production function be positive, indicating that as more of
the variable input is added to the production process, output will increase.

A sufficient condition, however, is that the second partial derivative be negative,

indicating that the additions to total output from additions of the variable input will become
smaller as shown hereunder:

Consider the following Cobb–Douglas production function:

Verify that this expression exhibits the law of diminishing marginal product with respect to
capital. Does it also hold for labor? Demonstrate.

THE OUTPUT ELASTICITY OF A VARIABLE INPUT

Another useful relationship in production theory is the coefficient of output elasticity of a
variable input, which illustrates an interesting relationship between the marginal product
and the average product of a productive input. The output elasticity of labor, by definition,
is

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
The output elasticity of labor is simply the ratio of the marginal product of labor and the
average product of labor. As we will see later, this relationship has some interesting
implications for production theory.

The Cobb–Douglas production function is widely used in economic and empirical analysis
because it possesses several useful mathematical properties. The general form of the
Cobb–Douglas production function is given as

where A is a positive constant and 0 < a < 1, 0 < b < 1.

1. Demonstrate the law of diminishing marginal return of both capital and labor;
2. Determine the output elasticity of labor.
3. Also, determine output elasticity of capital.

The Three Stages of Production

As shown in the diagram below, stage I of production is defined as the range of output
from L = 0 to, but not including, the level of labor usage at which APL = MPL. Alternatively,
stage I of production is defined up to the level of labor usage at which the average product
of labor is maximized. In this range, labor is over utilized, whereas capital is underutilized.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
This can be seen by the fact that MPL > APL thus “pulling up” output per unit of labor. If we
assume that the wage rate per worker and the price per unit of output are constant, then
increasing output per worker suggests that average revenue generated per worker is rising,
which suggests that average profit per worker is also rising.

Stage II of production is defined as labor usage levels 0E to 0F. In this region, the marginal
product of labor is positive but is less than the average product of labor, thus “pulling down”
output per worker, which implies that average revenue generated per worker is also falling.
In this region, labor becomes increasingly less productive on average.

Finally, stage III of production is defined along the TPL function for labor input usage in
excess of 0F, where MPL < 0. As it is apparent that production will not take place in stage I
of production because an incremental increase in labor usage will result in an increase in
output per worker and, under the appropriate assumptions, an increase in profit per worker,
so it is also obvious that production will not take place in stage III. This is because an increase
in labor usage will result in a decline in total output accompanied by an increase in total
cost of production, implying a decline in profit.

Stage III is also the counterpart to stage I of production. Whereas in stage I labor is
overutilized and capital is underutilized, in stage III the reverse is true; that is, labor is
underutilized and capital is overutilized. In other words, because of the symmetry of
production, labor that is overutilized implies that capital is underutilized, and vice versa.
Since stages I and III of production for labor have been ruled out as illogical from a profit
maximization perspective, it also follows that stages III and I of production for capital have
been ruled out for the same reasons.

We may infer that stage II of production for labor, and also for capital, is the only region in
which production will take place. The precise level of labor and capital usage in stage II
in which production will occur cannot be ascertained at this time. For a profit-maximizing
firm, the efficient capital–labor combination will depend on the prevailing rental prices of
labor (PL) and capital (PK), and the selling price of a unit of the resulting output (P). More
precisely, as we will see, the optimal level of labor and capital usage subject to the firm’s
operating budget will depend on resource and output prices, and the marginal
productivity of productive resources. A discussion of the optimal input combinations will be
discussed in the next chapter.

ISOQUANTS
A curve that defines the different combinations of capital and labor (or any other input
combination in n-dimensional space) necessary to produce a given level of output.

For any given production function there are an infinite number of isoquants in an isoquant
map. In general, the function for an isoquant map may be written

where Q0 denotes a fixed level of output. Solving Equation for K yields

Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
The slope of an isoquant is given by the expression

It measures the rate at which capital and labor can be substituted for each other to yield
a constant rate of output. It is also refer to as the marginal rate of technical substitution of
capital for labor (MRTSKL). The marginal rate of technical substitution summarizes the
concept of substitutability discussed earlier. MRTSKL says that to maintain a fixed output
level, an increase (decrease) in the use of capital must be accompanied by a decrease
(increase) in the use of labor. It may also be demonstrated that

If we assume two factors of production, capital and labor, the marginal rate of technical
substitution (MRTSKL) is the amount of a factor of production that must be added
(subtracted) to compensate for a reduction (increase) in the amount of a factor of
production to maintain a given level of output. The marginal rate of technical substitution,
which is the slope of the isoquant, is the ratio of the marginal product of labor to the
marginal product of capital (MPL/MPK).

By definition as illustrated in the diagram below, when we move from point A to point B on
the isoquant, output remains unchanged. We can conceptually break this movement
down into two steps. In going from point A to point C, the reduction in output is equal to
the loss in capital times the contribution of that incremental change in capital to total
output (i.e., MPK ∆K < 0). In moving from point C to point B, the contribution to total output
is equal to the incremental increase in labor time marginal product of that incremental
increase. Thus,

(i.e.,MPL ∆L > 0).

