Question #115659

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.

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.

Expert's answer

(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.

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