ECON 4410/6410 Fall 2022 Assignment #3

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ECON 4410/6410

Fall 2022

Assignment #3

1.  Suppose Marie has the following ranking over the policy characteristics of a presidential candidate:

Prefers lower taxes  ●  Prefers larger military  ●  Shares her religious beliefs.

(a)  Suppose you work for a think tank, doing research that involves predicting voter

preferences over candidates. Suppose there are three candidates:

· John Jackson, who favors lowering taxes and increasing military spending.   · Jack Jameson, who favors lowering taxes and shares Marie’s religious beliefs. · James Johnson, who favors increasing military spending and shares Marie’s

religious beliefs.

Use these to derive preference relations between each pair of candidates, based on these platforms. Are these preferences transitive? What is Marie’s preference ordering over all candidates?

(b) Now suppose she receives utility based on the policies enacted by these candidates

if elected, as follows:

· Utility of 8 if taxes are lowered after the election (and 0 if they are not).      · Utility of 6 if military spending increases after the election (and 0 otherwise). · Utility of 4 if the president shares her religious beliefs (and 0 otherwise).

What is Marie’s utility from each candidate, assuming their respective platforms would be enacted with probability 1 upon election? Does the ranking of numerical utilities match the preference ordering you derived in part (a)? What is the benefit of assuming numeric preferences over simply preference relations?

(c) Now suppose due to uncertainty as to which party will win the Senate, there is only a 25% chance that taxes could be lowered after the election and a two thirds probability that military spending could be increased.  What is Marie’s expected utility from each candidate?  Does this uncertainty change who she will vote for in the election?

2. Draw the indifference curves for the following bivariate utility functions (for q1 , q2  > 0): (a) u(q1 , q2 ) = q 1(a)q2(8), where α + β < 1.

(b) u(q1 , q2 ) = α ln(q1 ) + β ln(q2 ).

(c) u(q1 , q2 ) = q1 + q2 .

3.  M.A . students only.  Suppose a consumer has a utility function over a bundle of two goods, u(q1 , q2 ).   Suppose her preferences over bundles are strictly monotonic, such that  > 0 for each good j = 1, 2.  Use this fact to show that her indifference curve slopes downward for any fixed level of utility.