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Since to remain on the isoquant there must be no change in total output, it must be the
case that

Rearranging yields

This equation becomes, for instantaneous rate of change

One can also derive this relationship by the use of implicit function theorem and taking
the total derivative by setting it to zero to yield:

is set equal to zero because output remains unchanged in moving from point A to point B
in the diagram.

Another characteristic of isoquants is that for most production processes they are convex
with respect to the origin. That is, as we move from point A to point B in figure, increasing
amounts of labor are required to substitute for decreased equal increments of capital.
Mathematically, convex isoquants are characterized by the conditions dK/dL < 0 and
d2K/dL2 > 0. That is, as MPL declines as more labor is added by the law of diminishing
marginal product, MPK increases as less capital is used. This relationship illustrates that inputs
are not perfectly substitutable and that the rate of substitution declines as one input is
substituted for another. Thus, with MPL declining and MPK increasing, the isoquant becomes
convex to the origin.

The degree of convexity of the isoquant depends on the degree of substitutability of the
productive inputs. If capital and labor are perfect substitutes, for example, then labor and
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
capital may be substituted for each other at a fixed rate. The result is a linear isoquant,
which is illustrated in the figure below. Mathematically, linear isoquants are characterized
by the conditions dK/dL < 0 and d2K/dL2 = 0.

Examples of production processes in which the factors of production are perfect substitutes
might include oil versus natural gas for some heating furnaces, energy versus time for some
drying processes, and fish meal versus soybeans for protein in feed mix.

Some production processes, on the other hand, are characterized by fixed input
combinations, that is, MRTSK/L = KL. This situation is illustrated in the figure below. Note that
the isoquants in this case are “L shaped.” These isoquants are discontinuous functions in
which efficient input combinations take place at the corners, where the smallest quantity
of resources is used to produce a given level of output. Mathematically, discontinuous
functions do not have first and second derivatives.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Examples of such fixed-input production processes include certain chemical processes that
require that basic elements be used in fixed proportions, engines and body parts for
automobiles, and two wheels and a frame for a bicycle.

As an example, consider the general form of the Cobb–Douglas production function

be written as:

where A is a positive constant and 0 < a < 1, 0 < b < 1.

a. Derive an equation for an isoquant with K in terms of L.
b. Demonstrate that this isoquant is convex (bowed in) with respect to the origin.

2. The Spacely Company has estimated the following production function for sprockets:

a.Suppose that Q = 100. What is the equation of the corresponding isoquant in terms of L?
b. Demonstrate that this isoquant is convex (bowed in) with respect to the origin.

LONG-RUN PRODUCTION FUNCTION

Returns to Scale
Returns to scale refer to the proportional increase in output given some equal proportional
increase in all productive inputs. As discussed earlier, constant returns to scale (CRTS) refers
to the condition where output increases in the same proportion as the equal proportional
increase in all inputs. Increasing returns to scale (IRTS) occur when the increase in output is
more than proportional to the equal proportional increase in all inputs. Decreasing returns
to scale (DRTS) occur when the proportional increase in output is less than proportional
increase in all inputs. To illustrate these relationships mathematically, consider the
production function

where A is a positive constant and 0 < a < 1, 0 < b < 1. Specify the conditions under which
this production function exhibits constant, increasing, and decreasing returns to scale.

Coefficient of output elasticity

This represents the sum of the output elasticities of capital and labor and is expressed as

Consider the following Cobb–Douglas production function

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
a. Demonstrate that the elasticity of production with respect to labor is 0.72.
b. Demonstrate that the elasticity of production with respect to capital is 0.38.
c. Demonstrate that this production function exhibits increasing returns to scale.
d. Determine the coefficient of output elasticity.

EXERCISES
1. A firm has the following short-run production function: Q =150L+18L2 -1.5L3
where Q=quantity of output per week L=number of workers employed.
a. When does the law of diminishing returns take effect?
b. Calculate the range of values for labor over which stages I, II and III occur.
c. Assume that each worker is paid £15 per hour for a 40-hour week, and that the output is
priced at £5. How many workers should the firm employ?
2. The average product of labor is given by the equation

a. What is the equation for the total product of labor (TPL)?

b. What is the equation for the marginal product of labor (MPL)?
c. At what level of labor usage is APL = MPL?

COST OF PRODUCTION
The purpose of this section is to bridge the gap between production as a purely
technological relationship and the cost of producing a level of output to achieve a well-
defined organizational objective.

The Relationship between Production and Cost

The cost function of a profit-maximizing firm shows the minimum cost of producing various
output levels given market-determined factor prices and the firm’s budget constraint.
Although largely the domain of accountants, the concept of cost to an economist carries
a somewhat different connotation. Economists generally are concerned with any and all
costs that are relevant to the production process. These costs are referred to as total
economic costs. Relevant costs are all costs that pertain to the decision by management
to produce a particular good or service.

