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.
- 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. Hints: Remember that consumer surplus is found by using the formula for the area of a triangle, in this case:
.5*(500-E10)*B10. Total benefit is the sum of consumer surplus, net profit, and government tax revenue minus the external costs associated with pollution.
- 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.
- 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 5u ^{2 }; that is, it increases quadratically. By cleaning up pollution, producers avoid any tax. Thus, the government’s tax
A | B | C | D | E | F | G | H | ||||
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2 | COPING WITH AN EXTERNALITY | ||||||||||
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4 | Market Demand | LMC = LAC | ^{MC }EXT | ||||||||
5 | P = 500 – 10Q | 150 | 100 | ||||||||
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8 | Quantity | Tax | Clean Up (u) | Price | |||||||
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10 | 10 | 0 | 0 | 400 | |||||||
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13 | Con Surp | Net Profit | Govt Rev | External Cost | Total Benefit | ||||||
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15 | 500 | 2,500 | 0 | 1,000 | 2,000 | ||||||
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17 | Gross Profit | tax+clnup cost | tax – MCu | ||||||||
18 | |||||||||||
19 | 2,500 | 0 | 0 | ||||||||
20 |
revenue is given by R = t(Q – u), and the firms’ total pollution related costs are t(Q – u) + 5u ^{2 }(cell D19). Find the optimal output, tax, and cleanup. ( Hint:Maximize total benefits subject to cell E19 equaling zero. Remember that the firms will reduce pollution up to the point that the tax/unit equals the MC of cleaning up an extra unit and note that MC = 10u.) Explain your results.