SID: ________________________


The University of Sydney

Intermediate Microeconomics ECOS 2001


Mid-semester exam number 1



Instructions

Part A: Answer the multiple-choice questions on the answer sheet provided with a pencil.












Page 2 of 9
Part A: Multiple Choice (20 marks – each question is worth 1 marks each, with 2 possible bonus
questions). Choose the most correct answer.
Instructions: Answer all 22 questions by marking the computer cards provided


1. A consumer has homothetic preferences for goods 1 and 2. At her initial income the consumer
purchases 10 units of 1 and 15 units of 2. If the consumer’s income doubles, what can we say about
the consumer’s optimal consumption bundle?
a. The substitution effect suggests that the individual will buy more of good 1 following the change.
b. The consumer will buy 15 units of good 1 and 10 units of good 2
c. The consumer will buy 20 units of 1 and 30 units of 2.
d. It depends on whether this is an inferior or normal good.
e. Without more information about the consumer’s specific utility function, it is not possible to tell.

2. Let a consumer have preferences be 3/ 2 1/ 41 2U x x? . Find the marginal rate of substitution 2 1MRS ? .
a. 22 1
1
6xMRS
x?
? ?
b. 22 1
1
xMRS
x?
? ?
c. 22 1
1
3
4
xMRS
x?
? ?
d. 22 1
1
3
2
xMRS
x?
? ?
e. 22 1
14
xMRS
x?
? ? .





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3. A consumer has well-behaved preferences. Can her indifference curves cross (intersect)?
a. YES, it is possible if preferences are not homothetic.
b. NO, never.

4. A consumer has a utility function of U = x + y, where x and y are the quantities of goods x and y
consumed. The price for good x is $2 and the price for y is $1 and consumer’s income is $4. What is
the consumer’s budget constraint?
a. 4x + 2y = 4
b. x + y = 4
c. 4x + 4y = 4
d. 2x + y = 4
e. None of the above

5. A consumer has a utility function of U = x + y, where x and y are the quantities of goods x and y
consumed. The price for good x is $2 and the price for y is $1 and income consumer’s income is $4.
What is the consumer’s optimal (utility-maximising) consumption choice?
a. x* = 2, y* = 1
b. x* = 0, y* = 4
c. x* = 2, y* = 0
d. x* = 1, y* = 2
e. It is not possible to say.

6. A consumer has a utility function of U = x + y, where x and y are the quantities of goods x and y
consumed. The price for good x is $2 and the price for y is $1 and income consumer’s income is $4. If
the price for y falls to $0.5, which statement is true?
a. There is zero income effect; all of the change in the quantities demand results from the substitution
effect.
b. The income effect could be negative or positive
c. The substitution effect works in favour of greater consumption of good y; the income effect
suggests the consumer wishes to purchase more of both goods.
d. There is zero substitution effect; all of the change results from the income effect.
e. None of the above.
Page 4 of 9

7. A consumer – Anna - can buy either good 1 or good 2. Anna values one unit of good 1 the same as
she values 2 units of good 2. Anna has $200. The price of good 2 is $1 per unit. The price of good 1
depends on Anna’s consumption levels; for the first 100 units, the price of good 1 is $1, however for
every unit of good 1 that Anna buys over 100 units she must pay $2 per unit. What is the maximum
quantity Anna can buy of good 1 given her income of $200?
a. 100
b. 125
c. 150
d. 175
e. 200

8. The slope of the budget constraint:
a. represents the opportunity cost of one good in terms of the other.
b. is decreasing when the consumer has a diminishing marginal rate of substitution.
c. depends on the consumer’s preferences (indifference curves).
d. increases in absolute value when the income of the consumer increases.
e. None of the above.


9. If we say a consumer has well behaved preferences it means that:
a. The consumer’s preferences are strictly monotonic and concave.
b. The consumer prefers healthy products
c. The consumer’s preferences are convex and monotonic in the quantity of each good consumed.
d. The consumer’s preferences are monotonic in the quantity of each good consumed and the
consumer tends to prefer extreme bundles over averaged bundles
e. None of the above.



Page 5 of 9
10. Which is NOT a monotonic transformation of 1 2U x x? for 1 0x ? and 2 0x ? ?
a. V U?
b. V U? ?
c. V = U + 5
d. 2V U?
e. 2 15.073V U? ?

11. Consider a consumer facing the inter-temporal consumption problem studied in class in which
there are two periods. The consumer earns m1 in period 1 and m2 in period 2. The consumer has well
behaved preferences and can borrow or lend in the first period at interest rate r. At the initial interest
rate the consumer was a borrower. Following a decrease in the interest rate, which statement is true?
a. The consumer might remain a borrower but could decide to become a lender.
b. The consumer, if she remains a borrower, must be worse off after the interest rate falls.
c. The borrower must remain a borrower and will be better off from the decrease in the interest rate.
d. All of the above
e. None of the above


12. Consider a consumer facing the inter-temporal consumption problem studied in class in which
there are two periods. The consumer earns m1 in period 1 and m2 in period 2. The consumer has well-
behaved preferences and can borrow or lend in the first period at interest rate r. At the initial interest
rate the consumer was a borrower. Following an increase in the interest rate, which statement is true?
a. The consumer must become a saver in the first period.
b. The consumer, if she remains a borrower, must be worse off after the interest rate rise.
c. The consumer must increase their borrowing (c1 – m1) in the first period following the rate rise.
d. A and B are correct
e. None of the above.