Total economic costs include the explicit costs associated with the day-to-day operations
of a firm, but also implicit (indirect) costs. All costs, both explicit and implicit, are opportunity
costs. They are the value of the next best alternative use of a resource. Explicit costs are
sometimes referred to as “out-of-pocket” costs. Explicit costs are visible expenditures
associated with the procurement of the services of a factor of production. Wages paid to
workers are an example of an explicit cost. By contrast, implicit costs are, in a sense,
invisible: the manager will not receive an invoice for resources supplied or for services
rendered. As with any opportunity cost, implicit costs represent the value of the factor’s
next best alternative use and must therefore be taken into account.
Short-Run Cost

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
The theory of cost is closely related to the underlying production technology. We will begin
by assuming that the firm’s short-run total cost (TC) of production is given by the expression

Assuming only two factors of production, capital (K) and labor (L), and assuming that
capital is the fixed factor (K0), then the total cost equation may be written as

In other words, total cost is a function of output, which is a function of the production
technology and factors of production, and factors of production cost money.

This total cost eqution is a general statement that relates the total cost of production to the
usage of the factors of production, fixed capital and variable labor. It also makes clear that
total cost is intimately related to the characteristics of the underlying production
technology. As we will see, concepts such as total cost (TC), average total cost (ATC),
average variable cost (AVC), and marginal cost (MC) are defined by their production
counterparts, total physical product, average physical product, and marginal physical
product of both labor and capital.

To begin with, let us assume that the prices of labor and capital are determined in perfectly
competitive factor markets. The short-run total economic cost of production is given as

where PK is the rental price of capital, PL is the rental price of labor, K0 is a fixed amount of
capital, and L is variable labor input. The most common example of the rental price of labor
is the wage rate. An example of the rental price of capital might be what a construction
company must pay to lease heavy equipment, such as a bulldozer or a backhoe. If the
construction company already owns the heavy equipment, the rental price of capital may
be viewed as the forgone income that could have been earned by leasing its own
equipment to someone else. In either case, both PK and PL are assumed to be market
determined and are thus parametric to the output decisions of the firm’s management.
Thus, total cost function may be written

where TFC and TVC represent total fixed cost and total variable cost, respectively.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Total fixed cost is a short-run production concept. Fixed costs of production are associated
with acquiring and maintaining fixed factors of production. Fixed costs are incurred by the
firm regardless of the level of production. Fixed costs are incurred by the firm even if no
production takes place at all. Examples often include continuing expenses incurred under
a binding contract, such as rental payments on office space, certain insurance payments,
and some legal retainers.

Total variable costs of production are associated with acquiring and maintaining variable
factors of production. In stages I and II of production, total variable cost is an increasing
function of the level of output. Total cost is the sum of total fixed and total variable cost.

Key Relationships: Average Total Cost, Average Fixed Cost, Average Variable Cost, and Marginal
Cost

The definitions of average fixed cost, average variable cost, average total cost, and
marginal cost are, appropriately, as follows:

Average total cost is the total cost of production per unit. It is the total cost of production
divided by total output. Average total cost is a short-run production concept if total cost
includes fixed cost. It is a long-run production concept if all costs are variable costs.
Average fixed cost, which is a short-run production concept, is total fixed cost per unit of
output. It is total fixed cost divided by total output. Average variable cost is total variable
cost of production per unit of output. Average variable cost is total variable cost
divided by total output.

Marginal cost is the change in the total cost associated with a change in total output.
Contrary to conventional belief, this is not the same thing as the cost of producing the “last”
unit of output. Since it is total cost that is changing, the cost of producing the last unit of
output is the same as the per-unit cost of producing any other level of output. More
specifically, the marginal cost of production for a profit-maximizing firm is equal to average
total cost plus the per-unit change in total cost, multiplied by total output. Equation (6.8)
shows that marginal cost is the same as marginal variable cost, since total fixed cost is a
constant.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Related to marginal cost is the more general concept of incremental cost. While marginal
cost is the change in total cost given a change in output, incremental cost is the change
in the firm’s total costs that result from the implementation of decisions made by
management, such as the introduction of a new product or a change in the firm’s
advertising campaign. By contrast, sunk costs are invariant with respect to changes in
management decisions. Since sunk costs are not recoverable once incurred, they should
not be considered when one is determining, say, an optimal level of output or product mix.

The distinction between sunk and fixed cost is subtle. Suppose that when the firm operated
the loom to produce cotton fabrics, the rental price of the loom was $100,000 per year. This
rental price is invariant to the firm’s level of production. In other words, the firm would rent
the loom for $100,000 per year regardless of whether it produced 5,000 or 100,000 yards of
cloth during that period. A sunk cost is essentially the difference between the purchase
price of the loom and its salvage value.

Recalling that Q = f(K, L) and applying the chain rule we obtain

Recalling that TC = PKK0 + PLL, then marginal cost may be written as

where PL is the rental price of homogeneous labor input and MPL is the marginal product
of labor.

See the graphical illustration hereunder.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Exercise
A firm’s total cost function is

Suppose that the firm produces 10 units of output. Calculate total fixed cost (TFC), total
variable cost (TVC), average total cost (ATC), average fixed cost (AFC), average variable
cost (AVC), and marginal cost (MC).

