Given the popularity and cache of the club, she has a monopoly position in the market. The market demand curve is given by P = 176–q. Laura has a marginal cost per drink of MC = 4q and a fixed cost FC = $144. If Laura charges the same price to all customers, what is the resulting DWL? [Round your final answer to 2 decimal points when necessary
Question
Given the popularity and cache of the club, she has a monopoly position in the market. The market demand curve is given by P = 176–q. Laura has a marginal cost per drink of MC = 4q and a fixed cost FC = $144. If Laura charges the same price to all customers, what is the resulting DWL?
[Round your final answer to 2 decimal points when necessary
Solution 1
To find the Deadweight Loss (DWL), we first need to find the equilibrium quantity and price
Solution 2
To find the Deadweight Loss (DWL), we first need to find the equilibrium quantity and price in a perfectly competitive market (where P = MC) and in a monopoly (where MR = MC).
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Find the demand curve: P = 176 - q
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Find the marginal cost: MC = 4q
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Set P = MC to find the equilibrium in a perfectly competitive market: 176 - q = 4q Solve for q: q = 35.2 Substitute q into the demand equation to find the price: P = 176 - 35.2 = 140.8
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To find the monopoly equilibrium, we first need to find the marginal revenue (MR). The MR has the same intercept as the demand curve but twice the slope. So, MR = 176 - 2q
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Set MR = MC to find the monopoly equilibrium: 176 - 2q = 4q Solve for q: q = 29.33 Substitute q into the demand equation to find the price: P = 176 - 29.33 = 146.67
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The DWL is the area of the triangle formed by the vertical line at the monopoly quantity, the demand curve, and the marginal cost curve. The base of the triangle is the difference in quantities (35.2 - 29.33 = 5.87) and the height is the difference in prices (146.67 - 140.8 = 5.87).
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The area of a triangle is 0.5 * base * height, so the DWL = 0.5 * 5.87 * 5.87 = 17.22
So, the resulting Deadweight Loss (DWL) is 17.22.
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