Question

Assume the inverse demand curve a monopoly faces is p = 100 - 2Q, and MC is constant at 16.

Find the monopoly’s profit maximization output.

Find the monopoly’s profit maximization price.

Find the monopoly’s maximum profit.

Find the monopoly’s deadweight loss.

Please show work for parts c and d

Answer 1

To find the profit maximizing quantity and price we first need the MR curve for the monopolist

MR=100-4Q

A Monopolist sets its MR=MC for profit maximization quantity

So, 100-4Q=16 to solve for Q

or Q = 21

The profit maximization price

= P=100-2Q = 100-42=$58

Since Profit= Total Revenue-Total cost

So, TR = PxQ = 58x21=$1218

and TC = $16 per unit x 21 units = $336

Therefore, Profits = $1218-$336 = $882

The deadweight loss = (1/2)($58 per unit - $10 per unit)(84 units-21 units)

=$1512