A consumer's utility function is given by

u(x1, x2) = p

x1 + p

x2

3

Let p1 and p2 represent the prices of x1 and x2, and let m denote income.

(a) [5 points] Write down the Lagrangean for the utility maximization problem and

all the first order conditions.

(b) [5 points] Find the utility maximizing bundle as a function of prices and income.

(c) [5 points] Use the slutsky equation to find the slope of Hicksian demand for x1

with respect to p1, given p2 = 1.

(d) [5 points] Is the expenditure function for this consumer concave or convex?

Why? [Hint: You don't need to find the expenditure function to answer this, and you

can use a result from the slides.]

(e) [5 points]Write down the Lagrangean for the expenditure minimization problem

(for reference utility level u) and all the first order conditions.