[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

PRICE OF CDs ($)
11
10
Linear demand
curve
98 100
QUANTITY OF CDs
Figure 4.12
LINEAR DEMAND CURVE
The linear demand curve is a straight line; it is represented
algebraically by the equation Q = a − bp. The
slope of the demand curve is a constant. However,
the elasticity varies with output. At low outputs (high
prices), it is very high. At high outputs (low prices), it is
very low.
A
B
Appendix: Elasticity and
Slope
The elasticity of a curve is not the same as its slope. The best way to see
the distinction is to look at a linear demand curve. A linear demand
curve is a straight line, as depicted in Figure 4.12. With a linear demand
curve, a $1 change in price always leads to the same change in quantity
demanded, whether we start from a price of $2 or a price of $10. Table
4.3 contains information on price and quantity demanded for such a
curve, and we can use this information to calculate the elasticity of
demand at different prices. When the price increases from $1 to $2, a
100 percent increase, demand falls by 5 units, from 45 to 40. This represents
an 11 percent fall in demand. The elasticity of demand is 11 percent
divided by 100 percent, or 0.11. A $1 increase in price from $5 to
$6 represents a 20 percent price increase. Because the demand curve
is linear, the $1 price increase again reduces demand by 5 units, from
20 to 15 units. This is a 20 percent change in the quantity demanded.
The elasticity of demand is 20 percent divided by 20 percent, or 1. As
the price goes higher, a $1 change represents a smaller percentage
change in the price; moreover, quantity demanded drops, so the 5-unit
Table 4.3
ELASTICITY AND A LINEAR DEMAND CURVE
Quantity Change in Change in
Price demanded price (%) quantity (%) Elasticity
1 45
2 40
3 35
4 30
5 25
6 20
7 15
8 10
9 5
100 –11 0.11
50 –13 0.25
33 –14 0.43
25 –17 0.67
20 –20 1.00
17 –25 1.50
14 –33 2.33
13 –50 4.00
98 ∂ CHAPTER 4 USING DEMAND AND SUPPLY