Nir Dagan, Esther Hauk, and Albrecht Ritschl
Due Monday, 18 May, 1998
1. A consumer has the utility function
He had an income of m=100 and the prices were
p1=p2=5. Afterwards, p1
has changed to 10.
- 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:
Both Sara and Nuria have the following utility function:
All four have an income of m=$40 each. In addition p2=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:
- 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?