Quantitative methods in economics ECON1003
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Quantitative methods in economics ECON1003
Instructions:
Your exam consists of 20 selective questions including Multiple choice, True/False, Fill in the blanks and Numerical. Each question is worth 1 mark.
Permitted materials: Non-programmable calculators
1. Find t to solve 753e0.03t = 1750
a. t = 28.11
b. t = 30.25
c. t = 6.883
d. t = 6.2133
e. t = -3.4510
2. ln(22)+ln(2) is equal to
a. ln(24)
b. ln(44)
c. ln(20)
d. 0
e. ln(11)
3. The spread of a carrot fly through an untreated crop is modelled by the equation
Y = 500(1− e−0 5t. ) , where Y is the weight of infected carrots in tons, t is time in days. Calculate the time taken to infect 200 tons of carrots.
a. 1.0217 days
b. 2.4792 days
c. 1.8326 days
d. 2.3491 days
e. 3.4491 days
4. Find x to solve x2 + 6x + 5 = 0
a. x=1
b. x = 8 or -10
c. x = 14
d. x= -1 or -5
e. x = 2 or 10
5. The supply equation is Ps = Q2 + 6Q + 9 and demand is given by Pd = Q2 – 10Q + 25. What is the market equilibrium?
a. Q = 1; P = 16
b. Q = 16; P = 1
c. Q = 8; P = 106
d. Q = 1; P = 18
e. Q = 1; P = 25
6. If demand is given by P = 100 – Q, what is TR and MR for a monopolist?
a. TR = 100Q – Q2; MR = 0
b. TR = 100 – Q2; MR = 2Q
c. TR = 100Q – Q; MR = - 1
d. TR = 100Q – 2Q2; MR = 100 – 4Q
e. TR = 100Q – Q2; MR = 100 – 2Q
7. A consumer can buy good 1 or good 2 at prices p1 and p2. The quantity of good 1 purchased is x1 and the quantity of good 2 that the consumer buys is x2. What is the consumer’s budget line and budget set (the budget set is all the bundles that the consumer can afford to buy) with income M?
a. x1.p1 = M; x2.p2 ≤ M
b. x1.p2 +x2.p1 = M; x1.p2 +x2.p1 ≤ M
c. x1.p1 +x2.p2 < M; x1.p1 +x2.p2 = M
d. x1.p1 +x2.p2 = M; x1.p1 +x2.p2 > M
e. x1.p1 +x2.p2 = M; x1.p1 +x2.p2 ≤ M
8. What is the price elasticity of demand at q = 20 when the demand equation is P = 50 – 2q?
a. e = -0.25
b. e = -1
c. e = -1.5
d. e = -2
e. e = -4
9. A consumer can buy two goods, good 1 and 2 for prices $5 and $10 respectively. The consumer is currently buying 6 units of good 2 and is spending $100. What range of quantities of good 1 (q1) can the consumer buy that ensures they are in their budget set (that is, buying a set of goods that is affordable)?
a. q1 ≤ 8
b. q1 ≤ 4
c. q1 ≤ 16
d. q1 ≤ 10
e. q1 ≤ 5
10. Solve ex+5 = 1.56
a. x = 1.34
b. x = -2.713
c. x = -4.5553
d. x = 22.22
e. x = - 1.728
11. Solve 38 + 12e-0.5t = 208
a. t = -6.4012
b. t = 4.5
c. t = 0
d. t = -5.3018
e. None of the above
2x ln(x) +1
12. Differentiate y =
x
2 1
a. − 2
x x
b. ln(x) + 2 / x +1
c. ln(x) + 2 / x
d. 2ln(x) + 2
e. None of the above
13. Solve for x: x2 – 25 = 0
a. x = ±5
b. x = 5
c. x = 0
d. x = - 5
e. None of the above
14. Differentiate P = 
xex−5
a. 
xex−5
b. 
ex−5(1+ x)
c. 
xex +1
d. 
xe (x − 5)x
e. None of the above
15. Find Q to solve −12 = Q2 − 8Q
a. Q = 6
b. Q = 6 or 2
c. Q = 2.32
d. Q = -2 or 6
e. Q = 2 or 8
16. Solve: j(x − 5)0.2 dx :
a. 
(x − 5)1.2 + c
b. 2(x − 5)2 + c
c. (x − 5)−1.2 + c
d. (x − 5)1.2 + c
e. None of the above.
17. Consider a consumer with income M=100 who can consume two goods. The price of the first good is 1 per unit and the price of the second good is 2 per unit. Suppose that the consumer spends all of her income on good 1. Then she consumes …… units of good 1.
Answer:100
18. Consider a consumer with income M=100 who can consume two goods. The price of the first good is 1 per unit and the price of the second good is 2 per unit. Suppose that the consumer spends all of her income on good 2. Then she consumes …… units of good 2.
Answer:50
19. Answer True or False. The derivative of a linear function is a constant. TRUE
20. Answer True or False. Every maximization problem always has a solution. FALSE
21. Answer True or False. Consider the function f(x) = −x3 + 9x2 − 24x + 26 defined on the constraint set S = (−∞, ∞). Then x=2 is a local minimizer. TRUE
22. Answer True or False. Consider the function f(x) = −x3 + 9x2 − 24x + 26 defined on the constraint set S = (−∞, ∞). Then x=6 is a local maximizer. FALSE
23. Answer True or False. The indefinite integral of a linear function f(x) = kx where k > 0 is a constant. FALSE
2023-06-05