We must always remember not to confuse the elasticity of a curve with its slope. This distinction is easily seen when we exam-in the straight line demand curves that are often found in illustrative examples.We often depict demand curves as linear, or straight lines because they are easy to draw. So It’s only natural to uk. What Is the price elasticity of a straight-line demand curve?
That question turns out to have a surprising answer.Along a straight-line demand curve, the price elasticity varies from zero to infinity! Table 4-2 gives a detailed set of elasticity calculation using the same technique as that in Table 4-1.This table shows that linear demand curves start out with high price elasticity, where price is high and quantity is low, and end up with low elasticity, where price is low and quantity high.
This illustrates an important point. when you see a demand curve in a diagram, it is in general not true that a steep slop for the demand curve means inelastic demand and a flat slop signifies elastic demand. The slope is not the same as the elasticity because the demand curve’s slope depends upon the changes in P and Q. Whereas the elasticity depends upon the percentage change in P and Q. The only exceptions are the polar cases of completely elastic and inelastic demands.
one way to see this point is to examine figure 4-2(b).This demand curve is clearly not a straight line with constant slope. Yet it has a constant demand elasticity of ED = I because the percentage change in price is equal everywhere to the percentage in quantity. so remember: Elasticity is definitely different from slope.
Figure 4-4 illustrates the pitfall of confusing slope and elasticity. This figure plots a linear or straight-line demand curve. Because it is linear, it has the same slope everywhere. But the top of the line; near A, has a very small percentage price change and a very large percentage quantity change, and the elasticity is extremely large. Therefore, price elasticity is relatively large when we are high on the linear DD curve. Conversely, when we are in the bottom part of the linear demand curve, the price elasticity is less than unity. Near the horizontal axis, price elasticity is close to zero.
More generally, above the midpoint M of any straight line, demand is elastic, with ED> 1. At the midpoint, demand is unit-elastic, with ED= 1. Below the midpoint, demand is inelastic, with ED< I.
P denotes the change in price. i.e., P= P2 – PD>while Q- Q2 – Qr- To calculate numerical elasticity. the percentage change of price equals price change. AP. divided by average price [(P:z + P.)/2]; the percentage change in output is calculated as A Q divided by average price. [(Q2 + Q1)/2]. Treating all figures as Poitier numbers, the resulting ratio gives numerical price cellulite of demand, ED’ Note that for a Airtight line. elasticity is high at the top. low It the boom. and exactly 1 in the middle.
All points on the straight-line demand curve have the same slope. But above the midpoint, demand is elastic; below it.demand is inelastic; at the midpoint. demand is unit-elastic. Only in the case of vertical or horizontal curves. show nin Fig. 4-~. can you infer the price elasticity from slope alone.
In summary, while the extreme cases of completely elastic and completely inelastic demand can be determined from the slopes of the demand curves alone. for the in-between cases. which correspond to virtually all goods. elasticity cannot be inferred by slope alone. (See Figure 4-5 for. one way to calculate elasticity from a diagram.)
A Shortcut for Ca’cu’at/nl elasticities. A simple rule will allow you to calculate the price elasticity of a demand curve: The elasticity of a straight line at a point is given by the ratio of the length of the line segment below the point to the length of tile line segment above the point. To see this. first examine Figure 4-4. Note that at midpoint M the length of the segment above (AM) and that of the segment below (MZ) are exactly equal; hence the elasticity is MZ/AM = 1. At point B. this formula yields Eo = BZ/AB = 0/. = 3; at R. EiJ = 1/3.
Knowing how to calculate En for a straight line enables you to calculate it for any point along a curved demand curve. as shown in Figure 4-5. (1) Draw the straight line tangent to the curve at your point (e.g .• at B in Figure 4-5). and then (2) calculate Ev for the straight line at that point (e.g .• ED at B = 3). The result will be the correct elasticity for
the curve -at point B.
To calculate the demand elasticity. take the ratio of the length of the straight-line segment below the point to the length of the line segment above the point, Hence. at point B the elasticity can be calculated to be 3. For nonlinear demand curves. simply dra the tangent line and calculate its elasticity.
ELASTICITY AND REVENUE
Many businesses want to know whether raising price will raise or lower revenues. This question is of strategic importance for businesses like airlines. restaurants. and magazines. which must decide whether it is worthwhile. to raise prices and whether tile higher prices make up for lower demand. Let’s look at the relationship between price elasticity and total revenue.
TotaI revenue is by definition equal to price times quantity (or P X Q). If consumers buy 5 units at $3 each. total revenue is $15. If you know the price elasticity of demand. you know what will happen to total revenue when price changes:
I. When demand is price-inelastic. a price decrease reduces total revenue.
2. When demand is price-clastic. a price decrease increases total revenue.
3. In the borderline case of unit-elastic demand. a price decrease leads to no change in total revenue.
For example, business travelers have an inelastic demand for air travel. 50 an increase in business fares tends to raise revenue. By contrast. leisure travelers have a much more elastic demand for air travel, because they have a far greater choice about where and when they are traveling. As a result. railing leisure fares tends to decrease revenue.
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