Question

A monopoly firm has the following demand curve: Q = 2,000 – 25P
where Q is its monthly output. Assuming its monthly short-run total cost is described by the function
STC = 500 + 8Q + 0.035Q2 Answer the following questions:
i. What will be its profit-maximising price and output?
ii. How much profit will it have at the preceding output?

Answer 1

$$p=80-0.04Q$$

$$TR=80Q-0.04Q^2$$

$$MR=80-0.08Q$$

$$MC=8+0.07Q$$

$$MR=MC$$

$$Q=480$$

$$p=60.8$$

$$\pi=TR-STC=72Q-0.07Q^2-500$$

$$\pi=17,932$$