Question 3 (10 points)

Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q² + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q + 30 since MC is the derivative of TCwith respect to output.)

The demand in the community is approximated by the equation Q_d = 60 - P/2 (alternatively, you can write the demand equation as Q_d = 60 - 0.5P).

• Graphically depict the demand curve as well as the marginal cost (MC) curve.
• If the cable company is free to choose its own price P_m and quantity Q_m, graphically depict the monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome.
• Compute and state the exact monopolist equilibrium price P_m and quantity Q_m that you depicted graphically.