# Why does marginal revenue equal marginal cost?

Marginal revenue is the additional revenue earned by selling an additional unit of output. For example, if you owned a coffee shop which sold coffees for \$5 each, the marginal revenue would be \$5.

Marginal cost is the additional cost a firm must incur when it sells an additional unit of output. For example, in that same coffee shop if the ingredients for the coffee costed \$3 dollars, than the marginal cost is \$3. We would not factor in the cost of rent and wages (unless employees were paid per coffee sold) as these "factors of production" have already been purchased and do not vary with each sale of coffee in this example.

There are three possible situations which can occur:

 1. Marginal revenue is larger than marginal cost

In the above example, marginal revenue was \$5 and marginal cost was \$3 so marginal revenue is larger than marginal costs. In this case, we have made \$2 variable profit (which is profit which doesn't factor in fixed costs). Therefore, if marginal revenue is larger than marginal cost we should sell more output, or in the above example, more coffees.

In summary: If Marginal Revenue is greater than marginal costs, sell more output.

 2. Marginal revenue is less than marginal cost

In economics, it is assumed that as we sell more output, our costs of producing goods increase. This phenomena is known as Diminishing returns to scale. It's similar to the idea of "too many cooks in the kitchen" whereby adding more cooks you eventually just end up getting in each others way reducing efficiency.

Suppose that in this case the marginal cost of another coffee is \$7. In this case, marginal cost is greater than the marginal revenue and thus our variable profit is -\$2. Since we would be losing money by selling more coffees, we should stop selling coffees.

In summary: If Marginal Revenue is lesser than marginal costs, sell less output.

 3. Marginal revenue is equal to marginal cost

By deduction, since in both other cases we should sell either more of less output, it must be that our equilibrium solution is when marginal revenue equals marginal costs. The logic is you continue to sell more output, which causes your costs to rise, until you reach the point that selling another unit of output does not yield you any further variable profit. At this point, you stop. Thus marginal revenue equals marginal cost is the equilibrium condition.