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Solution to the practice problems 1. D. 6000/200=30 150/15=10. 2. D 3. C. 4. 1/4. Sort people from the poorest to the richest. Then, the first quarter of the population will earn nothing. So, the Lorenz curve passes through (1/4, 0). Lorenz curve also goes through (0,0) and (1,1). Hence, the area between the Lorenz curve and the 45 degree line is just the area of a triangle with a base of 1/4 and a height of 1, which is 1/2*1/4*1=1/8. The Gini coefficient is twice this area, which is 1/8*2=1/4. 5. D. 6. 0.4. ((10-1) /10+(10-2) /10+(10-7)/10)/5=0.4 7. 0.308. ([(10-1) /10]^2+[(10-2) /10]^2+[(10-7)/10]^2)/5=0.308 8. D. 9. E. 10. 2.5. 0.15*10+0.1*10=2.5 11. B. 12. bch. 13. ej. 14. bfe. 15. D. 16. Chips 1, French fries 0.5 17. A, E. 18. Chips 2, French fries 0 19. Chips 1, French fries 1 20. B. 21. 3.5. 0*15+0.05*5+0.20*10+0.10*10+0.05*5+0*15=3.5 22. 40. 1*15+1*5+0.60*10+0.60*10+0.40*5+0.40*15=40 23. 1.075. [0.05*1*5+0.20*0.60*10+0.10*0.60*10+0.05*0.40*5]/2=1.075 24. app’a’ 25. j’k’ 26. ftpp’f ’. As a result of moving to free trade, the country's domestic production decreases from bn to bf. The producer surplus decreases by bfpA whereas the consumer surplus increases by btpA, where A is the intersection between the vertical axis and a horizontal line that goes through p. The damage cost due to pollution decreases by pp'f'f. 27. flm'f'+rr't.. CS changes from btc to b'r'c. PS changes from afb to al'b'. Damage cost changes from aff'a' to al'm'a'. Tariff revenue changes from 0 to lrr'l'. So the efficiency loss is (btc+afb-aff'a'+0)-(b'r'c+al'b'-al'm'a'+lrr'l')=flm'f'+rr't.. 28. Mean independence: Measurement units doesn’t affect the inequality measure. Population replication invariance: Population size doesn’t affect the inequality measure. Symmetry (anonymity): Only the distribution of incomes, and not who has how much, determines the inequality measure. Pigou-Dalton transfer principle: A small amount from the rich to the poor cannot increase the inequality measure. 29. The term, “tragedy of commons,” describes the tendency that open-access resources, which are rivalrous and non-excludable, tend to be overexploited. This term was popularized by Hardin, and originates from an observation that communally-owned grazing land, or commons, tend to be overgrazed. This overgrazing occurs because of the stock externality, in which grazing by one cattle rancher negatively affects other ranchers through the depletion of the stock of grass. Open-sea fishery, among other resources, faces a similar problem because the fishers have little incentive to conserve the stock. A possible policy prescription is to define the property rights for the resource, so that the owner of the grazing land has an incentive to conserve the stock. Another policy prescription is to internalize the stock externality by making the users pay. For example, the individual transferable quota has been used to make the fishers pay for the usage of the stock of fish. Taxation on the use of stock can also achieve a similar effect. (163 words) 30. D 31. D 32. 0.13. 33. bribe 34. A. 35. C. If both produce potatoes: Expected Utility = [(4+4)/2]^0.5 = 2 If both produce wheat: Expected utility = (2/5)(3/5)(2)[(16+0)/2]^0.5 + (2/5)(2/5)[(16+16)/2]^0.5 + (3/5)(3/5)[(0+0)/2]^0.5 = 1.998 If 1 produce wheat and 1 produce potato: Expected utility = (2/5)(1)[(4+16)/2]^0.5 + (3/5)(1)[(4+0)/2]^0.5 = 2.113 36. D. Let p be the probability of good weather. The expected utility from potatoes is E[u]=4, and that from wheat is E[u]=p x 5 + (1-p) x 3 = 3+2p. So, one prefers potato production if and only if 4>3+2p, or p<0.5. 37. B. Note that the weather is perfectly negatively correlated. Thus, when the weather is good for Andrew, it is bad for Ben. This in turn means that Andrew's profit from wheat production is 25 and Ben's profit is 9. Therefore, the total profit is 34, and each will get 17. If the weather for Andrew is bad, then it is good for Ben. This means that Andrew's profit is 9 and Ben's profit is 25. Again, the total profit is 34, and each will get 17. In sum, the wheat production provides a profit of 17 with probability one (regardless of the probabilities of good weather for Andrew or Ben). Therefore, expected utility from wheat production is sqrt(17), which is obviously larger than that from potato production (i.e. sqrt(16)=4). 38. C. 39. D. 40. capital dilution