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