hw2ans - Department of Agricultural and Resource Economics...

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1 Department of Agricultural and Resource Economics EEP101/ECON125 University of California, Berkeley David Zilberman Solutions to Problem set 2 1. Uncertainty (Weitzman’s model, see Chapter 6, pp11-16). We know that MSC = 2 + x, MB = 20 – 0.5 x, Thus social optimal outcome is when MSC = MB Î 2 + x = 20 – 0.5 x Î x* = 12 . If government believe that MB H = 30 – 0.5 x, they will choose output standard such that MSC = MB H Î 2 + x = 30 – 0.5 x Î x H = 18.7 . If the government like to use tax, and they believe that the optimal outcome should be 18.7 as calculated above, then tax rate t* = MSC (x H ) = 2 + 18.7 = $20.7. Since the true demand is MB = 20 – 0.5 x, by t* = MB = $20.7 Î x H TAX = (20 – 20.7) * 2 = -1.4 < 0, thus the outcome will be x H TAX = 0 (nonnegativity constraint). If government believe that MB L = 10 – 0.5 x, they will choose output standard such that MSC = MB L Î 2 + x = 10 – 0.5 x Î x L = 5.3 . If the government like to use tax, and they believe that the optimal outcome should be 5.3 as calculated above, then tax rate t* = MSC (x L ) = 2 + 5.3 = $7.3. Since the true demand is MB = 20 – 0.5 x, by t* = MB = $7.3 Î x L TAX = (20 – 7.3) * 2 = 25.4 . (a) Under direct control policy, if the government overestimated the demand, the output is 18.7; if the government underestimated the demand, the output is 5.3. The social optimal output level is 12, thus the deviation is +/- 6.7. Under tax policy, if the government overestimated the demand, the output is 0; if the government underestimated the demand, the output is 25.4. The social optimal output level is 12, thus the deviation is –12 and + 13.4. Conclusion, direct control policy is more desirable as it leads less deviation from the social optimum. (b) If true demand is MB = 20 – 3 x, Î x* = 4.5 High demand is MB H = 30 – 3 x, Î x H = 7, x H TAX = 3.7 Low demand is MB H = 10 – 3 x, Î x L = 2, x L TAX = 5.3 Now tax policy is more desirable because it leads less deviation from the social
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This note was uploaded on 08/01/2008 for the course ECON 101 taught by Professor Wood during the Spring '07 term at University of California, Berkeley.

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hw2ans - Department of Agricultural and Resource Economics...

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