Question

A monopolist faces market demand given by P = 220 – 5Q. For this market, MR = 220 - 100 and MC = 10Q. What is the deadweight loss due to the monopoly? Draw a diagram to illustrate your thinking To receive full mark for this question, you are also expected to show all steps of your work (e.g., step 1 _I determined...; step 2 – now I can calculate... etc.) and provide all necessary explanations.

Answer 1

To determine the deadweight loss due to the monopoly, we need to compare the monopolist's output level and price with the competitive equilibrium.

Step 1: Determine the monopolist's equilibrium output level:
Set MR = MC:
220 - 100 = 10Q
120 = 10Q
Q = 12

Step 2: Determine the monopolist's equilibrium price:
Substitute Q into the demand equation:
P = 220 - 5Q
P = 220 - 5(12)
P = 160

Step 3: Calculate the competitive equilibrium output level:
Set market demand equal to market supply:
220 - 5Q = MC
220 - 5Q = 10Q
220 = 15Q
Q = 14.67

Step 4: Calculate the competitive equilibrium price:
Substitute Q into the demand equation:
P = 220 - 5Q
P = 220 - 5(14.67)
P = 150

Step 5: Calculate the deadweight loss:
Deadweight loss = 0.5 * (Q_monopoly - Q_competitive) * (P_monopoly - P_competitive)
Deadweight loss = 0.5 * (12 - 14.67) * (160 - 150)
Deadweight loss = 0.5 * (-2.67) * 10
Deadweight loss = 13.35

Therefore, the deadweight loss due to the monopoly is 13.35.