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Microeconomics — class 2

1.

Check properties of the preference relation from excercise 9 from previous class (continuity, monotonicity, strict monotonicity, local nonsatiation, concavity and strict concavity).

2.

Prove or find a counterexample:

a) If there exists a continuous utility function for , then  is continuous.

b) If there exists a concave (strictly concave) utility function for , then  is convex (strictly convex).

c) If there exists a monotone (strictly monotone) utility function for , then  monotone (strictly monotone).

d) Every utility function for monotone (strictly monotone) preferences is monotone (strictly monotone) .

e) Every utility function for continuous preferences is continuous.

3.

Maximize Cobb-Douglasa utility function u(x1, u2) = xa1·xb2over Walrasian budget set Bp,m.

4.

Maximize perfect substitutes utility function u(x1, u2) = a·x1+b·x2over Walrasian budget set Bp,m.

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