Microeconomics – class 4
Agnieszka Wiszniewska-Matyszkiel
1.
Calculate the indirect utility function and demand correspondence for utility functions u(x1, x2) equal to
a) a1· x1+ a2· x2 for ai > 0 (perfect substitutes);
b) min{a1· x1, a2· x2} for ai > 0 (perfect complements);
c) xa11 · xa22 for ai > 0 (Cobb-Douglasa utility).
2.
Calculate the indirect utility function and demand correspondence for utility function (called CES by economists) u(x1, x2) = (xρ1+ xρ2)1ρ.
Hint! – first check, how concavity or quasi-concavity of u is related to ρ.
3.
Can v be the indirect utility function of a consumer with locally nonsatiated preferences and contuinuous utility function?
Assuming, that it is possible, calculate x.
a) v(p, m) = 2 ln(m) − ln(p1· p2) + C;
b) v(p, m) = √p m3
1+p2−1 if p1+ p2 > 1, 0 otherwise;
c) v(p, m) = 2010mp
1+p2.
What was the assumption? Is really the calulated x equal to the demand?
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