Nir Dagan, Esther Hauk, and Albrecht Ritschl

**Due Monday, 18 May, 1998**

**1.** A consumer has the utility function
`u(x _{1},x_{2})=2log(x_{1})+2log(x_{2})`.
He had an income of

- Find the change in the net benefit (consumer's surplus) of
consuming good
`1`due to its price change. - Find the compensating and equivalent variations corresponding the price change.

**2.** A consumer consumes `10` units of a discrete
commodity. When the price changes from `$5` to `$6`
per unit he cuntinues to consume `10` units. Find the change
in in the gross and net benefit.

**3.** Marc and Toni have identical utility functions:
`u(x _{1},x_{2})=log(x_{1})+3log(x_{2})`.

Both Sara and Nuria have the following utility function:

__ v(x_{1},x_{2})=\/x_{1}+x_{2}

All four have an income of `m=$40` each. In addition `p _{2}=1`.

- Find the aggregate demand function for good
`1`. - The right wing government is interested in increasing income
inequality. It therefore takes
`$10`from Marc and gives them to Toni. Does the aggregate demand for good`1`changes? Explain your answer. - Now assume that the government
*alternatively*applies the policy to Sara and Nuria, instead of to Marc and Toni. What will be the new demand function? - Due to pressure from women's rights groups, the government decides to
abolish the previously mentioned policies and take
`$10`from Toni and give them to Nuria. What will be now the new demand function? Explain your answer.

**4.** The demand function is:

__ D(p)=1000/(\/p )

- What is the gross benefit when one unit is consumed?
- What is the change in consumers' surplus when the price
rises from
`1`to`5`? - Find the absuolute value of the elasticity of demand when
`p=1`and when`p=5`. What is the corresponding revenue for these two prices?