Mathematical Relationship Between ATC And MC

Consider, again, the definition of average total cost

Minimizing this relationship by taking the first derivative with respect to output and setting
the results equal to zero yields

Since Q2>0, then, the equation becomes

That is, the first-order condition for a minimum ATC is

The second-order condition for minimum is that

Suppose that the total cost function of a firm is given as

a) Determine the output level that minimizes average total cost (ATC).
b) At this output level, what is TC? ATC? MC? Verify that at this output level MC = ATC,
and that ATC intersects MC from below.
c) Determine the output level that minimizes average variable cost (AVC).
a) At this output level, what is TC? AVC? MC?

Long-Run Cost
In the long run all factors of production are assumed to be variable. Since there are no
fixed inputs, there are no fixed costs. All costs are variable. Unlike the short-run production

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
function, however, there is little that can be said about production in the long run. There is
no long-run equivalent of the law of diminishing marginal product.

The relation between total output and all inputs, the long-run total product curve (LRTP) is
illustrated hereunder. Although the shapes of the long-run and short-run total product
curves are similar, the reasons are quite different.

The short-run total product curve derives its shape from the law of diminishing marginal
product. The long-run total product curve derives its shape from quite different
considerations. To begin with, firms might experience increasing returns to scale during the
early stages of production because of the opportunity for increased specialization of both
human and nonhuman factors, which would lead to gains in efficiency. Only large firms,
for example, can rationalize the use of in-house lawyers, accountants, economists, and so
on. Another reason is that equipment of larger capacity may be more efficient than
machinery of smaller capacity.

Eventually, as the firm gets larger, the efficiencies from increased size may be exhausted.
As a firm grows larger, so too do the demands on management. Increased administrative
layers may become necessary, resulting in a loss of efficiency as internal coordination of
production processes become more difficult. At some large level of output, factors of
production may become overworked and diminishing returns to management may set
in. Problems of interdepartmental and interdivisional coordination may become endemic.
The result would be decreasing returns to scale.

Since there are no fixed costs in the long run, the firm’s corresponding long-run total cost
curve (LRTC), which is similar in appearance to the short-run total cost curve, intersects TC
at the origin. This is illustrated in the below figure.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
ECONOMIES OF SCALE
Scale refers to size. What is the effect on the firm’s per-unit cost of production following an
increase in all factors of production? In other words, does the size of a firm’s operations
affect its per-unit cost of production? The answer to the second questions is that it may.
Regardless of what we have learned about the short-run production function and the law
of diminishing marginal product, it is difficult to make generalizations about the effect of
size on per-unit cost of production, although we may speculate about the most likely
possibilities.

Economies of scale are intimately related to the concept of increasing returns to scale. If
per-unit costs of production decline as the scale of a firm’s operations increase, the firm is
said to experience economies of scale. The reason is simple. If we assume constant factor
prices, while the firm’s total cost of production rises proportionately with an increase in total
factor usage, per-unit cost of production falls because output has increased more than
proportionately. In other words, an increase in the firm’s scale of operations results in a
decline in long-run average total cost (LRATC). Conversely, diseconomies of scale are
intimately related to the concept of decreasing returns to scale. Once again, the
explanation is straightforward. Assuming constant factor prices, the firm’s total cost of
production rises proportionately with an increase in total factor usage, but the per-unit
cost of production increases because output increases less than proportionately. In other
words, an increase in the firm’s scale of operations results in an increase in the firm’s long-
run average total cost.

Finally, in the case of constant returns to scale, per-unit cost of production remains constant
as production increases or decreases proportionately with an increase or decrease in
factor usage. In other words, an increase or decrease in the firm’s size will have no effect
on the firm’s long-run average total cost.

As an example, a firm’s long-run total cost (LRTC) equation is given by the expression

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
a. What is the firm’s long-run average cost equation?
b. What is the firm’s minimum efficient scale (MES) of production?

Reasons for Economies and Diseconomies of Scale

As firms grow larger, economies of scale may be realized as a result of specialization in
production, sales, marketing, research and development, and other areas. Specialization
may increase the firm’s productivity in greater proportion than the increase in operating
cost associated with greater size. Some types of machinery, for example, are more efficient
for large production runs. Examples include large electrical-power generators and large
blast furnaces that generate greater output than smaller ones. Large companies may be
able to extract more favorable financing terms from creditors than small companies.

Large size, however, does not guarantee that improvement in efficiency and lower per-
unit costs. Large size is often accompanied by a disproportionately great increase in
specialized management. Coordination and communication between and among
departments becomes more complicated, difficult, and time-consuming. As a result, time
that would be better spent in the actual process of production declines and overhead
expenses increase disproportionately. The result is that diminishing returns to scale set in,
and per-unit costs rise. In other words, growth usually is accompanied by diseconomies
of scale.

