# Maths for Economists: Multiple Choice Test 3

Reproduced by permission of Hilary Lamaison, Brunel University, ecsthjl@brunel.ac.uk. Hosted by the Economics Network.

EC1011 Mathematics for Economics
Multiple Choice Test 3 for self-assessment

In answering each of the following questions, click the boxes next to each correct answer. More than one may be correct in some cases. Do not guess. There are 20 correct choices in total. The feedback box at the foot of the page will tell you how many of your answers are correct.

Time allowed = 15 minutes.

1: f(x) = 3x3 - 4x2 + 10 implies

f(1) = 10
f '(x) = 9x2 - 8x + 10
f ''(x) = 18x - 8
f '(2) = 20

2: Which of the following are true?

f(x) = axn implies f '(x) = anxn-1
f(x) = 4x5 - 3x2 implies f '(x) = 20x-5 - 6x-2
f(x) = 4x + 3/x2 implies f '(x) = 4 - 6/x3
f(x) = ln(x) implies f '(x) = x-1

3: y = 100/x + 4x has

a maximum point where x = 5
a minimum point where x = 5
a maximum point where x = -5
a minimum point where x = -5

4: Which of the following statements are (in general) true?

Marginal cost (MC) is minimised where MC = Average Variable Cost (AVC)
Average Total Cost (ATC) is minimised where MC = ATC
Average Variable Cost (AVC) is minimised where MC = AVC
Total revenue is maximised where MC = Marginal Revenue (MR)

5: Which of the following functions have unit elasticity at P = 6?

Demand: Qd = 10/P
Demand: log Qd = 100 - 3 log P
Demand: Qd = 24 - 2 P
Supply: Qs = 5 P

6: For the demand function Q1 = 10 - 9 P1 + P2 + 0.01Y which of the following statements are true?

dQ1 / dP1 = -9 + P2 + 0.01Y
dQ1 / dP1 = -9
dQ1 / dP2 = P2
dQ1 / dY = 0.01

7: For the function Q = AKaLb which of the following statements are true?

dQ/dL = AbKaLb-1
Marginal Product of Labour (MPL) = AaKa-1Lb
Marginal Product of Capital (MPK) = aQ / K
Marginal rate of substitution of capital for labour (MRS) = |dK / dL|

8: Which of the following functions are homogeneous of degree 1 (i.e. linear homogeneous)?

Q = 100 K1/4 L3/4
Q = 20 KaL1-a
Q = K2 + 2KL + L2
Q = (K2 + 2KL + L2)1/2

Attempts: