Advanced Microeconomics
Instruction:
1. The utility maximization problem of a consumer is given by
max X1, X2
U(X1,X2)=X1Ξ±X21-Ξ±
s.t. π1x1 + π2x2 = π
+ |
Where πΌ β ,[0,1] & π₯1, π₯2 β real number . Assume that price vectors is π = (π1, π2) > 0,
and income π > 0.
a) Find the Marshallian demand functions
b) Find the budget share and price of x1 and income elasticity
c) Show that the Walrasian demand function is homogeneity of degree zero in
(p, m)
d) Show that π(p, u) is homogeneous of degree one in π
e) Show that π£(p, m) is strictly increasing in m and non-increasing π
f) Show that Hicksian demand functions is homogeneous of degree zero in p.
g) Evaluate the Walrasian demands x(p, m) at m = e(p; u), and show that Walrasian and Hicksian demands coincide, that is,
x(p, e(p, u)) = h(p; u):
h) Evaluate the Hicksian demands h(p, u) at u = v(p, m), and show that Hicksian and Walrasian demands coincide, that is,
h(p, v(p, m)) = x(p, u):
i) Evaluate the indirect utility function v(p, m) at m = e(p, u), and show that v(p, e(p, u)) = u:
j) Evaluate the expenditure function e(p, u) at u = v(p, m), and show that e(p, v(p, m)) = m:
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