Nir Dagan, Esther Hauk, and Albrecht Ritschl

**Due Monday, 11 May, 1998**

**1.** Rafael has a utility function of
`u(x,y) =x ^{2} + 2y^{2}`
(

Note: In the printed Spanish version the goods are donated by

- Draw indifference curves of Rafael's utility function.
- What bundle will Rafael choose to consume if
`p`,_{x}= 1`p`and_{y}= 2`m = 6`? - Are Rafael's preferences homothetic? are they convex?
- Assume that
`p`and_{y}= 2`m = 6`. Is there a value of`p`in which Rafael has more than one optimal choice? If so, what is it?_{x} - Find the demand function for
`x`, and draw the corresponding demand curve when`p`and_{y}= 2`m = 6`.

**2.** Miguel consumes two goods (how not?) `x _{1}` and

- may we conclude that
`x`is normal or inferior, ordinary or Giffen? Explain your answer._{1} - does his behavior violates the weak axiom of revealed preference?

**3.** Susana choses the bundle `(6,6)` when the prices are `(6,5)`
and the bundle `(10,0)` when the prices are `(5,5)`.

- Does Susana violate the weak axiom of revealed preference?
- Is one of the bundles revealed preferred to the other? And if so what is it?

**4.** Eva has the utility function:
`u(x _{1},x_{2}) = ln(x_{1})
+ 0.5ln(x_{2})`.

- Find the demand functions.
- Draw an Engel curve of good
`x`._{1} - Eva has an income of a
`$100`, and the prices are`p`and_{1}= 2`p`. Find the change in the demanded quantity of_{2}= 1`x`if the price of_{1}`x`is now_{1}`1`. Decompose the change in quantity demanded to income and substitution effects.