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) Derive the uncompensated demand functions and indirect utility functions for both Abigail and Brian;
(b) 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;
(c) 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 ;
(d) Briefly explain why this measure may be viewed as a deadweight loss to (social) economic efficiency;
(e) 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 goodrising to 2 (with the price of goodremaining unchanged);
(f) Using the individuals’ indirect utility function derived in (a) calculate the two individual deadweight losses,. Explain why does or does not equal DWL.