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Spike the Bulldog is the only seller of Zagopoly board games in Spokane. The inverse demand curve for this game is given by P = 40 – 0.5Q, where Q is in hundreds of games per month. Spike's marginal cost of producing board games is 7 + 0.1Q. a. If Spike cannot price-discriminate, what is his profit-maximizing level of output? What is his profit-maximizing price? b. How much consumer surplus will buyers of the board game receive? How much producer surplus will end up in Spike's pockets? How much deadweight loss is created by the board game monopoly? c. Suppose Spike is a magnificent salesman, able to discern perfectly his customers' willingness to pay. If he leverages this information to begin perfectly price discriminating, how many board games will he sell? d. How much surplus will buyers receive from a perfectly price- discriminating Spike? How much producer surplus will Spike capture? What will the deadweight loss due to monopoly be?

Spike the Bulldog is the only seller of Zagopoly board games in Spokane. The inverse demand curve for this game is given by P = 40 – 0.5Q, where Q is in hundreds of games per month. Spike's marginal cost of producing board games is 7 + 0.1Q. a. If Spike cannot price-discriminate, what is his profit-maximizing level of output? What is his profit-maximizing price? b. How much consumer surplus will buyers of the board game receive? How much producer surplus will end up in Spike's pockets? How much deadweight loss is created by the board game monopoly? c. Suppose Spike is a magnificent salesman, able to discern perfectly his customers' willingness to pay. If he leverages this information to begin perfectly price discriminating, how many board games will he sell? d. How much surplus will buyers receive from a perfectly price- discriminating Spike? How much producer surplus will Spike capture? What will the deadweight loss due to monopoly be?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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I just need help on c and d

Here's a detailed transcription and explanation suitable for an educational website: --- ### Monopoly Pricing and Consumer/Producer Surplus Analysis Spike the Bulldog is the sole seller of Zagopoly board games in Spokane. The market conditions and cost structure for Spike’s business are represented by the following inverse demand curve and marginal cost function: **Inverse Demand Curve:** \( P = 40 - 0.5Q \) where \( P \) is the price and \( Q \) is the quantity of games (in hundreds) sold per month. **Marginal Cost (MC) Function:** \( MC = 7 + 0.1Q \) Let's explore the following aspects of Spike’s monopoly: **a. Profit-Maximizing Output and Price:** If Spike cannot engage in price discrimination, his profit-maximizing level of output is determined by equating marginal cost (MC) to marginal revenue (MR). The steps involve: - Deriving the total revenue (TR): \( TR = P \times Q \) - Finding the marginal revenue (MR): derived from total revenue - Equating MR to MC and solving for \( Q \) - Using the inverse demand curve to determine the optimal price \( P \). **b. Consumer Surplus, Producer Surplus, and Deadweight Loss:** Consumer Surplus (CS) is the difference between what consumers are willing to pay and what they actually pay. Producer Surplus (PS) is the difference between the actual revenue Spike receives and the marginal cost of producing the games. Deadweight Loss (DWL) represents the lost efficiency due to monopoly pricing, where total surplus (sum of consumer and producer surplus) is not maximized. To compute these: - Calculate equilibrium quantity and price. - Integrate the area under the demand curve above the price level to find CS. - Integrate the area above the MC curve up to the quantity to find PS. - Identify the area representing DWL. **c. Perfect Price Discrimination:** If Spike can perfectly price discriminate, he charges each buyer the maximum they are willing to pay. This eliminates consumer surplus as all surplus is captured by the producer. - Determine the output level where P = MC to maximize total surplus. - Calculate the total quantity sold under perfect price discrimination. - Find the new producer surplus, which in this case equals the area under the demand curve above the MC curve. **d. Effects of Perfect Price Discrimination:** With perfect price discrimination: -
Transcribed Image Text:Here's a detailed transcription and explanation suitable for an educational website: --- ### Monopoly Pricing and Consumer/Producer Surplus Analysis Spike the Bulldog is the sole seller of Zagopoly board games in Spokane. The market conditions and cost structure for Spike’s business are represented by the following inverse demand curve and marginal cost function: **Inverse Demand Curve:** \( P = 40 - 0.5Q \) where \( P \) is the price and \( Q \) is the quantity of games (in hundreds) sold per month. **Marginal Cost (MC) Function:** \( MC = 7 + 0.1Q \) Let's explore the following aspects of Spike’s monopoly: **a. Profit-Maximizing Output and Price:** If Spike cannot engage in price discrimination, his profit-maximizing level of output is determined by equating marginal cost (MC) to marginal revenue (MR). The steps involve: - Deriving the total revenue (TR): \( TR = P \times Q \) - Finding the marginal revenue (MR): derived from total revenue - Equating MR to MC and solving for \( Q \) - Using the inverse demand curve to determine the optimal price \( P \). **b. Consumer Surplus, Producer Surplus, and Deadweight Loss:** Consumer Surplus (CS) is the difference between what consumers are willing to pay and what they actually pay. Producer Surplus (PS) is the difference between the actual revenue Spike receives and the marginal cost of producing the games. Deadweight Loss (DWL) represents the lost efficiency due to monopoly pricing, where total surplus (sum of consumer and producer surplus) is not maximized. To compute these: - Calculate equilibrium quantity and price. - Integrate the area under the demand curve above the price level to find CS. - Integrate the area above the MC curve up to the quantity to find PS. - Identify the area representing DWL. **c. Perfect Price Discrimination:** If Spike can perfectly price discriminate, he charges each buyer the maximum they are willing to pay. This eliminates consumer surplus as all surplus is captured by the producer. - Determine the output level where P = MC to maximize total surplus. - Calculate the total quantity sold under perfect price discrimination. - Find the new producer surplus, which in this case equals the area under the demand curve above the MC curve. **d. Effects of Perfect Price Discrimination:** With perfect price discrimination: -
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