Chapter 6 practice questions
4.
Fill in the blanks:
a.
If price falls and total revenue falls, demand must be ________.
b.
When demand is inelastic, a decrease in price causes quantity demanded to ________and
total revenue to ________.
c.
If price rises and total revenue rises, demand must be ________.
d.
When demand is elastic, an increase in price causes quantity demanded to ________and
total revenue to ________.
e.
If price rises and total revenue stays the same, demand must be ________ elastic.
f.
When demand is unitary elastic, an decrease in price causes quantity demanded to
________and total revenue to ________.
c.
Beef in the short run or beef in the long run
7. Use the demand curve below to answer the following questions:
a.
The interval elasticity of demand over the price range $2 to $4 is ________.
b.
The interval elasticity of demand over the price range $8 to $9 is________.
c.
The interval elasticity of demand over the price range $14 to $16 is ________.
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8. Info from Technical Problem 5: Demand function: Q = 50,000 – 2,500*P
a.
For the linear demand curve in Technical Problem 5, compute the price elasticity
at each of the price points given in the following table. Make the elasticity calculations
using the two alternative formulas, E = (DQ / DP) ´ (P / Q) and E = P / (P - A) .
E=
Price
Point
$
DQ
DP
´
P
Q
E=
P
P- A
4
________
________
8.50
________
________
11.50
________
________
18
________
________
b. Which formula is more accurate for computing price elasticities? Explain.
10. Use the figure below to answer the following questions:
a.
Calculate price elasticity at point g using the method E =
DQ P
´ .
DP Q
b.
Calculate price elasticity at point g using the method E =
P
.
P- A
c.
Compare the elasticities in parts a and b. Are they equal? Should they be equal?
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d.
Calculate price elasticity at point h.
e.
Which method did you use to compute price elasticity at point h? Why?
16. The general linear demand for good X is estimated to be
Q = 18,000 -175P + 0.35M -16PR
where P is the price of good X, M is average income of consumers who buy good X, and P is
the price of related good R. The values of P, M, and P are expected to be $65, $52,000, and
$100, respectively. Use these values at this point on demand to make the following
computations.
R
R
a.
Compute the quantity of good X demanded for the given values of P, M, and P .
b.
Calculate the price elasticity of demand E. At this point on the demand for X, is demand
elastic, inelastic, or unitary elastic? How would increasing the price of X affect total
revenue? Explain.
c.
Calculate the income elasticity of demand E . Is good X normal or inferior? Explain how
a 1.75 percent decrease in income would affect demand for X, all other factors affecting
the demand for X remaining the same.
d.
Calculate the cross-price elasticity E . Are the goods X and R substitutes or complements? Explain how a 2.5 percent increase in the price of related good R would affect
demand for X, all other factors affecting the demand for X remaining the same.
R
M
XR
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Answers:
4. a. inelastic
b. increase; fall
c. inelastic
d. decrease; fall
e. unitary elastic
f. increase; stay the same
7. a. Eef =
b. Ecd =
c.
Eab =
DQ
DP
´
Pmidpoint
Qmidpoint
=
300
3
´
= -0.24
-2 1850
DQ Pmidpoint 111 8.5
´
=
´
= -1
DP Qmidpoint
-1 944.5
DQ Pmidpoint 250 15
´
=
´
= -3.95
DP Qmidpoint
-2 475
8. a. At $4: -2,500 ´ (4 / 40,000) = -0.25 = 4 / (4 - 20)
At $8.50: -2,500 ´ (8.50 / 28,750) = -0.74 = 8.5 / (8.5 - 20)
At $11.50: -2,500 ´ (11.50 / 21,250) = -1.35 = 11.5 / (11.5 - 20)
At $18: -2,500 ´ (18 / 5,000) = -9 = 18 / (18 - 20)
b. Neither formula is “more accurate” since they give identical numerical values, as
demonstrated in part a.
10. a. E =
b. E =
DQ P +3,000 100
´ =
´
= -2
DP Q -150 1,000
P
100
=
= -2
P - A 100 -150
c. The values of E in parts a and b are equal, as they should be, because the two methods
are mathematically equivalent formulas for computing price elasticity.
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d. E =
P
25
=
= -0.50
P - A 25 - 75
e. At point h, Q is not given, and thus
P
DQ P
is the only
´ cannot be computed, and
P- A
DP Q
method to use at point h.
16. a. 23,225 = 18,000 – 175(65) + 0.35(52,000) – 16(100)
b. E = –0.490 = –175  (65/23,225); inelastic since |E| < 1. Increasing price at an inelastic
point on demand causes total revenue to rise because the price effect (which is pushing
total revenue higher) dominates the quantity effect (which is pushing total revenue
lower).
c. EM = 0.784 = 0.35  (52,000/23,225); normal. A 1.75 percent decrease in M, all else
constant, causes Q to decrease by 1.37 percent (= –1.75%  0.784).
d. EXR = –0.069 = –16  (100/23,225); complements. A 2.5 percent increase in PR, all else
constant, causes Q to decrease by 0.172 percent (= 2.5%  0.069).
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