# Relationship between total revenue and demand curve

### Elasticity, Total Revenue and Marginal Revenue

If we were to calculate elasticity at every point on a demand curve, we could divide . the relationship between the price elasticity of demand and revenue is TRUE? Suppose that, if the price of a good falls from $10 to $8, total expenditure on. Total Revenue (TR) and Elasticity (With Diagram) We have noted that the slope of the demand curve is not the same as its Relation among TR, MR & Ep. Total Revenue Along a Demand Curve. With elastic demand – a rise in price lowers total revenue. TR increases as price falls. With inelastic demand – a rise in.

And you could graph these just to get a sense of how total revenue actually changes with respect to price or quantity. Lets plot the total revenue with respect to quantity.

So let's try it out. So if you-- let me plot it out. So this is going to be total revenue. And this axis right over here is going to be quantity. And we're going to, once again, go from-- let's see. And this is 20 right over here. And then total revenue. Let's see, it gets as high-- it gets pretty close to This is 10 20, 30, 40, and So that's 50, 40, 30, 20, and So when our quantity is 2, and our price is 9.

Well, we don't have price on this axis right over here. But when our quantity is 2, our total revenues So it's going to be something like there. Then, when our quantity is 4, our total revenue is Then, when our quantity is 9, our total revenue is almost So right over there.

And then, when it's 11, it's also at that same point right over there. And then, when we are quantity is 16, our total revenues And then finally, when our quantity is 18, our total revenue is And what you see is that it's plotting out a curve that looks like this.

And if you remember some of your algebra 2, this is a concave downwards parabola right over here. And you can see there was actually some point at which you could maximize your total revenue.

And if you really tried all the points here, you would see that maximum point is if you tried this point right over here, right at price 5 and quantity Now, the whole reason why I'm talk think about this. I could have talked about this independently of any discussion of elasticity just to see how total revenue relates to price and quantity at different points on the demand curve.

But there is an interesting relationship. In that very first video, and we actually used this exact demand curve for it. When we explored elasticity, we saw that up here at this part of the curve-- let me do this in a different color. At this point of the curve in orange for any change-- when you do a change in your price since the prices are pretty high, that is a much lower percent change in price than the impact that you get on quantity.

Because over here, although they look like they're close. Or I should say the absolute. For every 1 that down we move in price, we're moving 2 up quantity. But that 1 down in price is a very small percentage of price because our prices are high here. And it's a very large percentage of quantity right over here. So you get huge changes in percent quantity for very small changes in price in this part of the curve.

So this part of the curve is elastic. Or you could say that its price elasticity for demand is greater than 1. You get larger changes in percent quantity for a given change in percent price. Now, these parts of the curve down here, we saw is the opposite's happening. You move 1 down, 1 unit down in price, you move 2 units to the right in quantity. But over here, price is a much lower. So this is a much larger percentage change in price.

And this is a much smaller percentage change in quantity. So you get large percentage changes in price for small percentage change in quantity. That means that here, you are relatively inelastic. And then right over here, right at this point, right in this region, right over here, we saw that we had unit-- we were unit elastic right over there.

So there's an interesting relationship going on. While we were, so while we were elastic, this part right over here, when we lowered price in this region. While we were elastic, when we lowered price, we got increases in revenue. So let me write this down.

- Total Revenue (TR) and Elasticity (With Diagram)
- Total revenue and elasticity

And this is generally, too, there's a couple of boundary cases on the math that make it a little bit, you can't make it absolutely true. But while we are elastic, at the elastic points of our demand curve, a decrease in price. Total revenue was going up. You do a price cut on this part of the demand curve, you get more revenue. Then, when you are at unit elasticity, what was happening? At unit elasticity, you were right at this point right over here. Right at this point over here.

And roughly, when you do a price cut-- and I'm going to say this is roughly true-- your total revenue stays constant. But just right at that point, right when you're going through that unit elasticity point. And then finally, when you are inelastic when a large percent changes in price result and not so large percent change is in quantity demanded, then a price change going down resulted in lower total revenue. Resulted in total revenue going down.

**Deriving Marginal Revenue From the Demand Curve**

And this should, hopefully, make a little bit of intuitive sense. Because over here, this point, if given percent change in price, you were getting a larger percent change in quantity. So the percent in price went down. Your percent in quantity grew even more. Then we can write Equation 3 as 4. It turns out that the elasticity will not be constant as we move along the curve.

As shown in Figure 3 below, the elasticity of supply is calculated in exactly the same way as the elasticity of demandthe only difference is that the elasticity of supply is positive while the elasticity of demand is negative, reflecting the fact that the supply curve is upward sloping and the demand curve negatively sloped. The total revenue to the seller of a commodity, or total expenditure by the purchaser, is obtained by multiplying the price by the quantity.

It appears in Figure 4 as the area of a rectangle whose bottom left corner is the origin and top right corner is a point on the demand curve.

The top left and bottom right corners equal price and quantity respectively. It is also clear in the above Figure that the total revenue varies as we move along the demand curve. Marginal revenue is defined as the change in total revenue that occurs when we change the quantity by one unit.

The marginal revenue is thus the slope of the total revenue curve in Figure 5. At quantity zero, the marginal revenue is equal to the priceselling the first unit adds one times the price of that unit to the total revenue. As quantity increases the marginal revenue falls because as we add successive units not only is the price of the last unit lower than the price of the previous unit but all previous units have to be sold at this lower price.

## Total revenue test

Marginal revenue for each quantity sold is given in Figure 5 as the distance between the thick line and the horizontal axis at that quantity.

This distance is equal to the slope of the total revenue curve at that quantity. The marginal revenue curve thus crosses the horizontal axis at the quantity at which the total revenue is maximum. Past the mid-point of a straight line demand curve, the marginal revenue becomes negative.

### Total revenue test - Wikipedia

Why is marginal revenue important? This question is best answered by way of example. Consider the market for fresh eggs in a locality. Suppose that the government permits producers to establish an Egg Marketing Board with the power to set the price of eggs to the consumer and allocate output quantities to all individual producers.

Purchases of eggs from outside the local area are prohibited.

This situation is shown in Figure 6. A horizontal supply curve is a reasonable assumption here because most of the inputs used to produce eggs can be purchased by egg producers at fixed market pricesthese inputs are used by other industries and producers of eggs use a small fraction of the available supply. This implies that chicks can be hatched and raised to hens at constant cost.

Egg producers like this arrangement because it enables them to sell their eggs to consumers at a price above the cost of production, yielding a profit indicated by the shaded area in Figure 6. The problem faced by the Marketing Board, acting on their behalf, is to determine the quantity level that will maximize that profit.

At a lower output quota there is a gain from a higher price, but the quantity producers sell will be less.