Question 1:

Assume that a monopolist is facing a linear demand given as Q_d = 360 - 0.5P, and that their marginal cost is represented by a linear function MC = Q (this is a simplifying assumption so that you do not have to graph quadratic equations). Additionally, assume that the monopolist is required to sell their product at a uniform price.

• If the firm is free to choose its own price P_mand quantity Q_m, graphically depict this monopoly equilibrium price and quantity. Your graph should include the demand curve, marginal cost curve, and any other curves necessary to identify the equilibrium price and quantity.
• Indicate numerically all relevant intercepts for your demand and marginal cost curves on your graph.
• Compute and clearly indicate on the graph the exact monopolist equilibrium P_m and quantity Q_m that you depicted graphically.
• Compute and clearly indicate on the graph the socially optimal price P_SOC and quantity Q_SOC in this market. For this computation, you may assume that the marginal cost curve of the monopolist represents the sum of marginal costs of individual firms.

Question 2:

Using the graph you produced in your answer to Question 1:

• Graphically identify and label the consumer surplus (CS_m), producer surplus (PS_m), and deadweight loss (DWL_m) when the monopolist sells Q_m units at price P_m.
• Compute and label the numerical values of the consumer surplus (CS_m), producer surplus (PS_m), and deadweight loss (DWL_m) when the monopolist sells Q_m units at price P_m. Please remember to indicate the units in which consumer surplus, producer surplus, and deadweight loss are measured.

Question 3:

Briefly explain why it is that the monopoly equilibrium results in a deadweight loss.