Multiproduct Cost Functions

We have thus far discussed manufacturing processes involving the production of a single
output. Yet, many firms use the same production facilities to produce multiple products.
Automobile companies, such as Ford Motor Company, produce both cars and trucks at
the same production facilities. Chemical and pharmaceutical companies, such as Dow
Chemical and Merck, use the same basic production facilities to produce multiple different
products. Computer companies, such as IBM, produce monitors, printers, scanners,
modems and, of course, computers. Consumer product companies, such as General
Electric, produce a wide range of household durables, such refrigerators, ovens, and light-
bulbs. In each of these examples it is reasonable to suppose that total cost of production is
a function of more than a single output. In the case of a firm producing two products, the
multiproduct cost function may be written as

where Q1 and Q2 represent the number of units produced of goods 1 and 2, respectively.

Two examples of multiproduct cost relationships are economies of scope and cost
complementarities.

Economies of Scope
Economies of scope exist when the total cost of using the same production facilities to
produce two or more goods is less than that of producing these goods at separate
production facilities. In the case of a firm that produces two goods, economies of scope
exist when

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
It may be less expensive, for example, for Ford Motor Company to produce cars and trucks
by more intensively utilizing a single assembly plant than to produce these products at two
separate, less intensively utilized, manufacturing facilities. It is less expensive for the
restaurants in the Olive Garden chain to use the same ovens, tables, refrigerators, and so
on to produce both pasta and parmigiana meals than to duplicate the factors of
production.

Cost Complementarities
Cost complementarities exist when the marginal cost of producing Q 1 is reduced by
increasing the production of Q2. From the below equation, the marginal cost of producing
Q1 may be written as

The multiproduct cost function exhibits cost complementarities if the cross-second partial
derivative of the multiproduct cost function is negative, that is,

This implies that an increase in the production of Q2 reduces the marginal cost of producing
Q1.

As an example, suppose that a firm’s total cost function is

where Q1 and Q2 represent the number of units of goods 1 and 2, respectively.

a. If the firm produces 2 units of good 1 and 4 units of good 2, do cost complementarities
exist?
b. Do economies of scope exist for this firm?
c. How will the firm’s total cost of production be affected if it decides to discontinue the
production of good 2?

Finding the Optimal Input Combination

Given the prices of productive resources and the firm’s operating budget, and assuming
only two factors of production, labor and capital, the various combinations of inputs that
a firm can employ in the production process may be summarized as

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
In general, this isocost line may be written as

Which indicates that the rate at which a unit of labor may be substituted for a unit of capital
is given by the ratio of the input prices. In summary, the isocost line denotes the various
combinations of inputs that a firm may hire at a given cost.

The optimum input combination can obtained by equating the slopes of Isocost and
Isoquant.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Recall that the slope of the isoquant is given by the marginal rate of technical substitution,
or

Likewise, the slope of the isocost line is given by the expression

At point C on the diagram we note that the absolute value of the slope of the isoquant is
less than of the isocost line. That is

Rearranging, this expression becomes

Says that at point C, the marginal product of labor per dollar spent on labor is less than the
marginal product of capital per dollar spent on capital. It should be clear, therefore, that
by reallocating a dollar from the fixed operating budget from labor into capital, and we
should generate a net increase in output. Similarly, at point A in the diagram we have

Rearranging, this expression becomes

says that reallocating a dollar from capital to labor should generate an increase in output.

The only point at which no gain in output will result by reallocating the firm’s fixed operating
budget dollars is point B, where

In other words, only where the isocost line is just tangent to the isoquant will the firm be
hiring the proper combination of labor and capital to generate the most output possible
from its fixed operating budget. Of course, rearranging this expression yields

The same optimization conditions apply to the slightly different problem of minimizing the
firm’s total cost of production subject to a fixed level of production.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
In general, to minimize total production costs subject to a fixed level of output, or to
maximize total output subject to a fixed operating budget, the marginal product per last
dollar spent on each input must be the same for all inputs. That is, efficient production
requires that the isoquant be tangent to the isocost line.

Suppose for instance that a firm produces at an output level where the marginal product
of labor (MPL) is 50 units and the wage rate (PL) is $25. Suppose, further, that the marginal
product of capital (MPK) is 100 units and the rental price of capital (PK) is $40.
a. Is this firm producing efficiently?
b. If the firm is not producing efficiently, how might it do so?

Mr. Darkie Tire, Inc., a small producer of motorcycle tires, has the following production
function:

During the last production period, the firm operated efficiently and used input rates of 100
and 25 for capital and labor, respectively.
a. What is the marginal product of capital and the marginal product of labor based on the
input rates specified?
b. If the rental price of capital was $20 per unit, what was the wage rate?
c. Suppose that the rental price of capital is expected to increase to $25 while the wage
rate and the labor input will remain unchanged under the terms of a labor contract. If the
firm maintains efficient production, what input rate of capital will be used?

Expansion Path
The expansion path is the locus of points for which the isocost and isoquant curves are
tangent. It represents the cost-minimizing (profit maximizing) combinations of capital and
labor for different operating budgets.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
 It says that a profit-maximizing firm will allocate its budget in such a way that the last dollar
spent on labor will yield the same additional output as the last dollar spent on capital.

1. Suppose you are given the production function

where input prices are PL = 20 and PK = 30. Determine the expansion path including its slope.

