# Problem set 5 of Economic Theory I

Nir Dagan, Esther Hauk, and Albrecht Ritschl

Due Monday, 18 May, 1998

1. A consumer has the utility function u(x1,x2)=2log(x1)+2log(x2). He had an income of m=100 and the prices were p1=p2=5. Afterwards, p1 has changed to 10.

1. Find the change in the net benefit (consumer's surplus) of consuming good 1 due to its price change.
2. 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(x1,x2)=log(x1)+3log(x2).
Both Sara and Nuria have the following utility function:

```          __
v(x1,x2)=\/x1+x2```

All four have an income of m=\$40 each. In addition p2=1.

1. Find the aggregate demand function for good 1.
2. 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.
3. 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?
4. 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 )```
1. What is the gross benefit when one unit is consumed?
2. What is the change in consumers' surplus when the price rises from 1 to 5?
3. 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?