## Profit Maximiztion

Since the general goal of companies is to maximize profit, it's important to understand the components of profit. On one side, firms have revenue, which is the amount of money that it brings in from sales. On the other side, firms have the costs of production. Let's examine different measures of production cost.

## The Costs of Production

In economic terms, the true cost of something is what one has to give up in order to get it. This includes explicit monetary costs of course, but it also includes implicit non-monetary costs such as the cost of one's time, effort, and foregone alternatives. Therefore, reported economic costs are all-inclusive opportunity costs, which are the sums of explicit and implicit costs.

In practice, it's not always obvious in example problems that the costs given in the problem are total opportunity costs, but it's important to keep in mind that this should be the case in virtually all economic calculations.

## Total Cost

Total cost, not surprisingly, is just the all-inclusive cost of producing a given quantity of output. Mathematically speaking, the total cost is a function of quantity.

One assumption that economists make when calculating total cost is that production is being carried out in the most cost-effective way possible, even though it may be possible to produce a given quantity of output with various combinations of inputs (factors of production).

## Fixed and Variable Costs

*Fixed costs* are upfront costs that don't change depending on the quantity of output produced. For example, once a particular plant size is decided upon, the lease on the factory is a fixed cost since the rent doesn't change depending on how much output the firm produces. In fact, fixed costs are incurred as soon as a firm decides to get into an industry and are present even if the firm's production quantity is zero. Therefore, the total fixed cost is represented by a constant number.

*Variable costs*, on the other hand, are costs that do change depending on how much output the firm produces. Variable costs include items such as labor and materials since more of these inputs are needed in order to increase output quantity. Therefore, total variable cost is written as a function of output quantity.

Sometimes costs have both a fixed and a variable component to them. For example, despite the fact that more workers are needed in general as output increases, it's not necessarily the case that the firm will explicitly hire extra labor for each additional unit of production. Such costs are sometimes referred to as "lumpy" costs.

That said, economists consider fixed and variable costs to be mutually exclusive, which means that total cost can be written as the sum of total fixed cost and total variable cost.

## Average Costs

Sometimes it's helpful to think about per-unit costs rather than total costs. To convert a total cost into an average or per-unit cost, we can simply divide the relevant total cost by the quantity of output being produced. Therefore,

- Average Total Cost, sometimes referred to as Average Cost, is Total Cost divided by quantity.
- Average Fixed Cost is Total Fixed Cost divided by quantity.
- Average Variable Cost is Total Variable Cost divided by quantity.

As with total cost, the average cost is equal to the sum of the average fixed cost and average variable cost.

## Marginal Costs

*Marginal cost* is the cost associated with producing one more unit of output. Mathematically speaking, marginal cost is equal to the change in total cost divided by the change in quantity.

Marginal cost can either be thought of as the cost of producing the last unit of output or the cost of producing the next unit of output. Because of this, it's sometimes helpful to think of marginal cost as the cost associated with going from one quantity of output to another, as shown by q1 and q2 in the equation above. To get a true reading on marginal cost, q2 should be just one unit larger than q1.

For example, if the total cost of producing 3 units of output is $15 and the total cost of producing 4 units of output is $17, the marginal cost of the 4th unit (or the marginal cost associated with going from 3 to 4 units) is just ($17-$15)/(4-3) = $2.

## Marginal Fixed and Variable Costs

Marginal fixed cost and marginal variable cost can be defined in a way similar to that of overall marginal cost. Notice that marginal fixed cost is always going to equal zero since the change in fixed cost as quantity changes are always going to be zero.

Marginal cost is equal to the sum of the marginal fixed cost and marginal variable cost. However, because of the principle stated above, it turns out that marginal cost only consists of the marginal variable cost component.

## Marginal Cost Is the Derivative of Total Cost

Technically, as we consider smaller and smaller changes in quantity (as opposed to discrete changes of while number units), marginal cost converges to the derivative of total cost with respect to quantity. Some courses expect students to be familiar with and able to use this definition (and the calculus that comes with it), but a lot of courses stick to the simpler definition given earlier.