A monopolist faces the demand curve $P = 20 - Q$ and has a constant marginal cost of $MC = 4$. Find the profit-maximising output and price.

A monopolist faces the demand curve P = 20 - Q and – Class 12 Business Economics

Numerical Problems · Q10

P = 20 - Q

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The demand (AR) curve is $P = 20 - Q$ , so total revenue is

TR = P \times Q = (20 - Q)Q = 20Q - Q^{2}.

Marginal revenue is the rate of change of TR with output:

MR = 20 - 2Q.

The monopolist maximises profit where $MR = MC$ :

20 - 2Q = 4 \Rightarrow 2Q = 16 \Rightarrow Q = 8.

Price is read from the demand (AR) curve at this output:

$P = 20 - Q = 20 - 8 = 12.$ …