Part A: Multiple Choice Questions [15 marks]
For Q1-5: Consider the function () = ି
భ
ೣ.
1. Let = (). Express in terms of .
(a) = ln ()
(b) = ቂln ቀଵ
௬
ቁቃ
ିଵ
(c) = − ln ቀଵ
௬
ቁ
(d) = −ln (−)
(e) = ଵ
୪୬ (ି௬)
2. Suppose > 0. What is the range of the function ()?
(a) < 0
(b) > 0
(c) > 1
(d) 0 < < 1
(e) 0 ≤ ≤ 1
3. Which of the following statements is/are true?
(i) () is not continuous at = 0.
(ii) () is not differentiable at = 0.
(iii) () is not continuous at = 1.
(a) (i) only
(b) (ii) only
(c) (iii) only
(d) (i) and (ii) only
(e) (ii) and (iii) only
4. What is the first order derivative of ()?
(a) ଵ
௫మ
ି
భ
ೣ (b) − ଵ
௫మ
ି
భ
ೣ (c) ଵ
௫మ
+ ି
భ
ೣ (d) ି
భ
ೣ + ଵ
௫మ
ି
భ
ೣ (e)
భ
ೣమ
5. Suppose the inverse supply function is = (), , > 0. Find the point elasticity of supply.
(a) ଵ
ொ
(b) 1
(c)
(d) ଶଵ/ொ
(e) ିଶିଵ/ொ
6. To prepare for Mimi’s increasing expenditure, Simon considers investing in a fixed-income
security at the start of the year. The security will pay out $100 at the end of each year for the
next 10 years. Suppose the annual interest rate is 2%. What is the present value of the security?
(a) $82
(b) $898
(c) $916
(d) $1000
(e) $1074
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For Q 7-9: Suppose the consumption function of Mimo’s kingdom is = ௒
ଶ௒ାଵ
, where C is the
consumption and Y is the aggregate income (measured in billion dollars).
7. What is the marginal propensity to consume?
(a) ଵ
(ଶ௒ାଵ)మ
(b) ଵ
ଶ௒ାଵ
(c) ଶ௒
(ଶ௒ାଵ)మ
(d) ଶ௒
ଶ௒ାଵ
(e) (2 + 1)ଶ

8. If the aggregate income is $0.5 billion, what is the marginal propensity to save?
(a) 0.2
(b) 0.25
(c) 0.5
(d) 0.75
(e) 0.8

9. According to the analysis by Baobao, the Chief Economist of Mimo’s kingdom, the investment
function is = 0.25 + 0.025, and the government spending is = 0.1. What is the equilibrium
aggregate income?
(a) −0.25
(b) 0.25
(c) 0.5
(d) 1
(e) 2

10. Which of the following statements is/are true about the number గ
ଷ
?
(i) It is a rational number.
(ii) It is a real number.
(iii) It is a complex number.
(a) (i) only
(b) (ii) only
(c) (i) and (ii) only
(d) (ii) and (iii) only
(e) (i), (ii) and (iii)

11. Which of the following is the largest domain of () = logଶ ቀ−
ଵ
௫
ቁ?
(a) < −2
(b) < 0
(c) −1 < < 1
(d) > 0
(e) > 2

12. Under the domain in Q 11, what is the first-order derivative of () = logଶ ቀ−
ଵ
௫
ቁ?
(a) ଵ
௫௟௡ଶ
(b) ିଵ
௫௟௡ଶ
(c) ିଵ
௫మ௟௡ଶ
(d) ௟௡ସ
௫
(e) ି௟௡ସ
௫మ




4

For Q 13-15: Suppose Simon owns a Ramen noodle factory. The production function is given by
(, ) = 6ଵ/ଷଵ/ଶ, where is capital and is labour.
13. Which of the following statements is true?
(a) Simon’s factory enjoys a constant production of scale.
(b) Simon can double outputs by doubling both the capital and labour inputs.
(c) Simon can triple outputs by tripling the capital inputs and doubling the labour inputs.
(d) Outputs will reduce by less than half if both capital and labour inputs are halved.
(e) Outputs will remain the same if capital inputs are tripled but labour inputs are halved.

14. Which of the following is the marginal rate of technical substitution?
(a) ଷ௄
ଶ௅
(b) ଶ௄
ଷ௅
(c) ଷ௄
భ/య
ଶ௅భ/మ
(d) ଷ௅
భ/మ
ଶ௄మ/య
(e) ଶ௅
భ/మ
ଷ௄మ/య
15. Which of the following statements is true?
(a) capital is more productive than labour at (, ) = (1,1).
(b) capital is more productive than labour at (, ) = (2,3).
(c) capital is more productive than labour at (, ) = (3,2).
(d) capital and labour are equally productive at (, ) = (1,1).
(e) capital and labour are equally productive at (, ) = (2,3).
Part B: Long Questions [20 marks]
1. Differentiate = ௫√௫ା଴.ହ(ଶ௫ାଵ)షభ/మ with respect to . [3 marks]
[Hint: Simplify first before differentiation. This could make your life easier…]

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2. Hungry Bob has a factory that produces orange juice. His total cost function is:
= ଶ − 4 + 9 ( measured in cubic metres).

a. Plot the total cost function. Mark the intercept(s) and the minimum/maximum
point(s) clearly. [2 marks]
b. Derive the average cost function and the marginal cost function. [2 marks]
c. Suppose the demand function is = 8 − 2.
i. Derive the profit function. [1 mark]
ii. Find the value(s) of Q such that Carol breaks even. [2 marks]
iii. Give the range of Q on which Carol is at a loss. [2 marks]
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3. What is the time required to double the initial deposit at 6% annual interest rate
compounded quarterly? Express your answer in number of years, and round it to 2 decimal
places. [3 marks]
4. It is given that the demand for butter is = 5 + ଶ
௉
( is in grams, is the price per gram).
a. Derive the point elasticity of demand ஽. Express your answer in terms of only.
[2 marks]
b. Find the valid range of ஽. Is the demand for butter elastic or inelastic? [3 marks]
END OF PAPER
Part A:
1. B 2. D 3. D 4. A 5. C
6. B 7. A 8. D 9. C 10. D
11. B 12. B 13. D 14. A 15. E
Part B:
1. ସ௫ାଵ
√ଶ
2. a)
b) = − 4 + ଽ
ொ
, = 2 − 4.
c) (i) () = −3ଶ + 12 − 9
(ii) = 1 = 3
(iii) 1 < < 3
3. ቀ1 + ଴.଴଺
ସ
ቁ
ସ௫
= 2
= ௟௡ଶ
ସ௟௡ଵ.଴ଵହ
≈ 11.64
4. a) = ହ
ொ
− 1
b) −1 < < 0 > 5
⇒ inelastic demand
9
(2, 5)
TC
Q
D
5
Q
↑ E↑0
E↓-1 →
SOLUTION