Assume that housing output is a function of the quantities of capital (k) and land (l) employed by a developer, y = h(l, k), where h( ) is the housing production function. Also, assume that the developer’s long-run cost function is c = rl + ik,
Assume that housing output is a function of the quantities of capital (k) and land (l) employed by a
developer, y = h(l, k), where h( ) is the housing production function. Also, assume that the developer’s
long-run cost function is c = rl + ik, where r =
(a) Draw an arbitrary cost-minimizing scenario for this developer using isoquants and iso-cost
lines. Identify the cost-minimizing bundle as (l*, k*). Be sure to plot k along the y-axis. Please
label your graphs. 5pt
(b) Within a city, the price of capital, i, does not typically vary with a development’s distance from
the city center. However, the price of land traditionally declines as distance from the center
rises. Using the cost-minimizing framework set up above, show how homes’ capital-to-land
ratios likely change as distance to the city center rises, holding housing output fixed. 5pt
(c) Does your answer from above do anything to explain the differences in the types of homes that
people occupy if living in downtown Chicago or its suburbs?
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