### Excise Tax Impact on Monopoly Pricing **Problem Statement:**_For a monopolist facing a linear demand function $ P = a - bQ $ for their product and a constant marginal cost $ (MC = c) $, how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?_**Explanation:**In this scenario, we are analyzing the impact of an excise tax on a monopolist's pricing strategy. Here's a step-by-step breakdown of the key concepts involved:1. **Demand Function:** - The demand function given is $ P = a - bQ $, where: - $ P $ is the price of the product. - $ Q $ is the quantity of the product. - $ a $ and $ b $ are constants that describe the linear relationship between price and quantity.2. **Marginal Cost:** - It is provided that the marginal cost (MC) is constant and denoted as $ c $. 3. **Excise Tax:** - The excise tax imposed is $6 per unit. **Analysis:**When an excise tax of $6 is imposed, the firm's marginal cost increases by the tax amount. Therefore, the new marginal cost becomes:\[ MC_{\text{new}} = c + 6 \]In a monopolistic market, the firm maximizes profit by setting marginal revenue (MR) equal to marginal cost (MC). The marginal revenue can be derived from the demand function. Without the excise tax, the profit-maximizing condition is:\[ MR = MC \]With the excise tax, the new condition becomes:\[ MR = MC_{\text{new}} \]Given that the only change is the increase in marginal cost by $6, the monopolist will adjust the price to reflect the higher cost.**Conclusion:**The price increase due to the $6 excise tax would be determined by the monopolist passing some or all of the tax onto consumers. The exact amount of the price increase would depend on the elasticity of demand and the specific values of $ a $ and $ b $. In a typical analysis, if the monopolist can pass the entire tax to consumers, the price would increase by $6.

Given Demand equation P =a-bQ ... (1) Marginal cost MC=c+ Excise tax=6

For a monopolist facing a linear demand function (P = a - bQ) for their product and a constant marginal cost (MC = c), how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?

For a monopolist facing a linear demand function (P = a - bQ) for their product and a constant marginal cost (MC = c), how much would they raise the price they charge if a $6 per unit excise tax were to be imposed?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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