microeconomics-cost benefit analysis - 經濟

不好意思 是經濟新手 一點概念都沒有 所以不曉得算得對不對^^"
請大家幫我修正觀念和算法
謝謝^__^

題目：a country imports 3 billion barrels of crude oil per year and
domestically produces another 3 billion barrels of crude oil per year.
The world price of crude oil is $18 per barrel. Assuming linear
schedules, economists estimate the price elasticity of domestic supply
to be 0.25 and the price elasticity of domestic demand to be 0.1 at
current equilibrium.

(a) consider the changes in social surplus that world result from
imposition of a $6 per barrel import fee on crude oil that would
involve annual administrative costs of $50 million. Assume that the
world price will not change as a result of the country imposing
the import fee, but that the domestic price will increase by $6 per
barrel. Also assume that only producers, consumers and
taxplayers(government) within the country have standing.

Determine the quantity consumed, the quantity produced domestically,
and the quantity imported after the imposition of the import fee,
and estimate the annual net social benefits of the import fee policy.

想法：很簡單的代入彈性需求公式(斜率倒數*18/6=0.1) 得到需求斜率= -30,
再代入P=18, Q=6 得到y=-30x+198這條需求線
所以代入P=24, 得到Q*=5.8

因此知道quantity consumed=5.8
quantity produced domestically 還是3
quantity imported after the imposition of import fee=5.8-3=2.8

同樣，代入彈性供給公式(斜率倒數*18/6=0.25) 得到供給斜率=12
代入P=18, Q=6 得到y=12x-54
所以代入P=24, 得到Q*=6.5

這樣就可以算出消費者剩餘 = 6*5.8+0.5*0.2*6 = 35.4
跟生產者剩餘 = 6*6+0.2*0.5*6 = 37.5

所以NSB=-35.4+37.5-0.05=2.05
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(b) assume the marginal excess burden of taxation in the country is 0.25,
re-estimate the net social benefits assuming that 20% of the increase
in producer surplus is collected as profit tax under the existing
system. Assumeing that increases in tax revenue from the profit tax
minus the cost of administrating the import fee are used to reduce
domestic taxes.

想法： 就只是很簡單的代入公式
NSB=消費者剩餘+生產者剩餘+ [(1+METB)*△GR]
=-35.4+37.5+[(1+0.25)*(37.5*0.2-0.05)]
= 11.4125
==============================================================================
(c) the reduction in the country's demand for imports may affet the
world price of crude oil. Assuming that the import fee reduces the
world price from$18 to $16 per barrel, the after tax domestic price
is $16+$6=$22 per barrel, a net increase in domestic price of $4 per
barrel, repeat (a) and (b).

想法： 我看不太懂這題@@"
這是指需求價格變成$16, 所以代入彈性公式(斜率倒數*16/6=0.1)
得到斜率＝-26.67
再用P=16, Q=6去代 得到Y=-26.67x+176
所以if p=22, x=5.775

因此知道quantity consumed=5.775
quantity produced domestically 還是3
quantity imported after the imposition of import fee=2.775 ???

至於供給彈性就沒有變 跟a剛剛算的一樣？
所以if p =22 x =6.33

這樣就可以算出△CS=6*5.775+0.225*0.5*6=35.325
△PS=4*6+2*4*0.33=24.66
NSB=-35.325+24.66-0.05=-10.715

至於考慮到METB (repeat (b))
NSB=-35.325+24.66+(1.25*(24.66*0.2-0.05))=-4.61084
===============================================================================

不好意思問題那麼長
請問一下我的觀念跟算法正確嗎@@"
這對版上的大大可能是小兒科
可是我相當不確定我的答案 搞不好全部都算錯>"<

還請各位大大指教

謝謝^___^




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