Question

The demand curve for a product is given by:
P = 3.2 – 0.2Q
where:
Q is the quantity in kg and
P is the price in £ per Kg.

The cost of production (£) is determined by the equation:
C = 1.0 + 0.15Q + 0.15Q2

Assume that Q can take a continuous range of values.

(a) Show that this coincides with the point at which Marginal Revenue is equal to Marginal Cost.

Answer 1

(a) Marginal Revenue is equal to Marginal Cost when profit-maximizing output Q is produced.

$MR = TR'(Q) = (PQ)' = 3.2 - 0.4Q,$

$MC = TC'(Q) = 0.15 + 0.3Q,$

$3.2 - 0.4Q = 0.15 + 0.3Q,$

Q = 4.36.