2. Suppose that you are given the following production function:

Q = 250(L+ 4K)
Suppose further that the price of labor (w) is $25 per hour and the rental price of capital (r)
is $100 per hour.
a. What is the optimal capital/labor ratio?
b. Suppose that the price of capital were lowered to $25 per hour? What is the new optimal
ratio of capital to labor?
c. Determine the expansion path of this firm.

Assignment due on the 18th of February 2023@11:00GMT. Clarity and orderliness of work will
be highly appropriate. Solve all these questions with understanding.

1.
Suppose that a firm has the following production function:

Suppose, further that the firms operating budget is TC = $500 and the rental price of labor
and capital are $5 and $7.5, respectively.
a. If the firm’s objective is to maximize output, determine the optimal level of labor and
capital usage.
b. At the optimal input levels, what is the total output of the firm?
2.
Suppose that a firm has the following production function:

Determine the firm’s expansion path if the rental price of labor is $25 and the rental price
of capital is $50.
3.
The total revenue and total cost equations of a firm are

a. Graph the total revenue and total cost equations for values Q = 0 to Q = 200.
b. What is the total profit function?
c. Use optimization analysis to find the output level at which total profit is maximized?

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
d. Graph the total profit equation for values Q = 0 to Q = 200. Use your graph to verify your
answer to part c.
4.
Magnavox installs MP3 players in automobiles. Magnavox production function is:

where Q represents the number of MP3 players installed, L the number of labor hours, and
K the number of hours of installation equipment, which is fixed at 250 hours. The rental price
of labor and the rental price of capital are $10 and $50 per hour, respectively. Magnavox
has received an offer from Cheap Rides to install 1,500 MP3 players in its fleet of rental cars
for $15,000. Should Magnavox accept this offer?
Determine the return to scale of this production function of Magnavox
5.
Suppose that a firm’s production function exhibits increasing returns to scale. It must also
be true that the firm’s expansion path increases at an increasing rate. Do you agree with
this statement? Explain.
6.
A firm has the following short-run production function: Q =150L+18L2 -1.5L3
where Q=quantity of output per week L=number of workers employed.
a. When does the law of diminishing returns take effect?
b. Calculate the range of values for labor over which stages I, II and III occur.
c. Assume that each worker is paid £15 per hour for a 40-hour week, and that the output is
priced at £5. How many workers should the firm employ?
7.
The average product of labor is given by the equation

a. What is the equation for the total product of labor (TPL)?

b. What is the equation for the marginal product of labor (MPL)?
c. At what level of labor usage is APL = MPL?
8.
The total cost equation for a firm producing two products is

a. Do cost complementarities exist for this firm?

b. Under what circumstances do economies of scope exist for this firm?
c. Suppose that the firm is currently producing 5 units of Q1 and 10 units of Q2.What is the
firm’s total cost of production?
9.
The long-run average total cost equation for a perfectly competitive firm is

a. Determine the minimum efficient scale of production.

b. Calculate total cost at the minimum efficient scale of production.
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
c. If the total level of output in the industry is 50,000 units, how many firms can profitably
operate in this industry?
10.
The total cost equation of a firm is given by the equation

where TC is total cost and Q is the level of output.

a. What is the firm’s total fixed cost?
b. What is the equation for the firm’s total variable cost (TVC)?
c. What is the equation for the firm’s average total cost (ATC)?
d. What is the equation for the firm’s marginal cost (MC)?
e. Determine the output level that minimizes average total cost.
f. Calculate average total cost and marginal cost at the level of output that will minimize
average total cost.

11.
Suppose that the wage rate (PL) is $25 and the rental price of capital (PK) is $40. In addition,
suppose that the firm’s operating budget is $2,500.
a. What is the isocost equation for the firm?
b. If capital is graphed on the vertical axis, what happens to the isocost line if the wage
rate increases?
c. If capital is graphed on the vertical axis, what happens to the isocost line if the rental
price of capital falls?
d. If the wage rate and the rental price of capital remain unchanged, what happens to
the isocost line if the firm’s operating budget falls?
e. If the firm’s operating budget remains unchanged, what happens to the isocost line if
the wage rate and the rental price of capital fall by the same percentage?
12.
Suppose that a firm’s production function is Q = 75K0.4L0.7.What is the value of the output
elasticity of labor? What is the value of the output elasticity of capital? Does this firm’s
production function exhibit constant, increasing, or decreasing returns to scale?
13.
Suppose that output is a function of labor and capital. Assume that labor is the variable
input and capital is the fixed input. Explain the law of diminishing marginal product. How is
the law of diminishing marginal product reflected in the total product of labor curve?
14.
Define each of the following:
a. Stage I of production
b. Stage II of production
c. Stage III of production
15.
Suppose that a firm’s production function

a. Determine the marginal rate of technical substitution.

Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
 b. Demonstrate that this isoquant is convex.

MARKET STRUCTURE

Market structure refers to the environment within which buyers and sellers interact. That is,
it is defined in terms of the proportion of total market demand that is satisfied by the output
of each firm in the industry.

