Question
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
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.
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