ColombiaLink.com – PROFIT MAXIMIZATION – MICROECONOMICS

See
also: List of Economic Topics

PROFIT
MAXIMIZATION
– microeconomics

In
economics, profit maximization is the process by which a firm determines the price
and output level that returns the greatest profit. There are several approaches
to this problem. The total revenue — total cost method relies on the fact that
profit equals revenue minus cost, and the marginal revenue — marginal cost method
is based on the fact that total profit in a perfect market reaches its maximum
point where marginal revenue equals marginal cost.

Basic
Definitions

Any
costs incurred by a firm may be classed into two groups: fixed cost and variable
cost. Fixed costs are incurred by the business at any level of output, including
none. These may include equipment maintenance, rent, wages, and general upkeep.
Variable costs change with the level of output, increasing as more product is
generated. Materials consumed during production often have the largest impact
on this category. Fixed cost and variable cost, combined, equal total cost.

Revenue
is the total amount of money that flows into the firm. This can be from any source,
including product sales, government subsidies, venture capital and personal funds.

Average
cost and revenue are defined as the total cost or revenue divided by the amount
of units output. For instance, if a firm produced 400 units at a cost of 20000
USD, the average cost would be 50 USD.

Marginal
cost and revenue, depending on whether the calculus approach is taken or not,
are defined as either the change in cost or revenue as each additional unit is
produced, or the derivative of cost or revenue with respect to quantity output.
For instance, taking the first definition, if it costs a firm 400 USD to produce
5 units and 480 USD to produce 6, the marginal cost of the sixth unit is approximately
80 dollars, although this is more accurately stated as the marginal cost of the
5.5th unit due to linear interpolation. Calculus is capable of providing more
accurate answers if regression equations can be provided.

Total
Cost-Total Revenue Method

To
obtain the profit maximizing output quantity, we start by recognizing that profit
is equal to total revenue minus total cost. Given a table of costs and revenues
at each quantity, we can either compute equations or plot the data directly on
a graph. Finding the profit-maximizing output is as simple as finding the output
at which profit reaches its maximum. That is represented by output Q in the diagram.

Profit
Maximization –
The
Totals Approach

There
are two graphical ways of determining that Q is optimal. Firstly, we see that
the profit curve is at its maximum at this point (A). Secondly, we see that at
the point (B) that the tangent on the total cost curve (TC) is parallel to the
total revenue curve (TR), the surplus of revenue net of costs (B,C) is the greatest.
Because total revenue minus total costs is equal to profit, the line segment C,B
is equal in length to the line segment A,Q.

Computing
the price at which to sell the product requires knowledge of the firm’s demand
curve. The price at which quantity demanded equals profit-maximizing output is
the optimum price to sell the product.

Marginal
Cost-Marginal Revenue Method

If
total revenue and total cost figures are difficult to procure, this method may
also be used. For each unit sold, marginal profit equals marginal revenue minus
marginal cost. Then, if marginal revenue is greater than marginal cost, marginal
profit is positive, and if marginal revenue is less than marginal cost, marginal
profit is negative. When marginal revenue equals marginal cost, marginal profit
is zero. Since total profit increases when marginal profit is positive and total
profit decreases when marginal profit is negative, it must reach a maximum where
marginal profit is zero – or where marginal cost equals marginal revenue. This
intersection of marginal revenue (MR) with marginal costs (MC) is shown in the
next diagram as point A. If the industry is competitive (as is assumed in the
diagram), the firm faces a demand curve (D) that is identical to its Marginal
revenue curve (MR), and this is a horizontal line at a price determined by industry
supply and demand. Average total costs are reprsented by curve ATC. Total economic
profits are represented by area P,A,B,C. The optimum quantity (Q) is the same
as the optimum quantity (Q) in the first diagram.


Profit
Maximization – The Marginal Approach

If
the firm is operating in a non-competitive market, minor changes would have to
be made to the diagrams.

Modes
of Operation

It
is assumed that all firms are following rational decision-making, and will produce
at the profit-maximizing output. Given this assumption, there are four categories
in which a firm’s profit may be considered.

A
firm is said to be making an economic profit when its average total cost is greater
than the price of the product at the profit-maximizing output. The economic profit
is equal to the quantity output multiplied by the difference between the average
total cost and the price.

A
firm is said to be making a normal profit when its economic profit equals zero.
This occurs where average total cost equals price at the profit-maximizing output.

If
the price is between average total cost and average variable cost at the profit-maximizing
output, then the firm is said to be in a loss-minimizing condition. The firm should
still continue to produce, however, since its loss would be larger if it was to
stop producing. By continuing production, the firm can offset its variable cost
and at least part of its fixed cost, but by stopping completely it would lose
equivalent of its entire fixed cost.

If
the price is below average variable cost at the profit-maximizing output, the
firm is said to be in shutdown. Losses are minimized by not producing at all,
since any production would not generate returns significant enough to offset any
fixed cost and part of the variable cost. By not producing, the firm loses only
its fixed cost.

See
also

Supply
and demand
Market forms, Microeconomics
pricing
production, costs, and
pricing