 Microeconomics_4__Besanko

DisciplinaMicroeconomia I7.656 materiais206.285 seguidores
Pré-visualização50 páginas
falls to 0.10
Using equation (2.3), we see that the price elasticity of demand for the linear
demand curve in Figure 2.16 is given by the formula
(2.4)
This formula tells us that for a linear demand curve, the price elasticity of demand
varies as we move along the curve. Between the choke price (where Q \ufffd 0) and a
price of at the midpoint M of the demand curve, the price elasticity of demand is
between \ufffdq and \ufffd1. This is known as the elastic region of the demand curve. For
prices between and 0, the price elasticity of demand is between \ufffd1 and 0. This
is the inelastic region of the demand curve.
a\ufffd2b
a\ufffd2b
a\ufffdb
\ufffdQ, P \ufffd
¢Q
¢P

P
Q
\ufffd \ufffdb
P
Q
a\ufffdb
P \ufffd
a
b
\ufffd
1
b
Q
choke price The price
at which quantity
demanded falls to 0.
10You can verify that quantity demanded falls to 0 at the choke price by substituting P \ufffd into the
equation of the demand curve:
\ufffd 0
\ufffd a \ufffd a
Q \ufffd a \ufffd b aa
b
b
a\ufffdb
Pr
ic
e
(do
lla
rs
pe
r u
nit
)
0
\u3b5Q,P = \u2013\u221e
\u3b5Q,P = \u20131
\u3b5Q,P = 0
Q = a \u2013 bP
P = \u2013
or
a
b
a a
2
a
b
Q
b
a
2b
Quantity (units per year)
M
D
Elastic region
\u3b5
Q
,P between \u2013
\u221e
and \u20131
Inelastic region
\u3b5
Q
,P between \u20131
and 0
FIGURE 2.16 Price Elasticity of
Demand along a Linear Demand Curve
In the region to the northwest of the mid-
point M, demand is elastic, with the price
elasticity of demand between minus infinity
and \ufffd1. In the region to the southeast of
the midpoint M, demand is inelastic, with
the price elasticity of demand between \ufffd1
and 0.
c02demandandsupplyanalysis.qxd 6/14/10 1:39 PM Page 46
2.2 PRICE ELASTICITY OF DEMAND 47
Equation (2.4) highlights the difference between the slope of the demand curve,
\ufffdb, and the price elasticity of demand, . The slope measures the absolute
change in quantity demanded (in units of quantity) brought about by a one-unit change
in price. By contrast, the price elasticity of demand measures the percentage change in
quantity demanded brought about by a 1 percent change in price.
You might wonder why we do not simply use the slope to measure the sensitivity
of quantity to price. The problem is that the slope of a demand curve depends on the
units used to measure price and quantity. Thus, comparisons of slope across different
goods (whose quantity units would differ) or across different countries (where prices
are measured in different currency units) would not be very meaningful. By contrast,
the price elasticity of demand expresses changes in prices and quantities in common
terms (i.e., percentages). This allows us to compare the sensitivity of quantity
demanded to price across different goods or different countries.
Constant Elasticity Demand Curves
Another commonly used demand curve is the constant elasticity demand curve,
given by the general formula: Q \ufffd aP\ufffdb, where a and b are positive constants. For the
constant elasticity demand curve, the price elasticity is always equal to the exponent
\ufffdb.11 For this reason, economists frequently use the constant elasticity demand curve
to estimate price elasticities of demand using statistical techniques.
\ufffdb(P\ufffdQ)
total revenue Selling
price times the quantity of
product sold.
constant elasticity
demand curve A
demand curve of the form
Q \ufffd aP\ufffdb where a and b
are positive constants. The
term \ufffdb is the price elas-
ticity of demand along this
curve.
11We prove this result in the appendix to this chapter.
Problem
(a) Suppose a constant elasticity demand curve is given
by the formula . What is the price elasticity
of demand?
(b) Suppose a linear demand curve is given by the
formula . What is the price elasticity of
demand at P \ufffd 30? At P \ufffd 10?
Solution
(a) Since this is a constant elasticity demand curve, the
price elasticity of demand is equal to everywhere
along the demand curve.
