Optimizing Profit
Overview
Optimizing profit, within the context of a business model, means choosing the price to charge
(and hence the amount of product to produce, given the demand curve) for
a given product in order to maximize a firms profits. This assumes that the firm is actively minimizing
the costs for the given amount of product produced.
{% Profits = Revenue - Costs %}
Profitability is a function of the amount of product sold, q, and the price per unit, p.
{% \pi(p,q) %}
(note: {% \pi %} is the variable often used to denote profits)
As a general rule, the product price and amount of product sold are not independent. Changes in one will change the other.
As such, the manager wishing to optimize profit really only has to adjust one lever, typically taken to
be the price. That is, the manager sets the price, and then the quantity sold
is determined by the normal
supply and demand
dynamics.
Pricing Effects
To understand how price affects profitability, one can separated the effects of
price on both terms in the profitability equation. The working assumption when determining the effects of price changes
is that the firm will produce the exact amount of goods that the market demands at any price point. That is, if the firm raises
prices, it will then decrease production to match the new demand.
Marginal Cost equals Marginal Revenue
Under the classical assumptions,
the price at which an optimal profit is achieved is the point where the cost of producing one extra unit of the product equals the
price that consumers will bear for that amount of product.
{% Marginal \, Cost = Marginal \, Revenue %}
That is, as a firm produces more goods, the average cost of producing those goods goes up. Meanwhile, the price that the firm
can charge for those goods goes down. Initially, the costs are lower than the price, and it makes sense to increase production
until these values cross.
See
Derivation for a more comprehensive treatment.
Profitability Ratios
