Maths for Economists: Multiple Choice Test 2

1: Which of the following is/are true?

x / x = x⁰
x^b−1 / x^b = x
x^b / x^b+1 = x^-1
x^b . x = x^b+1

2: log ab may be expressed as:

log a + log b
log a . log b
log ( a + b )
b log a

3: £100 invested for 5 years at 6% per annum interest compounded annually will grow to:

106⁵
100[1 + (.06)(5)]
100(1 + .06)⁵
[100(1.06)]⁵

4: d(√x) =
    d(x)

 1 
     √x
 1 
    2√x
√x
      2
 x^-1/2
      2

5: Which of the following are true?

f(x) = ax³ − bx + c implies f'(x) = 3ax² − b + c
f(x) = 4x + 3 / x² implies f'(x) = 4 − 6/x³
f(x) = 3x^2/3 implies f'(x) = 6x^-1/3
f(x) = 6x³ − 3x^-2 + 5x + 7 implies f'(x) = 18x² + 6x^-3 + 5

6: For the following total cost function, find marginal cost (MC), average total cost (ATC) and average variable cost (AVC) and then decide which of the following are true. TC = 0.1Q³ − 4Q² + 80Q + 150 implies

MC = 0.3Q² − 8Q + 80
ATC = 0.1Q² − 4Q + 80
AVC = 0.1Q² − 4Q + 80
MC = AVC at Q = 20

7: The function y = f(x) reaches a (relative) minimum where:-

f(x) = 0 and f'(x) < 0
f(x) = 0 and f'(x) > 0
f'(x) = 0 and f''(x) < 0
f'(x) = 0 and f''(x) > 0

8: A demand function is given by: Q_d = 52 − P²
At the point (P,Q) = (2,48) the price elasticity of demand
PED = P . dQ
         Q   dP
is equal to:

2 − 104/Q
-1/6
-1/8
-4

  Attempts:

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