Maths for Economists: Multiple Choice Test 3

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) = anx^n-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: Q_d = 10/P
Demand: log Q_d = 100 − 3 log P
Demand: Q_d = 24 − 2 P
Supply: Q_s = 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 = AK^aL^b which of the following statements are true?

dQ/dL = AbK^aL^b−1
Marginal Product of Labour (MPL) = AaK^a−1L^b
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 K^1/4 L^3/4
Q = 20 K^aL^1−a
Q = K² + 2KL + L²
Q = (K² + 2KL + L²)^1/2

  Attempts:

(This will erase your answers)