下面是我遇到的一个高微题目，希望得到高人指点啊~
Consider an economy with two consumers, Abigail and Brian, and two goods, denoted
and . Abigail’s preference relation can be represented by the utility function
while Brian’s preference relation can be represented by the utility function .
(a) Given that aggregate wealth in this economy is divided evenly between Abigail and Brian, show that the representative indirect utility function can “rationalize” aggregate demand;
(b) Recall that the equivalent variation of a change in prices and income from
is defined as . If EV>0, what does this signify and why? If , and the change in prices are caused by the imposition of commodity taxes, then the deadweight loss (DWL) or excess burden of the taxes is given by , where ;
(c) Briefly explain why this measure may be viewed as a deadweight loss to (social) economic efficiency;
(d) Suppose that the initial aggregate budget constraint has
and . Using the representative indirect utility function given in (b) calculate the “aggregate” DWL of the imposition of a specific tax of 1 on good , that leads to the price of good rising to 2 (with the price of good remaining unchanged);
(e) Using the individuals’ indirect utility function derived in (a) calculate the two individual deadweight losses, . Explain why
does or does not equal DWL.