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A drug company has Monopoly on a new class of corticosteroid

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A drug company has Monopoly on a new class of corticosteroid. The market demand is given by P=210−0.003QP=210−0.003Q. The monopolists costs are described by TC=3,000,000+3QTC=3,000,000+3Q. Calculate profit maximizing quantity, price, and profits.

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Given P=210−0.003QP=210−0.003Q, the total revenue is:

  • TR=P×QTR=(210−0.003Q)QTR=210Q−0.003Q2TR=P×QTR=(210−0.003Q)QTR=210Q−0.003Q2

The marginal revenue is thus:

  • MR=dTRdQMR=210−0.006QMR=dTRdQMR=210−0.006Q

Given TC=3,000,000+3QTC=3,000,000+3Q, the marginal cost is:

  • MC=dTCdQMC=3MC=dTCdQMC=3

The profit-maximizing quantity can be found by equating marginal cost and marginal revenue:

  • MR=MC210−0.006Q=30.006Q=207Q∗=34,500MR=MC210−0.006Q=30.006Q=207Q∗=34,500

So the profit maximizing quantity is 34,500 units.

The profit-maximizing quantity price is:

  • P∗=210−0.003(34,500)P∗=210−0.003(34,500) = $106.5

Profits at the maximizing quantity and price are given by:

  • π=TR−TCTR=$106.5×34,500=$3,674,250TC=3,000,000+3(34,500)=$3,103,500π=$3,674,250−$3,103,500π=$570,750π=TR−TCTR=$106.5×34,500=$3,674,250TC=3,000,000+3(34,500)=$3,103,500π=$3,674,250−$3,103,500π=$570,750

So the profits are $570,750.