Revenue in Perfect Competition: Videos & Practice Problems

In perfect competition, total revenue (TR) is calculated as price (P) times quantity (Q). Average revenue (AR) equals total revenue divided by quantity, simplifying to AR = P, which also represents the demand curve. Marginal revenue (MR) is the change in total revenue from selling one more unit, also equating to P in this market structure. Thus, in perfect competition, AR = MR = P, highlighting the unique characteristic of a perfectly elastic demand curve where firms can sell any quantity at the market price.

Revenue in Perfect Competition

Alright, now let's discuss revenue in perfect competition and define average revenue and marginal revenue. We've talked about revenue before, and not much is changing here. Revenue is the money coming into the firm. We're going to say that our total revenue is going to be equal to the price times the quantity, right? Whatever price we sell at times the quantity we sell, that's all the money that we're going to bring in. So when we talk about revenues, these are the benefits to the firm. When we think about benefits, remember we're talking about marginal benefits and marginal costs? These would be the benefits to the firm. A marginal benefit to the firm would be how much more revenue we can get when we sell 1 more unit.

Let's dive into average revenue and marginal revenue, important concepts throughout all of these chapters, and see how it relates in perfect competition. We always label average revenue as AR for average revenue and marginal revenue as MR. Let's start with average revenue. Average revenue means to divide by Q, the quantity. We're going to take our total revenue and divide it by quantity. Total revenue, which is price times quantity, divided by quantity results in the quantities canceling out, leaving us with P. Average revenue equals P. This formula shows that average revenue always equals the price, which is also our demand curve. This is true for all market structures, not just perfect competition, so every market structure's average revenue equals price and is also the demand curve.

Now let's talk about marginal revenue. Marginal revenue equals the change in total revenue over the change in quantity. Marginal refers to what happens when we add one more unit. If we sell one more unit, how much more revenue are we going to get? This formula, the change in total revenue over the change in quantity, usually considers a single additional unit. In perfect competition, the price is fixed for the firm; the market sets the price, and the firm has to sell all its products at that price. The firm can sell as much as it wants and will always sell at this price. If the firm decides to increase its quantity by 1, it will sell that unit at the market price, which doesn't change because the firm increased its production. They sold one more unit for P, and the change in total revenue was P. Therefore, the marginal revenue is going to be equal to the price as well in perfect competition. If you want to sell 1 more unit, you'll bring in 1 more price worth of revenue. This conclusion, that the marginal revenue equals price and the average revenue equals the marginal revenue equals price, is true only for perfect competition.

This is a special case in perfect competition and leads to special outcomes in this market. In the next video, we'll discuss how this marginal revenue stays constant at the price with a numerical example to illustrate what this means in action. Let's do that now.

