Master Market Structures: Solved Problems for Monopoly & Oligopoly (Cournot, Stackelberg)

Microeconomics Practice Market Structures


Master Market Structures: Solved Problems
Detailed solutions for Monopoly and Oligopoly models.




Problem 1: Monopoly Maximization & Deadweight Loss
Question: A monopolist faces a market demand curve given by P (Q) = 100 − Q. The firm
has a total cost function C(Q) = 20Q + 500.

1. Find the profit-maximizing quantity (Qm ) and price (Pm ).

2. Calculate the monopolist’s profit.

3. Calculate the Deadweight Loss (DWL) compared to perfect competition.

Solution
Step 1: Find Marginal Revenue (MR) and Marginal Cost (MC)
Total Revenue R(Q) = (100 − Q)Q = 100Q − Q2 .
M R = 100 − 2Q.
dC
M C = dQ = 20.
Step 2: Equate MR = MC
100 − 2Q = 20 =⇒ 2Q = 80 =⇒ Qm = 40.
Step 3: Find Price
Pm = 100 − 40 = 60.
Step 4: Calculate Profit
π = R − C = (60 × 40) − (20(40) + 500) = 2400 − 1300 = 1100.
Step 5: Calculate Deadweight Loss
In Perfect Competition, P = M C. 100 − Qpc = 20 =⇒ Qpc = 80. The DWL is the area of the
triangle between Demand and MC from Qm to Qpc .

1
DW L = × (Qpc − Qm ) × (Pm − M C)
2
1 1
DW L = × (80 − 40) × (60 − 20) = (40)(40) = 800
2 2

Final Answer: Qm = 40, Pm = 60, Profit=1100, DWL=800.




Problem 2: Third-Degree Price Discrimination
Question: A monopolist sells in two separate markets. Market 1 Demand: p1 = 100 − q1 .
Market 2 Demand: p2 = 80 − 2q2 . Marginal Cost is constant at M C = 20. Find the optimal
prices and quantities for each market.




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