# Basic concept of revenue

Why is it said that the Average revenue of a given output is said to be equal to the price(Perfect competition)? Is it true when the price of each output is not constant and consistently changes?

EDIT Also is this table incorrect since isn’t TR equal to the sum of prices?

In perfect competition, the firm is a price taker, that is, the price $$P$$ stays the same independently of the quantity $$Q$$ it decides to produce, making a total revenue of $$TR = P \cdot Q$$. So $$AR = \frac{TR}{Q} = \frac{P\cdot Q}{Q} = P$$, having an average revenue equal to the price, but this price is independent of its actions, having a constant average revenue.

Since $$P$$ is constant with respect to the quantity it produces, its marginal revenue would be $$MR = \frac{dTR}{dQ} = P$$, and this $$P$$ being a constant, so the firm would have a constant marginal revenue as well.

That table is actually correct because the firm must sell all goods for the same price, so to sell an additional unit, the firm must lower the price not only for that extra unit but also for the units it would've already been able to sell as well.

If the firm was a monopoly, its actions would affect the price. Let's say the inverse demand function was the typical linear $$P = a - b Q$$. Then the firm's total revenue would still be $$TR = P \cdot Q$$, and its average revenue would be $$AR = \frac{TR}{Q} = \frac{P \cdot Q}{Q} = P$$ as well but now that $$P$$ isn't a constant, the average revenue which is still equal to the price is now a function of the quantity it decides to produce, $$AR = P = a - b Q$$, so now the firm has a decreasing average revenue.

In this example, the total revenue would equal $$TR = P \cdot Q = (a-bQ)Q = aQ - b Q^2$$. Since we got a quadratic with a negative leading term (an inverted parabola/ upside down U-shape), this total revenue starts to decrease from some point, acording to the marginal revenue $$MR = \frac{dTR}{dQ} = a - 2 b Q$$, which is decreasing, equals $$0$$ at $$Q = \frac{a}{2b}$$, and becomes negative for greater values of $$Q$$.

• Great answer but what is MR in the sense of a monopolistic market? Commented Feb 15, 2023 at 8:39
• @TheCuriousOne I calculated it in the last paragraph, it equals $a - 2bQ$, which is decreasing and eventually becomes $0$, then negative. Commented Feb 15, 2023 at 8:43
• I mean when we find the difference of the consecutive (Total Revenues), shouldn’t we divide the Total revenue by the output to get average and then subtract to get MR? Commented Feb 15, 2023 at 8:44
• @TheCuriousOne Your table calulates the marginal revenue (in a discrete way) by taking the differences of succesive total revenues (not the average ones). In my post, I did it by taking the derivative of the total revenue function (in a continuous way). The two methods exist because for an IRL firm that produces a lot of units, one extra unit would be considered "marginal" enough, so the two different ways of calulating it should return similar answers (the discrete one being an approximation of the continuous). Commented Feb 15, 2023 at 8:51

In perfect competition the assumption is that there is only one price $$P$$. There is a relationship between quantity ($$Q$$) and price. In this case: $$Q = 21 - 2P$$ Given a price $$P$$, the industry will sell $$Q$$ units of product, and collect a total amount of revenue $$P \cdot Q$$ for it.

• In monopolistic competition market. Why would the average revenue be equal to the price since price is always changing? Commented Feb 15, 2023 at 7:59
• Question states "perfect competition". Commented Feb 15, 2023 at 10:35