1. (20 points) Suppose that a dye factory is located next to a river. The marginal private cost of producing dye is given by: MPC-10+ 0.5D, where D is the quantity of dye produced. In addition to the marginal private cost, an external cost is incurred. Every unit of dye produced produces pollutant flows into the river which cause damage valued at $10. The marginal benefit to society of each unit of dye produced is given by: MB-30-0.5D. a. Draw a diagram illustrating the marginal private cost, marginal benefit, marginal external cost, and marginal social cost functions. b. Find the output of dye which would obtain in the market equi librium and calculate the corresponding consumer and producer surplus (assuming that consumers and producers are not them- selves affected by the polluted river), as well as any deadweight loss. What are the social net benefits? (Hint: Recall that Social Net Benefit Total Social Benefit - Total Social Cost) c. Find the socially optimal dye output and calculate the correspond- ing consumer and producer surplus (assuming that for each unit of dye they produce, firms are taxed $10). What are the social net benefits? d. Compare your answers from parts (b) and (e). Explain why the socially efficient output of dye is lower than the level produced in the market equilibrium. e. How large would marginal external cost have to be in order for it to be socially desirable that no dye is produced? f. Now suppose that the $10 per unit damage will be incurred two years from now, rather than today. If the discount rate is r = 2-1, find the socially optimal dye output. How does your answer compare to that from part (c)? Explain.