Nir Dagan, Esther Hauk, and Albrecht Ritschl
Due Monday, 11 May, 1998
1. Rafael has a utility function of
u(x,y) =x2 + 2y2
(x square plus 2y square)
Note: In the printed Spanish version the goods are donated by
x1 and x2.
- Draw indifference curves of Rafael's utility function.
- What bundle will Rafael choose to consume if
px = 1, py = 2
and m = 6?
- Are Rafael's preferences homothetic? are they convex?
- Assume that py = 2 and m = 6.
Is there a value of px
in which Rafael has more than one optimal choice? If so, what is it?
- Find the demand function for x, and draw the corresponding
demand curve when py = 2 and m = 6.
2. Miguel consumes two goods (how not?) x1 and
x2. He has an income of 50 Duros a week.
If the price of good x1 increases, and the income and
substitution effects go in opposite directions
- may we conclude that x1 is normal or inferior, ordinary or
Giffen? Explain your answer.
- 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(x1,x2) = ln(x1)
- Find the demand functions.
- Draw an Engel curve of good x1.
- Eva has an income of a $100, and the prices are
p1 = 2 and p2 = 1.
Find the change in the demanded quantity of x1 if
the price of x1 is now 1. Decompose
the change in quantity demanded to income and substitution effects.