Question

Assume that the daily inverse demand function for X-rays in a city with 1 X-ray provider is:

P=4000-100Qd

Calculate the profit-maximizing price for the following marginal costs:

1. $100
2. $200
3. $300

Answer 1

Answer

The X-ray provider is a monopoly, a monopoly produces at MR=MC

MR=4000-200Q .......... An MR curve is double sloped than an inverse linear demand curve

equating with MC=100

4000-200Q=100

200Q=3900

Q=19.5

P=4000-100*19.5=2050

the firm maximizes profit at 19.5 units and price of $2050

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equating with MC=200

4000-200Q=200

200Q=3800

Q=19

P=4000-100*19=2100

the firm maximizes profit at 19 units and price of $2100

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equating with MC=300

4000-200Q=300

200Q=3700

Q=18.5

P=4000-100*18.5=2150

the firm maximizes profit at 18.5 units and price of $2150