Ideology and Preferences of Politicians: Political scientists often assume that politicians have tastes that can be thought of in the following way: Suppose that the two issues a politician cares about are domestic spending and military spending. Put military spending on the horizontal axis and domestic spending on the vertical axis. Then each politician has some “ideal point” — some combination of military and domestic spending that makes him/her happiest.
A: Suppose that a politician cares only about how far the actual policy bundle is from his ideal point, not the direction in which it deviates from his ideal point.
(a) On a graph, pick any arbitrary “ideal point” and illustrate what 3 indifference “curves” would look like for such a politician. Put numerical labels on these to indicate which represent more preferred policy bundles.
(b) On a separate graph, illustrate how tastes would be different for a political conservative (who likes a lot of military spending but is not as keen on domestic spending), a liberal (who likes domestic spending but is not as interested in military spending) and a libertarian (who does not like government spending in any direction to get very large).
(c) This way of graphing political preferences is a short-cut because it incorporates directly into tastes the fact that there are taxes that have to pay for government spending. Most politicians would love to spend increasingly more on everything, but they don’t because of the increasing political cost of having to raise taxes to fund spending. Thus, there are really 3 goods we could be modeling: military spending, domestic spending and taxes, where a politician’s tastes are monotone in the first two goods but not in the last. First, think of this as three goods over which tastes satisfy all our usual assumptions — including monotonicity and convexity — where we define the goods as spending on military, spending on domestic goods and the “relative absence of taxes”. What would indifference “curves” for a politician look like in a 3-dimensional graph? Since it is difficult to draw this, can you describe it in words and show what a 2-dimensional slice looks like if it holds one of the goods fixed?
(d) Now suppose you model the same tastes, but this time you let the third good be defined as “level of taxation” rather than “relative absence of taxes”. Now monotonicity no longer holds in one dimension. Can you now graph what a slice of this 3-dimensional indifference surface would look like if it holds domestic spending fixed and has taxes on the horizontal and military spending on the vertical axis? What would a slice look like that holds taxes fixed and has domestic spending on the horizontal and military spending on the vertical axis?
(e) Pick a point on the slice that holds taxes fixed. How does the MRS at that point differ for a conservative from that of a liberal?
(f) Pick a point on the slice that holds domestic spending fixed. How would the MRS at that point differ for a libertarian compared to a conservative?
B: Consider the following equation u(x1,x2 ) = P −
¡ (x1 −a)2 +(x2 −b)2¢.
(a) Can you verify that this equation represents tastes such as those described in this problem (and graphed in part A(a))?
(b)What would change in this equation as youmodel conservative, liberal and libertarian politicians?
(c) Do these tastes satisfy the convexity property?
(d) Can you think of a way to write a utility function that represents the tastes you were asked to envision in A(c) and A(d)? Let t represent the tax rate with an upper bound of 1.