Question

Suppose that an industry is dominated by a single producer, the demand for it's product is Q=300-6p. Suppose further that TC=100+5Q+1/480Q×2 is the cost function of the firm.

What is the equilibrium quantity and price in this market given this information

Answer 1

$$TC=100+5Q+\frac {1}{480}Q^2$$

$$MC=5+\frac{1}{240}Q$$

$$Q=300-6p$$

$$p=50-\frac{1}{6}Q$$

$$5+\frac{1}{240}Q=50-\frac{1}{6}Q$$

$$Q=263$$

$$p=6$$