One important element in the firm’s ability to influence the economic environment within
which it operates is the nature and degree of competition. A firm operating in an industry
with many competitors may have little control over the selling price of its product because
its ability to influence overall industry output is limited. In this case, the manager will attempt
to maximize the firm’s profit by minimizing the cost of production by employing the most
efficient mix of productive resources. On the other hand, if the firm has the ability to
significantly influence overall industry output, or if the firm faces a downward-sloping
demand curve for its product, the manager will attempt to maximize profit by employing
an efficient input mix and by selecting an optimal selling price.

Characteristics of Market Structure

There are, perhaps, as many ways to classify a firm’s competitive environment, or market
structure, as there are industries. Consequently, not single economic theory is capable of
providing a simple system of rules for optimal output pricing. It is possible, however, to
categorize markets in terms of certain basic characteristics that can be useful as
benchmarks for a more detailed analysis of optimal pricing behavior. These characteristics
of market structure include: the number and size distribution of sellers, the number and size
distribution of buyers, product differentiation, and the conditions of entry into and exit from
the industry.

Number and Size Distribution of Sellers: The ability of a firm to set its output price will largely
depend on the number of firms in the same industry producing and selling that particular
product. If there are a large number of equivalently sized firms, the ability of any single firm
to independently set the selling price of its product will be severely limited. If the firm sets
the price of its product higher than the rest of the industry, total sales volume probably will
drop to zero. If, on the other hand, the manager of the firm sets the price too low, then
while the firm will be able to sell all that it produces, it will not maximize profits. If, on the
other hand, the firm is the only producer in the industry (monopoly) or one of a few large
producers (oligopoly) satisfying the demand of the entire market, the manager’s flexibility
in pricing could be quite considerable.

Number and Size Distribution of Buyers: Markets may also be categorized by the number and
size distribution of buyers. When there are many small buyers of a particular good or service,
each buyer will likely pay the same price. On the other hand, a buyer of a significant
proportion of an industry’s output will likely be in a position to extract price concessions from

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
producers. Such situations refer to monopsony (a single buyer) and oligopsony (a few large
buyers).

Product Differentiation: Product differentiation is the degree that the output of one firm differs
from that of other firms in the industry. When products are undifferentiated, consumers will
decide which product to buy based primarily on price. In these markets, producers that
price their product above the market price will be unable to sell their output. If there is no
difference in price, consumers will not care which seller to buy from. A given grade of
wheat is an example of an undifferentiated good. At the other extreme, firms that produce
goods having unique characteristics may be in a position to exert considerable control
over the price of their product. In the automotive industry, for example, product
differentiation is the rule.

Conditions of Entry and Exit: The ease with which firms are able to enter and exit a particular
industry is also crucial in determining the nature of a market. When it is difficult for firms to
enter into an industry, existing firms will have much greater influence in their output and
pricing decisions than they would if they had to worry about increased competition from
new comers, attracted to the industry by high profits. In other words, managers can make
pricing decisions without worrying about losing market share to new entrants. Thus if a firm
owns a patent for the production of a good, this effectively prohibits other firms from
entering the market. Such patent protection is a common feature of the pharmaceutical
industry.

Exit conditions from the industry also affect managerial decisions. Suppose that a firm had
been earning below-normal economic profit on the production and sale of a particular
product. If the resources used in the production of that product are easily transferred to the
production of some other good or service, some of those resources will be shifted to
another industry. If, however, resources are highly specialized, they may have little value in
another industry.

Firms differ in the proportion of total market demand that is satisfied by the production of
each. This is illustrated in the figure hereunder. At one extreme is perfect competition, in
which the typical firm produces only a very small percentage of total industry output. At
the other extreme is monopoly, where the firm is responsible for producing the entire output
of the industry. The percentage of total industry output produced is critical in the analysis
of profit maximization because it defines the shape of the demand curve facing the output
of each individual firm. The market structures that will be examined in this lesson can be
viewed as lying along a spectrum, with the position of each firm defined by the percentage
of the mark satisfied by the typical firm in each industry—from perfect competition at one
extreme to monopoly at the other.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
PERFECT COMPETITION
The expression “perfect competition” is somewhat misleading because overt competition
among firms in perfectly competitive industries is nonexistent. The reason for this is that
managers of perfectly competitive firms do not take into consideration the actions of other
firms in the industry when setting pricing policy. The reason for this is that changes in the
output of each firm are too small relative to the total output of the industry to significantly
affect the selling price. Thus, the selling price is parametric to the decision-making process.

The characteristics of a perfectly competitive market may be identified by using the criteria
previously enumerated. Perfectly competitive industries are characterized by a large
number of more or less equally sized firms. Because the contribution of each firm to the
total output of the industry is small, the output decisions of any individual firm are unlikely
to result in a noticeable shift in the supply curve. Thus, the output decisions of any individual
firm will not significantly affect the market price. Thus, firms in perfectly competitive markets
may be described as price takers. The inability to influence the market price through output
changes means that the firm lacks market power. Market power refers to the ability of a
firm to influence the market price of its product by altering its level of output. A firm that
produces a significant proportion of total industry output is said to have market power.

