Demand and Slutsky

There are two goods, 1 and 2 and Abby's preferences are given by the utility function:

u(x1, x2) = ln(x1) + (1 )ln(x2) where x1 the quantity consumed of good 1 and x1 the quantity consumed of good 2 and

0 < < 1. Take good 2 to be numeraire and let p1 = 1 and m = 10

(a) Derive the demand for good 1 as a function of .

(b) Sketch the Engel curve for = 1/2.

(c) Suppose now, maybe as the result of a production crisis, the price for good 1 increased from 1 to 2. Calculate the new demand.

(d) Explain how much of the change in demand is due to the income effect, how much is due to the substitution effect for = 1/2. Is good 1 a normal good?

(e) How do income effect and substitution effect change with ? Explain your results.