Problem 3.
Suppose David spends his income (I) on two goods, x and y, whose market prices
are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny. (MUx = 1/x, MUy = 2/y)
(a) Derive his demand functions for x and y.
(b) Assuming px = $1 and py = $2, graph his Engel curve for x.
(c) Assuming I = $60 and px = $1, graph his demand curve for y.
(d) From the result of (a), is good x normal good or inferior good? Explain why.
Problem 4.
Consider three consumers with the respective utility functions
U
A(x, y) = √xy (MRS(x,y)=y/x)
U
B(x, y) = x + y (perfect substitutes)
U
c
(x, y) = min(x, y) (perfect complements)
(a) a. Assume each consumer has income $120 and initially faces the prices px = $1
and py = $2. How much x and y would they each buy?
(b) Next, suppose the price of x were to increase to $4. How much would they each buy
now?
(c) Decompose the total effect of the price change on demand for x into the substitution
effect and the income effect. That is, determine how much of the change is due to each of
the component effects.
(Hint 1: For agent A, what two properties determine the location of z, the reference point
for distinguishing the income and substitution effects?
Hint 2: For agents B and C, identify the substitution effect, i.e., the point z, graphically by
moving the new budget line up until it just touches the original indifference curve.).
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