4. A competitive industry generates pollution, a negative production externality. The marginal private benefit of the good is decreasing in the quantity consumed, and the industry exhibits increasing marginal private costs. The marginal damage produced by the industry's pollution is increasing in the amount of the good produced. a. Graphically depict the efficient amount of production and the amount that the industry chooses in the absence of regulation. Shade the welfare loss associated with the unregulated amount of production. b. How can the government use a per-unit tax to ensure that the industry chooses the socially optimal amount of production? Mark the amount of the tax on the graph and draw the industry's new marginal cost curve. c. What other types of policies could be used to achieve the socially optimal level of production? What are their advantages and disadvantages with respect to efficiency, equity, and implementation? d. An environmental group argues that the tax you chose in part b was too low, and the resulting pollution from the regulated industry is still inefficiently high. Reframe this claim as a critique of the cost curves you used, and illustrate your answer graphically. 3. Consider the demand for apples. a. Provide a graphical derivation of the consumer's demand curve for apples. Explain how the consumer chooses optimal quantities, given preferences, prices, and income. b. Identify the assumptions underlying the model of consumer behavior that you used in part a. c. Choose one of the assumptions you identified in part b and provide an example of a behavior that violates the assumption