What is the deadweight loss associated with monopoly in question 1? (Round your answer to two decimal places.)
Question
What is the deadweight loss associated with monopoly in question 1? (Round your answer to two decimal places.)
Solution
To calculate the deadweight loss associated with the monopoly, we first need to find the quantity that would be produced in a perfectly competitive market.
Step 1: Find the Competitive Quantity (Qc) In a perfectly competitive market, firms produce up to the point where price equals marginal cost. So, we set P = MC and solve for Q:
95 - Q = 5 + Q 2Q = 90 Qc = 45
Step 2: Find the Competitive Price (Pc) Substitute Qc = 45 into the demand function P = 95 - Q to find the competitive price:
Pc = 95 - 45 = $50
Step 3: Calculate the Deadweight Loss (DWL) The deadweight loss is the area of the triangle formed by the monopoly quantity (Qm = 30), the competitive quantity (Qc = 45), and the difference between the monopoly price (Pm = $65) and the marginal cost at the monopoly quantity (MCm = 5 + Qm = 35). The formula for the area of a triangle is 0.5 * base * height:
DWL = 0.5 * (Qc - Qm) * (Pm - MCm) DWL = 0.5 * (45 - 30) * (65 - 35) DWL = 0.5 * 15 * 30 DWL = $225
So, the deadweight loss associated with the monopoly is $225.
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