(b) For this linear demand curve, we can find the price
elasticity of demand by using equation (2.4):
\ufffd1\ufffd2
Q \ufffd 400 \ufffd 10P
Q \ufffd 200P\ufffd
1
2
Elasticities along Special Demand Curves
Since b \ufffd \ufffd10 and Q \ufffd 400 \ufffd 10P,
when P \ufffd 30,
and when P \ufffd 10,
Note that demand is elastic at P \ufffd 30, but it is inelastic at
P \ufffd 10 (in other words, P \ufffd 30 is in the elastic region of
the demand curve, while P \ufffd 10 is in the inelastic region).
Similar Problems: 2.5, 2.6, 2.13
\ufffdQ, P \ufffd \ufffd10 a 10400 \ufffd 10(10)b \ufffd \ufffd0.33
\ufffdQ,P \ufffd \ufffd10 a 30400 \ufffd 10(30)b \ufffd \ufffd3
\ufffdQ, P \ufffd (\ufffdb)(P\ufffdQ)
L E A R N I N G - B Y- D O I N G E X E R C I S E 2 . 6
E
S
D
PRICE ELASTICITY OF DEMAND AND TOTAL REVENUE
Businesses, management consultants, and government bodies use price elasticities of
demand a lot. To see why a business might care about the price elasticity of demand,
let\u2019s consider how an increase in price might affect a business\u2019s total revenue, that is,
the selling price times the quantity of product it sells, or PQ. You might think that
c02demandandsupplyanalysis.qxd 7/14/10 11:10 AM Page 47
48 CHAPTER 2 DEMAND AND SUPPLY ANALYSIS
when the price rises, so will the total revenue, but a higher price will generally reduce
the quantity demanded. Thus, the \u201cbenefit\u201d of the higher price is offset by the \u201ccost\u201d
due to the reduction in quantity, and businesses must generally consider this trade-off
when they think about raising a price. If the demand is elastic (the quantity demanded
is relatively sensitive to price), the quantity reduction will outweigh the benefit of the
higher price, and total revenue will fall. If the demand is inelastic (the quantity
demanded is relatively insensitive to price), the quantity reduction will not be too
severe, and total revenue will go up. Thus, knowledge of the price elasticity of demand
can help a business predict the revenue impact of a price increase.
DETERMINANTS OF THE PRICE ELASTICITY OF DEMAND
Price elasticities of demand have been estimated for many products using statistical tech-
niques. Table 2.1 presents these estimates for a variety of food, liquor, and tobacco products
in the United States, while Table 2.2 presents estimates for various modes of transporta-
tion. What determines these elasticities? Consider the estimated elasticity of \ufffd0.107 for
cigarettes in Table 2.1, which indicates that a 10 percent increase in the price of cigarettes
would result in a 1.07 percent drop in the quantity of cigarettes demanded. This tells us
that cigarettes have an inelastic demand: When the prices of all the individual brands of
cigarettes go up (perhaps because of an increase in cigarette taxes), overall consumption of
cigarettes is not likely to be affected very much. This conclusion makes sense. Even
though consumers might want to cut back their consumption when cigarettes become
more expensive, most would find it difficult to do so because cigarettes are habit forming.
In many circumstances, decision makers do not have precise numerical estimates
of price elasticities of demand based on statistical techniques. Consequently, they have
to rely on their knowledge of the product and the nature of the market to make edu-
cated conjectures about price sensitivity.
TABLE 2.1 Estimates of the Price Elasticity of Demand for Selected Food,
Tobacco, and Liquor Products
Product Estimated Q,P
Cigars 0.756
Canned and cured seafood 0.736
Fresh and frozen fish 0.695
Cheese 0.595
Ice cream 0.349
Beer and malt beverages 0.283
Bread and bakery products 0.220
Wine and brandy 0.198
Cookies and crackers 0.188
Roasted coffee 0.120
Cigarettes 0.107
Chewing tobacco 0.105
Pet food 0.061
Breakfast cereal 0.031
Source: Emilio Pagoulatos and Robert Sorensen, \u201cWhat Determines the Elasticity of Industry
Demand,\u201d International Journal of Industrial Organization, 4 (1986): 237\u2013250.
c02demandandsupplyanalysis.qxd 6/14/10 1:39 PM Page 48
TABLE 2.2 Estimates of the Price Elasticity of Demand for Selected Modes