A second requirement of a perfectly competitive market is that there also be a large

number of buyers. Since no buyer purchases a significant proportion of the total output of
the industry, the actions of any single buyer will not result in a noticeable shift in the demand
schedule and, therefore, will not significantly affect the equilibrium price of the product.

A third important characteristic of perfectly competitive markets is that the output of one
firm cannot be distinguished from that of another firm in the same industry (product
homogeneity). The purchasing decisions of buyers, therefore, are based entirely on the
selling price. In such a situation, individual firms are unable to raise their prices above the
market-determined price for fear of being unable to attract buyers. Conversely, price
cutting is counterproductive because firms can sell all their output at the higher, market-
determined, price. Remember, the market clearing price of a product implies that there is
neither a surplus nor a shortage of the commodity.

A final characteristic of perfectly competitive markets is that firms may easily enter or exit
the industry. This characteristic allows firms to easily reallocate productive resources to be
able to exploit the existence of economic profits. Similarly, if profits in a given industry are
below normal, firms may easily shift productive resources out of the production of that
particular good into the production of some other good for which profits are higher.

Therefore, perfect competition refers to the market structure in which there are many utility-
maximizing buyers and profit-maximizing sellers of a homogeneous good or service in which
there is perfect mobility of factors of production and buyers, sellers have perfect
information about market conditions, and entry into and exit from the industry is very easy.
It is called a price taker because of its inability to influence the market price of its product

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
by altering its level of output. This condition implies that a perfectly competitive firm should
be able to sell as much of its good or service at the prevailing market price.

THE EQUILIBRIUM PRICE

As we have already discussed, the market-determined price of a good or service is
accepted by the firm in a perfectly competitive industry as datum. Moreover, the
equilibrium price and quantity of that good or service are determined through the
interaction of supply and demand. The relation between the market-determined price and
the output decision of a firm is illustrated in Figure 8.2.

The market demand for a good or service is the horizontal summation of the demands of
individual consumers, while the market supply curve is the sum of individual firms’ marginal
cost (above-average variable cost) curves. As discussed earlier, if the prevailing price is
above the equilibrium price (P*), a condition of excess supply forces producers to lower the
selling price to rid themselves of excess inventories. As the price falls, the quantity of the
product demanded rises, while the quantity supplied from current production falls (QF).
Alternatively, if the selling price is below P* a situation of excess demand arises. This causes
consumers to bid up the price of the product, thereby reducing the quantity available to
meet consumer demands, while compelling producers to increase production. This
adjustment dynamic will continue until both excess demand and excess supply have been
eliminated at P*.

Suppose that a perfectly competitive industry comprises 1,000 identical firms. Suppose,
further, that the market demand (QD) and supply (QS) functions are

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
SHORT-RUN PROFIT MAXIMIZATION PRICE AND OUTPUT
If we assume that the perfectly competitive firm is a profit maximizer, the pricing conditions
under which this objective is achieved are straight forward. First, define the firm’s profit
function as:

To determine the optimal output level that is consistent with the profit-maximizing objective
of this firm, the first-order condition dictates that we differentiate this expression with respect
to Q and equate the resulting expression to zero. This procedure yields the following results

That is, the profit-maximizing condition for this firm is to equate marginal revenue with
marginal cost, MR = MC.

where the selling price is determined in the market and parametric to the firm’s output
decisions. Thus, the profit-maximizing condition for the perfectly competitive firm become

To maximize its short-run (and long-run) profits, the perfectly competitive firm must equate
the market-determined selling price of its product with the marginal cost of producing that
product.

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
1. Consider the firm with the following total monthly cost function, which includes a normal
profit.

The firm operates in a perfectly competitive industry and sells its product at the market-
determined price of $10. To maximize total profits, what should be the firm’s monthly output
level, and how much economic profit will the firm earn each month?

2. A perfectly competitive industry consists of 300 firms with identical cost structures. The
respective market demand (QD) and market supply (QS) equations for the good produced
by this industry are

LONG-RUN PROFIT MAXIMIZATION PRICE AND OUTPUT

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
ECONOMIC LOSSES AND SHUTDOWN

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
Prepared by: Mr. Samuel F. Mulbah
Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr
1. A perfectly-competitive firm faces the following total variable cost function

where Q is quantity. Below what price should the firm shut down its operations?

2. Darkie and Sam Limited (DS) is a small distributor of food supplements in the highly
competitive health care products industry. The market-determined price of a 100-tablet
vial of DS’s most successful product, papaya extract, is $10. DS’s total cost (TC) function
is given as

a. What is the firm’s profit-maximizing level of output? What is the firm’s profit at the profit-
maximizing output level? Is DS in short-run or longrun competitive equilibrium? Explain.
b. At P = $10, what is DS’s break-even output level?
c. What is DS’s long-run break-even price and output level?
d. What is DS’s shutdown price and output level? Does this price–output combination
constitute a short-run or a long-run competitive equilibrium? Explain.

MONOPOLY

Prepared by: Mr. Samuel F. Mulbah

Lecturer, Department of Economics, University of Liberia, mulbahfs@ul.edu.lr