# Graphically illustrate elasticity and total revenue relationship

### Total revenue and elasticity (video) | Khan Academy

What you'll learn to do: explain the relationship between a firm's price elasticity of demand and total revenue. Price elasticity of demand describes how changes. The relationship between elasticity of demand and a firm's total revenue is an important one. Total Revenue (TR) and Elasticity (With Diagram) the demand for a commodity is said to be price elastic if total revenue increases (falls) as price increases (falls) . Three points are illustrated by Figure Relation among TR, MR & Ep.

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.

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. 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.

### Elasticity, Total Revenue and Marginal Revenue

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. And now, I want to think about something from the perspective of our burger stand. And think about, at any given point on this demand curve, how much revenue would we get per hour.

And when I talk about revenue, for simplicity, let's just think that's really just how much total sales will I get in a given hour. So let me just write over here total revenue. Well, the total revenue is going to be how much I get per burger times the number of burgers I get.

So the amount that I get per burger is price. So it's going to be equal to price. And then the total number of burgers in that hour is going to be the quantity. Now, let's think about what the total revenue will look like at different points along this curve right over here. And actually, let me just make a table right over here.

So I'll make one column price, one column quantity. And then let's make one column total revenue. So let's look at a couple scenarios here. Well, we could actually look at some of these points that we already have defined.

At point A over here, price is 9. So I'll do it in point A's color. And you can see it visually right over here. This height right over here is 9. And this width right over here is 2. And your total revenue is going to be the area of this rectangle.

Because the height is the price. And the width is the quantity. So that total revenue is the area right over there.

Now, let's go to point-- let me do a couple of them just to really make it clear for us. Let's try to point B.

### The Relationship Between Price Elasticity & Total Revenue | kultnet.info

So at point B when our price is 8 and our quantity is 4, 4 per hour. And once again, you can see that visually. The height here is 8. And the width here-- so the height of this rectangle is 8.

And the width is 4. The total revenue is going to be the area. It's going to be the height times the width just like that.

## Total revenue and elasticity

Now, let's go to a point that I haven't actually graphed here. Actually, let me just-- actually, I'll go through all the points just for fun.

So now at point C, we have 5. The quantity is 9. And you have another 4. So that is So once again, it's going to be the area of this rectangle. Area of that rectangle right over there. So you might already be noticing something interesting. As we lower the price, at least in this part of our demand curve, as we lower the price, we are actually increasing not just the quantity were increasing the total revenue. Let's see if this keeps happening.

So if we go to point D, I'll do it in that same color. And we are selling 11 units. Everyone has to drink water, so if the water company raises prices, people continue to consume and pay for it. Luxuries are optional; they aren't necessary to live. Large-screen HDTVs are nice to have, but if the prices go up, consumers can put off buying them. Share of the consumer's income: Products that consume a high proportion of a family's income are sensitive to price increases.

A car is a good example. Increases in car prices can cause a family to delay purchasing a new car. They keep their old car longer and make the necessary repairs. However, if a grocery store increases the price of toothpicks, consumers still buy them because the price isn't a big piece of their income. Short-term versus long-term timing: Gasoline is an excellent example of a product that prices inelastic in the short term but elastic in the long term.

When gas prices go up, the consumer still has to buy gas to get to work. However, if gas prices stay high for the long term, consumers make changes. They may buy more fuel-efficient cars, set up a carpool with other workers, or start taking a train or bus to work.