WHY IS TOTAL REVENUE MAXIMIZED WHEN DEMAND IS UNIT ELASTIC?

A firm maximizes revenue when demand is unit elastic because an increase or decrease in demand does not affect revenue so marginal revenue is zero.

To explain, let's first some important terms.

Total revenue is price times quantity. Marginal revenue is the additional revenue obtained from selling an additional unit of goods. 

A firm will maximize revenue when marginal revenue is equal to zero.

That is, a firm maximizes revenue when:

$$MR=0$$

Unit elastic demand means that an increase (or decrease) in price will result in a proportional decrease(or increase) in quantity demanded such that there is no effect on total revenue.

When demand is unit elastic, a change in price does not affect total revenue, hence marginal revenue is zero.

Given that this is a necessary condition for maximizing revenue, it can be concluded that when demand is unit elastic, a firm maximizes revenue.

In other words, a firm maximizes revenue when the elasticity of demand is equal to one.

However, it must be noted that maximizing revenue is not the same as maximizing profit.

Simply said, Profit maximization is not the same as revenue maximization.

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