Calculating Profit from a Table

Alright, so let's dive into this numerical example. Now generally when we deal with perfect competition or any of these structures, we don't usually do these types of boxes like we've seen in the past. We're going to be dealing with graphs or something like that, but this is a good way to just kind of introduce you to this concept of marginal revenue and how it stays constant. Okay, so let's go ahead and dive in here. What we've got is a market for wheat and the market price was $4 for a bushel. I don't know if that's a good price or not, but we're just keeping our example pretty simple here. Alright, so we got $4 a bushel and that's going to stay constant no matter how much we sell, right? There's not going to be an increasing quantity, decreasing price, none of that. So the price is going to stay constant, so let's think about this. In our little table here we've got, you know, quantities were given to us and the cost to produce those quantities. So let's go ahead and fill in this revenue. Our total revenue, right, that's our price times our quantity, right. Just like we're used to, well when we sell 0, we're not going to make any revenue, right? Our revenue is 0. 0×4=0. Now let's move on down. What about when we sell 1 unit? 1 unit for $4, we're going to bring in $4 right? How about 2 units? 2×4=8. Right? 3×4=12. 4×4=16. 5×4=20, and finally 6×4=24. Alright. Pretty simple. Just doing our our multiplications table right there. Then we've got our costs given to us and how about profit? Remember that profit is going to be that total revenue minus the total cost, right? Whatever's left over, that's profit. We brought in so much money, it cost us so much to get that money, what's left over? So let's see and when we sell 0 units, we've still got costs of $2.50. These could be some sort of fixed cost, right? No matter if we sell units or not, we're going to have this cost. So we've got 0−2.50 that gives us negative profit, right? We're losing $2.50 because we didn't bring anything in. How about the next one? Well, we brought in $4 but it cost us $4.50 so we're still losing money but we're losing less money. Negative 50¢. How about the next one? Double check on $8.70. Well, now we've got positive profit, right? We've finally brought in a dollar and then with 3 units, we bring in 12 but it costs us 10, so that's 2. 12−10=2. 16−13.50=2.50, then 20−18=2 and finally 24−24=0. Right? So now let's dive into marginal revenue and marginal cost. So marginal revenue, right, that's how our revenue changes as we increase output. So let's think about this in the first case right, so one zero we can't do it, but what about when we add 1 unit? We add the first unit, well we had 0 profit before and now we've brought, excuse me, 0 revenue before and now we've brought our revenue up to $4, right? So our revenue increased from 0 to 4, our marginal revenue is $4. How about the next one? Our revenue was already at 4, we added 1 more unit, and it brought our revenue up to 8. So we started at 4, then we got to 8, our marginal revenue is $4 again, right? Notice this constant marginal revenue, and this is because we're selling 1 more unit at that price. The next one, right? We were at 8 already, we sell 1 more unit for the price, and it brings us up to 12, right? Our marginal revenue is $4 again. Same thing all the way down. 12 to 16 marginal revenue of $4. 16 to 20, again $4 and the last one, $4 as well, right? Our marginal revenue is constant. It's constant $4 and that is equal to the price, right? Marginal revenue equal to average revenue equal to price, right? That's going to stay constant in perfect competition. How about our marginal cost? We've talked about this before, but let's go ahead and do it just to see our change in profit. Well, marginal cost right, that's how much does our cost change as we increase production. So here we started at $2.50, and it went up to $4.50, right? It increased by $2 right? Our marginal cost increased by $2 there and then the next one we were at $4.50 and it went up to $7, right? 7−4.50. Well, that's $2.50, right? $2.50 is going to be the marginal cost there and notice these are not constant, right? This is kind of what we expect from when we discuss marginal cost that marginal cost would generally increase as we get diminishing returns, Alright. So how about the next one? We were at 7 and the cost went up to $10. Well, 10−7, that's a marginal cost.

Here’s what students ask on this topic:

What is the relationship between average revenue and price in perfect competition?

In perfect competition, the relationship between average revenue (AR) and price (P) is straightforward: AR equals P. This is because average revenue is calculated as total revenue (TR) divided by quantity (Q). Since TR is the product of price and quantity (TR = P × Q), dividing TR by Q simplifies to AR = P. This relationship holds true across all market structures, but in perfect competition, it is particularly significant because the demand curve is perfectly elastic, meaning firms can sell any quantity at the market price. Therefore, AR = P represents both the average revenue and the demand curve.

How is marginal revenue calculated in a perfectly competitive market?

In a perfectly competitive market, marginal revenue (MR) is calculated as the change in total revenue (ΔTR) divided by the change in quantity (ΔQ). Mathematically, this is expressed as:

$\frac{\mathrm{\Delta TR}}{\mathrm{\Delta Q}}$

Since the price (P) is constant in perfect competition, selling one more unit increases total revenue by the price of that unit. Therefore, MR equals the price (P). This unique characteristic means that in perfect competition, MR = P, allowing firms to sell additional units at the same market price without affecting the overall price level.

Why does average revenue equal marginal revenue in perfect competition?

In perfect competition, average revenue (AR) equals marginal revenue (MR) because both are equal to the price (P). AR is calculated as total revenue (TR) divided by quantity (Q), which simplifies to AR = P. MR is the change in total revenue from selling one more unit, which also equals P because the price remains constant. Therefore, in perfect competition, AR = MR = P. This equality arises due to the perfectly elastic demand curve, allowing firms to sell any quantity at the market price without influencing the price.

What is the significance of a perfectly elastic demand curve in perfect competition?

A perfectly elastic demand curve in perfect competition signifies that firms can sell any quantity of their product at the market price without affecting the price. This occurs because the market price is determined by the overall supply and demand in the market, not by individual firms. As a result, the demand curve is horizontal, indicating that the price remains constant regardless of the quantity sold. This characteristic leads to the unique situation where average revenue (AR) and marginal revenue (MR) both equal the price (P), simplifying revenue calculations and decision-making for firms in this market structure.

How does the concept of marginal revenue differ in perfect competition compared to other market structures?

In perfect competition, marginal revenue (MR) equals the price (P) because firms can sell additional units at the market price without affecting the price. This is due to the perfectly elastic demand curve. In contrast, in other market structures like monopoly or monopolistic competition, MR does not equal P. Instead, MR is less than P because firms must lower the price to sell additional units, leading to a downward-sloping demand curve. This difference highlights the unique nature of perfect competition, where MR = AR = P, simplifying revenue analysis and firm behavior.