McMaster University
Economics 2Z03 - Midterm 1 Fall 2021
1) Consider a market demand function Qd = 12−2p and a market supply function Qs = 3+p.
What is the equilibrium quantity?
a. 2
b. 3
c. -3
D. 6
e. none of the above
In equilibrium 12 − 2p = 3 + p. Thus, equilibrium price is 3, equilibrium quantity is 6.
2) Consider an inverse market demand function p = 24 − 3Q and an inverse market supply
function p = Q. What is the price elasticity of demand when the price is 12?
A. -1
b. − 31
c. − 32
d. -3
e. -9
When p = 12, Q = 4. The slope of the demand curve Q = 24−p
is − 13 , so the elasticity
3
= −1.
equals − 13 12
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3) Suppose the price of good 1 is p1 = 3 and the price of good 2 is p2 = 1. If the consumer’s
income is m = 20, which of the following bundles can the consumer afford?
a. (2,10)
b. (10,1)
c. (5,5)
D. more than one of the above
e. none of the above
The bundles cost 16, 31, and 20 respectively.
4) A consumer has a utility function u(x1 , x2 ) = min{5x1 , 2x2 }. Which of the following
bundles give him utility 20?
a. (4,5)
b. (5,10)
1
c. (4,10)
D. more than one of the above
e. none of the above
Bundles b and c give utility 20.
5) A consumer with utility function u(x1 , x2 ) = x10.5 x20.5 chooses between two goods with
prices p1 = 2 and p2 = 1. Which of the following statements is true?
a. The slope of each of the consumer’s indifference curves equals -2.
b. The slope of each of the consumer’s indifference curves equals − 21 .
C. The slope of each of the consumer’s indifference curves equals the marginal
rate of substitution.
d. more than one of the above
e. none of the above
The consumer has Cobb-Douglas preferences, so the slope of his indifference curves is not
constant.
6) A consumer has the utility function u(x1 , x2 ) = 2x1 + x2 . The prices of the goods are
p1 = 3, p2 = 2. Currently, he has the bundle (x1 , x2 ) = (5, 3). If he were given an
additional dollar, it would be optimal to
A. spend it entirely on good 1
b. spend it entirely on good 2
c. spend some of it on good 1 and some of it on good 2
d. not spend it as he cannot increase his utility
e. none of the above
The consumer has “perfect substitutes” preferences. The ratio of marginal utility over
price is equal to 23 for good 1 and 21 for good 2.
7) A consumer has the utility function u(x1 , x2 ) = min{2x1 , x2 }. The prices of the goods
are p1 = 3, p2 = 2, and his income is m = 42. What is the consumer’s optimal bundle?
a. (14,0)
b. (10.5,5.25)
C. (6,12)
d. (8,7)
e. none of the above
The optimal bundle satisfies 2x∗1 = x∗2 . Plugging into the budget constraint 3x∗1 +2x∗2 = 42
yields answer c.
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8) A consumer has the utility function u(x1 , x2 ) = 3x1 + x2 . The prices of the goods are
p1 = 1, p2 = 2, and his income is m = 8. What is the consumer’s optimal bundle?
A. (8,0)
b. (2,3)
c. (3,1)
d. (0,4)
e. none of the above
Perfect substitutes. Good 1 is cheaper and more valuable, so consumer spends all his
income on good 1.
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9) A consumer has the utility function u(x1 , x2 ) = x13 x23 . The prices of the goods are
p1 = p2 = 2 and his income is m = 6. What is the consumer’s optimal bundle?
a. (1,1)
b. (2,4)
c. (0,3)
d. (4,2)
E. none of the above
Cobb-Douglas preferences. Consumer spends 31 of his income on good 1 and the remainder
on good 2. Optimal bundle (1, 2).
10) A consumer has the utility function u(x1 , x2 ) = x10.6 x20.4 . Which of the following gives the
consumer’s demand for good 2 as a function of income m, when prices are p1 = p2 = 2?
m
a. x2 = 0.4
0.6
b. x2 = 0.2
m
0.6
C. x2 = 0.2m
d. x2 = 0.4m
e. x2 = 0.6m
The consumer spends 0.4m on good 2. Thus, he buys 0.2m units of it.
11) A consumer has income m = 10. The prices of good 1 and 2 are p1 = 2, p2 = 3. Suppose
the price of good 1 increases to 4. What is the increase in income that would compensate
the consumer for the resulting loss of purchasing power, used in the computation of the
Slutsky substitution effect?
a. 1
b. 2
c. 4
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d. none of the above
E. cannot be determined without further information
We need to know the preferences of the consumer.
12) A consumer has a utility function u(x1 , x2 ) = x1 + x2 . The prices of good 1 and 2 are
p1 = 2, p2 = 3 and his income is 6. Suppose the price of good 2 increases to 4. What is
the Slutsky substitution effect of this price increase on the consumer’s demand for good
2?
a. -2
b. -1
C. 0
d. none of the above
e. cannot be determined without further information
The consumer spends all his income on good 1 before and after the price increase. The
adjusted income is m′ = 6 and demand for good 2 remains at 0.
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13) A consumer has a utility function u(x1 , x2 ) = x14 x24 . The prices of good 1 and 2 are
p1 = p2 = 1 and his income is 16. Suppose the price of good 1 increases to 2. What is
the Slutsky substitution effect of this price increase on the consumer’s demand for good
1?
a. 0
B. -1.5
c. -3
d. -4.5
e. none of the above
Original demand = 12. Demand under new price = 6. Total effect=-6.
Original bundle (12, 4). To afford it under the new prices, consumer’s income must be
28. Demand under new prices and modified income = 10.5.
Hence, SE=-1.5, IE=-4.5.
14) Consider the consumer from the previous problem. What is the Slutsky income effect of
that price increase on the consumer’s demand for good 1?
a. 0
b. -1.5
c. -3
D. -4.5
e. none of the above
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15) A consumer considers potatoes an inferior good, but not a Giffen good. What is true of
the Slutsky substitution and income effects (SE and IE respectively) of an increase in the
price of potatoes on the consumer’s demand for potatoes?
a. IE ≥ 0 and SE ≥ 0
B. IE ≥ 0 and SE ≤ 0
c. IE ≤ 0 and SE ≥ 0
d. IE ≤ 0 and SE ≤ 0
e. cannot be determined without further information
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