4. There are n firms in a competitive industry, with the following market p=50-2Q. A firm's cost function is q². To mitigate the negative impact of the pandemic, the government provides a per-unit subsidy s> 0 to the firms. That is, for each unit of goods sold, the firm receives p+s in total, where p is paid by consumers and s by the government. So the profit of a firm is π = (p+s)q-q². Derive the consumer surplus, denoted by CS. Is this subsidy policy effective at stimulating goods surply and benefiting consumers? Explain the intuition of your answer. demand:

4. There are n firms in a competitive industry, with the following market p=50-2Q. A firm's cost function is q². To mitigate the negative impact of the pandemic, the government provides a per-unit subsidy s> 0 to the firms. That is, for each unit of goods sold, the firm receives p+s in total, where p is paid by consumers and s by the government. So the profit of a firm is π = (p+s)q-q². Derive the consumer surplus, denoted by CS. Is this subsidy policy effective at stimulating goods surply and benefiting consumers? Explain the intuition of your answer. demand:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 3 A monopolist has a cost function of c(x) = x so that its marginal cost is constant at $1 per unit. It faces the following demand curve: D(p) = {100/p 100/p if p > 20 if p ≤ 20 A. What is the profit-maximizing choice of output/price for the monopolist? Graphically represent the monopoly market. B. If the government sets a price ceiling on the monopolist in order to force it to act as a competitor, what price should the government set? C. What output would the monopolist produce if forced to behave as a competitor? D. Based on the information in parts A - C, find the consumer-, producer-, and social surpluses before and after the government intervention.
Item 7 Suppose a monopolist’s profit-maximizing output is 400 units per week and that the firm sells its output at a price of $40 per unit. The firm has total costs of $8,000 per week. Assume the monopolist is maximizing its profit and earns $20 per unit from the sale of the last unit produced each week.
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The inverse demand function of a monopolist is p(y) = 12 – y, and total costs is C(y)= y2 -20y +10. a. What is the profit-maximizing level of production? b. Suppose the government decides to tax the monopolist so that for each unit the monopolist sells it has to pay a tax of $2. What is the optimal output under this tax? c. Suppose the government now imposes a tax of 10% on the monopolist’s profits. What is the optimal output under this tax?
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