Quality of Life Indexes: Every year, various magazines publish lists of “The 10 Best Cities for Living" or “The 10Worst Cities”. These lists are constructed by magazines weighting various factors such as climate, public amenities (like school quality and crime rates), local taxes and housing prices. Economist often sneers at these lists. Here is why.
A. Consider two cities that are identical in every way —same climate, same public amenities, same housing prices. Suppose for simplicity, unless otherwise stated, that everyone rents housing and everyone has the same tastes and income.
(a) Begin by drawing two side-by-side graphs of the housing markets in city A and city B.
(b) Suppose city A elects a new mayor who is superb at what he does. He finds ways of improving the schools, lowering crime and building better public parks — all while lowering local tax rates. What will happen to the demand for housing in city A? What about in city B?
(c) Depict the new equilibrium. Will housing prices still be the same in the two cities? Why or why not?
(d) Last year, two magazines independently ranked the quality of life in city A and city B as equal. This year, one magazine ranks the quality of life in city A higher than in city B and the other does the reverse. When pressed for an explanation, the first magazine highlights all the wonderful improvement in city A while the second one highlights the “excessively high” housing prices in city A and the “housing bargains” in city B. Which magazine is right?
(e) What happens to the population size in cities A and B? What happens to the average house and lot size in cities A and B?
(f) True or False: If city A is large relative to the national housing market, the mayor’s actions make everyone in the country better off — i.e. not all of the benefits of the mayor’s ingenuity stay in city A.
(g) If you like public amenities more than the average person, will you be better off? What if you like them less than the average person?
(h) True or False: If city A is small relative to the national housing market, the primary beneficiaries of the mayor’s actions are landlords in city A (i.e. those who owned land and housing in city A prior to the mayor’s actions).
B. Suppose that individuals have tastes over housing h, consumption x and public amenities y and these tastes can be represented by the utility function u (h,x, y) = h0.25x0.75y. Suppose everyone rents rather than owns housing.
(a) In city A, the average resident earns $50,000 in income, faces a rental price for housing equal to $5 per square foot, and enjoys amenity level y = 10. Assuming everyone maximizes utility, what utility level does the average resident attain? (Hint: Note that y is not a choice variable.)
(b) Suppose the housing market across the nation is in equilibrium. If households can move across cities to maximize utility, can you tell what this implies about the utility level households attain in city B?
(c) Now suppose the new mayor in city A is able to increase the public amenity level y from 10 to 11.25. If utility for residents remains unchanged because of an increase in housing prices, how much will housing consumption have to fall for each household?
(d) Suppose that city A is small relative to the nation — and thus does not affect housing price elsewhere. Can you tell how much the rental price of housing must have increased from the initial price of 5 as a result of the mayor’s innovation?
(e) Are renters in city A better off as a result of the mayor’s innovations? What about landlords who own land and housing?