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Constructing A Model Of The Firm
We are now aware that firms are interested (at all times) in maximizing their
revenues. From the Law of Supply we learned that one way this can be accomplished is
by continually raising the price of the goods we sell. This is certainly an easy approach
to satisfy our goal but not however realistic because consumers are at the same time price
sensitive, and seek to maximize their individual self interest.
Since consumers are hesitant to continually pay more for the goods they desire,
firms must then seek alternative ways to maximize their revenues. One way is through
growth. The larger the firm the greater the probability that larger amounts of output can
be generated through a more efficient production process. Thus if more is being
produced, and costs of production fall, then revenues must rise.
A firm we must realize is an organization designed to produce goods. The owner
decides how much to produce as well as how to mix the inputs to gain profit or suffer
losses. The exact mixture of inputs to gain profit or suffer losses. The exact mixture of
inputs depends upon the technicalities specified by his production function.
An input is any good or service that contributes to the production of output.
Inputs are specified as either fixed or variable. A fixed input is necessary for production,
but its quantity is invariant with respect to the quantity of output produced. The quantity
of a variable input depends upon the quantity of output produced.
Analysis of the firm is similar to the analysis of the consumer. The consumer
purchases goods which produced satisfaction; the entrepreneur purchases inputs which
produces commodities. The consumer possesses a utility function; the firm, a production
function. The consumers budget constraint is a linear function of the amounts of goods
he purchases; the competitive firm’s cost equation is a linear function of the inputs it
purchases. The rational consumer desires to maximize the utility he obtains from the
consumption of goods; the rational entrepreneur desires to maximize profit.
Consider a simple production process where a firm uses two variable inputs (x1 &
x2), and one or more fixed inputs in order to produce a single output (Q). The firm’s
production function would be Q = f(X1,X2). Now since a producer is interested in
maximizing output it would be important to examine the technicalities of production.
When we examined consumer behavior with the hopes of maximizing utility, it was
necessary to construct indifference curves. An isoquant is the firm’s counterpart to the
indifference curve. An isoquant is the locus of all combinations of X1 and X2 which
yield a specified output level. The existence of one isoquant suggests the existence of an
infinite number, giving rise to a isoquant map.
X2
Isoquant Map
q3
q1
q2
X1
Where q3>q2>q1
Each isoquant being portrayed in the above graph represents a specific level of
output. The isoquant demonstrates that input levels can vary, that is the mixture of inputs
may vary but the output will remain constant. The only way greater levels of output can
be generated is with greater levels of inputs. Thus output level q3 is greater than level
q2, with q1 being the lowest level of output.
Another way of thinking about this is by a simple example. Suppose our firm
produces one pound cans of mixed nuts. Let X1 = peanuts and X2 = cashews. Peanuts
and cashews then represent the inputs in our production process. Final output will be
determined by the total amount of inputs available. If our firm has 100 pounds of peanuts
and 100 pounds of cashews then isoquant q1 on the above graph represents 200 one
pound cans of mixed nuts we can produce. Isoquant q1 also shows that while the mixture
of peanuts and cashews that goes into each can may vary the total amount that can be
produced from the available supply of inputs is only 200 one pound cans.
If our firm wishes to increase production then a greater supply of peanuts and
cashews is required. With more inputs higher levels of output can be achieved allowing
the firm to move from isoquant q1 to q2 and so on. To acquire additional inputs more
financial capital must be available. With each level of operating capital a firm attempts
to maximize its production. To show this a isocost line can be added to our isoquant map
to symbolize the limits of our financial capital. An isocost line is the locus of input
combinations that may be purchased for a specified total cost. The construction of an
isocost line in this case is very similar to constructing a budget constraint in the case of
the rational consumer model.
If we put all our capital into the purchase of input X1 we would be at point “a” on
the graph below. On the other-hand if our capital is spent exclusively on input X2 then
we would be at point “b” on the graph. Connecting points a & b gives rise to an isocost
line.
X2
b
Isocost Line
a
X1
Now adding the isocost line to an isoquant map indicates the maximum amount
that can be produced with the available financial capital. This maximum amount can be
found by locating the point of tangency between the isocost line and an isoquant that lies
the furthest to the right.
X2
q3
q1
q2
X1
The above graph demonstrates that with the capital available this firm can
produce q1 levels of output. To produce more greater levels of financial capital is
necessary. This can be accomplished any number of ways, but most commonly firms
would seek either more partners or incorporate. However, no matter how the additional
financial capital is raised it would be shown by a shifting to the right of the isocost line
on the graph.
X2
q3
q1
q2
X1
The above model shows that to realize higher levels of output more financial
capital is necessary to purchase additional inputs.
Firms are always experimenting with the mixture of their inputs seeking ways to
minimize costs. Sometimes, however, the selected mixture is unacceptable to the
consumer. Perhaps this can be best demonstrated using our example of mixed nuts.
When consumers buy mixed nuts they have a certain anticipation of the cans contents.
Some consumers prefer cans with more peanuts than cashews, while others prefer more
cashews than peanuts. If a producer combines these two inputs in a manner that is
unacceptable to the consumer then future sales of his product will most likely fall.
Through the process of trial and error, along with market research, producers will attempt
to discover the maximum and minimum mixture of inputs that is acceptable to the
consumer. This can be demonstrated in our model by constructing ridge lines. Ridge
lines indicate the parameters of the production process.
X2
Ridge
Lines
q3
q1
q2
X1
Producers will attempt to keep the combination of inputs within the maximum and
minimum range described by the above ridge lines.
Now if we connect the equilibriums formed by the tangency of the isocost lines
and isoquants we can complete our model of the theory of the firm. Connecting the three
equilibriums gives rise to a line called the expansion path. An expansion path
demonstrates the natural tendency for a firm to grow through expansion of its operating
capital.
X2
Expansion path
q3
q1
q2
X1
The expansion path demonstrates how firms grow by raising more financial
capital which allows them to purchase more inputs thus allowing increased levels of
production.
Firms can then legally exist in three basic forms: proprietorship, partnership, and
corporation. Each form does have some advantages and disadvantages associated with it,
however, although firms can differ in their structure they do share on common
concern—costs or actually the minimization of costs.