13. Consider an individual with a utility function ? ?1 2min 3 , 2U x x? where x1 and x2 are the
quantities of goods 1 and 2 consumed, respectively. If the prices of good 1 is $5 and the price of good
2 is $10 and the consumer’s income is $60, how much of goods 1 and 2 does she buy?
Page 6 of 9
a. 1 24, 4x x? ?
b. 1 26, 3x x? ?
c. 1 28, 2x x? ?
d. 1 210, 1x x? ?
e. 1 23, 4.5x x? ?

14. Consider a consumer facing the inter-temporal consumption problem studied in class in which
there are two periods. The consumer earns m1 in period 1 and m2 in period 2. The consumer has well-
behaved preferences and can borrow or lend in the first period at interest rate r. At the initial interest
rate the consumer was a borrower. Following an increase in the interest rate, which statement is
always true?
a. The consumer cannot be made better off
b. The consumer will remain a borrower.
c. The consumer could move to a higher indifference curve following the rate rise, but only if they
become a lender.
d. It is not possible to ascertain the quantity the consumer will borrow in the first period, but the
consumer will never become a lender.
e. None of the above.

15. A consumer consumes two goods, 1 and 2, and has well-behaved preferences. The government
decides to give the consumer an in-kind transfer of a quantity of good 1. This transfer is provided in
addition to the consumer’s normal budget. Which statement is true?
a. The consumer cannot be made worse off by the transfer.
b. The consumer could be made better off from the in-kind transfer
c. The consumer could be even better off if the government provided a monetary transfer exactly
equal to the market value of the in-kind transfer (that is, give the consumer the amount of money
required to purchase the in-kind transfer in the market).
d. All of the above
e. A and B are correct but C is incorrect.

16. Consider an economy with two goods – goods 1 and 2. The government currently taxes both
goods with an ad valorem sales tax of t per cent (an ad valorem tax is a percentage tax, for example a
Page 7 of 9
GST of 10% is an ad valorem tax). There is a new proposal to eliminate the sales tax on both goods
and institute an income tax. The objective, however, is to leave each consumer’s budget constraint
unchanged in the process. What is the percentage level of income tax that is needed to ensure that
consumer’s budget constraint is unchanged after the removal of the sales taxes?
a. t/(1 + t)
b. t
c. (1+t)/t
d. 1/(1+t)
e. (1+t)2


17. TRUE or FALSE? If a consumer has monotonic and strictly-convex preference, the 2 1MRS ? is
increasing (becoming less negative – that is a flatter slope) as consumption of good 1 2 1MRS ?
increases (where 2 1MRS ? is defined as the marginal rate of substitution of good 2 for good 1, in the
usual manner).
a. TRUE.
b. FALSE

18. A consumer has a utility function of ? ? ???? for good 1 and 2. The price of one unit of good 1 is
2 and the price of good 2 is 5 per unit. What is the marginal utility of good 1?
a. ? ?? ? ??
b. ? ?? ? ??
c. ? ?? ? 2??
d. ? ?? ? ??? ?
e. None of the above



19. A consumer has a utility function of ? ? ???? for good 1 and 2. The price of one unit of good 1 is
2 and the price of good 2 is 5 per unit. What is the ????→??
a. ????→? ? ? ?????
Page 8 of 9
b. ????→? ? ?????
c. ????→? ? ? ????
d. ????→? ? ???
e. None of the above


20. A consumer has a utility function of ? ? ???? for good 1 and 2. The price of one unit of good 1 is
2 and the price of good 2 is 5 per unit. In this case, if the consumer is choosing the optimal (utility-
maximising) bundle:
a. ???? ?
?
?
b. ???? ?
?
?
c. ???? ?
?.?
?
d. ???? ? 50
e. None of the above

21. A consumer has a utility function of ? ? ???? for good 1 and 2. The price of one unit of good 1 is
2 and the price of good 2 is 5 per unit. The consumer’s income is 50. What is the optimal (utility-
maximising) bundle for the consumer?
a. ??? ? 5, ??? ? 3
b. ??? ? 2, ??? ? 4
c. ??? ? 12.5, ??? ? 5
d. ??? ? 10, ??? ? 1
e. None of the above

22. Consider a consumer with a utility function 2U y z? , where y and z are the quantities of each
good consumed. Let the price of good y be 6 and the price of z be 2. The consumer’s income is 180.
What is the optimal quantity of y and z consumed?
a. y = 30; z = 30
b. y = 60; z = 10
Page 9 of 9
c. y = 20; z = 60
d. y = 20; z = 30
e. y = 15; z = 10.





********** END OF THE EXAM **********