Using the relationship between elasticity and total revenue along a demand curve.

The relationship between demand elasticity and revenue is very straight-forward, but often it is ignored. If a person does not respond very much to an increase in price, then the amount they spend on an item will rise as the price rises. If, on the other hand, they respond a great deal to in increase in price, they will spend less on that item as the price rises. This relationship is very important in making decisions about pricing for firms, and taxing for governments.

Exploration: How might an increase change in the cigarette tax affect not only the level of teen smoking, but also the level of revenue generated to tobacco companies.

The graphs above are linked together. On the left is a demand curve and on the right the associated expenditure (revenue). The link between these is elasticity. When elasticity is above 1 (in absolute value), increasing price will result in decreased revenue. When elasticity is below 1, increasing price will increase revenue. It is the case that for every straight-line demand function, elasticity is above 1 to the left of the center, and below one to the right of the center. Thus revenue maximizes at elasticity equal to 1; in the exact center of any linear demand function. Initially in this exercise the demand curve has a slope of -1. This is adjustable by dragging the D to the left or right. Price is also adjustable, by dragging the green triangle up and down. Practice moving them around and observe how the expenditure relationship changes.

1. Beginning with the existing graph pair, the price of cigarettes is $3 and the quantity sold is 3000 per week for $9000 in total expenditure. If we pass a tax, which increases the price of cigarettes by 50 cents (use the green triangle to drag the Price up to $3.50 from $3.00 and watch the "Price = X" in the box to determine when you are exactly on $3.50), what will the resultant change in revenue to the seller be? (Remember that the revenue to the seller is the amount the seller receives minus any amount they must pass on to the taxing agency.)
   
   
2. Now, suppose the demand for cigarettes is more elastic than in the original example. Click the Reset button to return to the original situation and then increase the elasticity of demand at the current price of $3.00. To do this you need to flatten the demand curve by dragging the D out to the right. So that we are all "on the same page," for this example drag the Quantity-Intercept out from 6 to 7. (To tell when you are precisely at an intercept of 7, watch the Elasticity = X section of the box. When the elasticity is 1.33 at a price of $3.00, the intercept is at 7.) How will a tax that results in a 50-cent increase in the price of cigarettes affect the firm's revenue now?
   
   
3. Under which of these demand structures will the tax be most effective at curbing teen smoking?
   
   
4. Which one is the seller likely to support?
   
   
5. What if the demand for cigarettes among teenagers is relatively inelastic – how will this affect the revenue gained by shop-owners from a tax that increases the price of cigarettes by 50 cents a pack? Beginning from the original starting point, but with a more inelastic demand, what will be the impact on revenue to shop-owners from the 50-cent increase in the price of cigarettes due to a tax?
   
   

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Exercise picked up from the 2e Economics textbook.