Question

- Find the derivative of the following functions:
(i) Y = X 3 – 8X 2 + 57X + 2 (1 mark)
(ii) TC = 0.04Q 3 – 0.9Q 2 + 10Q + 5 (1 mark)

- The following relations describe monthly demand and supply for a computer support service
catering to small business:
Q d = 1,500 – 5 P
Q s = -500 + 5 P
Where Q is the number of business that need services and P is the monthly fee, in dollars
a. Find the equilibrium price/output level
b. Calculate point elasticity of demand for this demand function. Is it elastic, inelastic or
unitary elastic?
c. Calculate the Total Revenue at the equilibrium price

Answer 1

(i) d(y) / dx = 3x² - 16x + 57

(ii) d(TC)/ dx = 0.12q² - 0.18q + 10

Answer (a) Q_{​​​​​​d} = Q_{​​​​​s}

1500 - 5 P = - 500 + 5 P

2000 = 10 P

P = 2000/10 = 200

P = $200

Equilibrium price is $200.

Output level is -500 + 5 P = - 500 + 5 × 200 = -500 + 1000 = 500.

Output level is 500.   

Answer (b) Price elasticity of demand = % change in demand / % change in price = 500 / 200 = 2.5

Price elasticity of demand is Elastic i.e 2.5 that is > 1.

Answer (c) Total Revenue is 500 units of output × $200 per unit = $100,000

Total revenue is $100,000.

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