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ECON 4402 - Microeconomic Theory

Practice questions for mid test

2022

1. A person who consumes two goods has preferences that are represented by the utility function max(x1 ,x2 ). Verify that these preferences are transitive.

2. An individual consumes two goods,  x1   and x2 .   His utility function is u(x1 ,x2 )  = [min(2x1 + x2 ;x1+ 2x2 )]2 . Verify if the utility function is homogeneous and if so, state its degree.

3. A consumer has preferences that are represented by the utility function u(x1 ,x2 ) = x1(2)x2 + 4lnx1 + 2lnx2 .

(a) Find her Marshallian demand as a function of prices (p1 ,p2 )

(b) Find her indirect utility function.

4. Suppose that your friend prefers a certain outcome of $20 to a lottery that pays $100 with probability 1/4 and $0 with probability 3/4.  Also suppose that he prefers lottery A to lottery B, described as below:

❼ Lottery A: outcome of $100 with probability 1/8, and $0 with probability 7/8; 

❼ Lottery B: outcome of $20 with probability 1/2, and $0 with probability 1/2.

Is there a Von Neumann–Morgenstern utility function that is consistent with your friend’s preferences? If so, describe it. If not, explain why.

5. Consider a situation in which a consumer has to choose a bundle that can include 3 dif-

ferent goods, x1 , x2  and x3 . Preferences are represented by the function u(x1 , x2 , x3 ) = 3(x1x2x3 )1/3 . Find the Marshallian demand function for each good and the indirect util- ity function.