Reference no: EM133907709
Question 1.
In this exercise you will analyze the supply-demand equilibrium of a city under some special simplifying assumptions about land use. The assumptions are: (i) all dwelling must contain exactly 1,500 square feet of floor space, regardless of location, and (ii) apartment complexes must contain exactly 15,000 square feet of floor space per square block of land area. These land-use restrictions, which are imposed by a zoning authority, mean that dwelling sizes and building heights do not vary with distance to the central business district, as in the basic model. Distance is measured in blocks.
Suppose that income per household equals $25,000 per year. It is convenient to measure money amounts in thousands of dollars, so this means y=25, where y is income. Next suppose that the commuting cost parameter t equals .01. This means that a person living ten bocks from the CBD will spend .01*10=.1 per year (in other words, $100) getting to work.
The consumer's budget constraint is c+pq=y-tx, which reduces to c+1500p=25-.01x under the above assumptions. Since housing consumption is fixed at 1500, the only way that utilities can be equal for all urban residents is for bread consumption c to be the same at all locations. The consumption bundle (the bread, nousing combination will then be the same at all locations, yielding equal utilities.
For c to be constant across locations, the price per square foot of housing must vary with x in a way that allows the consumers to afford a fixed amount of bread after paying his rent and his commuting cost. Let c* denote this constant level of bread consumption for each urban resident. For the moment, c* is taken as given. We'll see below, however that c* must take on just the right value or else the city will not be in equilibrium. Boost your grades with expert assignment help today!
(a) Substituting c* in place of c in the budget constraint c+1500p=25-.01x solve for p in terms of c* and x. The solution tells what the price per square foot must be at a given location for the household to be able to afford exactly c* worth of bread. How does p vary with location?
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