Consider once again the combination of market failures outlined in Problem 3. Recall that the demand for wood pulp is described by P = 500 − 10Q, where Q is measured in thousands of units. The long-run cost of production exhibits constant returns to scale: LAC = LMC = 150. Producing a unit of wood pulp generates one unit of pollution, and the marginal external cost is estimated to be 100 per extra unit of pollution.

a. Create a spreadsheet similar to the one shown to model this setting. In the spreadsheet, cells B10, C10, and D10 contain numerical values. The entries in rows 15 and 19 and cell E10 are computed by formulas linked to the numerical cells.

b. Using the spreadsheet, confirm the output and price results for each of the analyst’s recommendations in Problem 3. Then find the optimal regulatory policy using the spreadsheet’s optimizer. That is, maximize total benefit by adjusting the output and tax cells.

c. Now suppose that the wood pulp producers can clean up part or all of their pollution at a cost. The total cost of cleaning up u units of pollution is: 5u²; that is, it increases quadratically. By cleaning up pollution, producers avoid any tax. Thus, the government’s tax revenue is given by R = t(Q − u), and the firms’ total pollution-related costs are t(Q − u) + 5u² (cell D19). Find the optimal output, tax, and cleanup.

Transcribed Image Text:

COPING WITH AN EXTERNALITY Market Demand MCEXT P- 500-10Q 150 100 Quantity Clean Up (u) Price ax 10 10 12 13 Con Surp Net Profit Govt Rev External Cost Total Benefit 15 16 17 18 19 2,500 1,000 2,000 Gross Profit tax +Clnup cost tax - MCu 2,500