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:
• all dwellings are situated within apartment complexes,
• all dwellings must contain exactly 1,500 square feet of floor space, re-
gardless of location, and
• 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 (CBD). 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 that y = 25, where y is income. Next suppose that the commuting cost parameter t equals 0.01. This means that a person living ten blocks from the CBD will spend 0.01 × 10 = 0.1 per year (in other words, $100) getting to work.
The consumer's budget constraint is c + pq = y − tx, which reduces toc + 1, 500p = 25 − 0.01x under the above assumptions. Since housing con- sumption is fixed at 1,500, 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, housing 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 consumer to afford a fixed amount of bread after paying her rent and her commuting cost. Let c∗ denote this
ECO333 Problem Set Page 2 of 3
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.
(f) Suppose that the population of the city grows to 255,000. Repeat (c), (d), and (e) for this case (but don't repeat the calculation involving c∗ =15.5). Explain your findings. How does population growth affect the utility level of people in the city? The answer comes from looking at the change in c∗ (since housing consumption is fixed at 1,500 square feet, the utility change can be inferred by simply looking at the change in bread consumption). Note that because they are fixed, housing consumption doesn't fall and building heights don't rise as population increases. Are the effects on r and x̄ the same?
(g) Now suppose that the population is back at 200,000 (as in (c)) but that rArises to 3 (that is, farmers now offer $3000 rent per square block). Note that the x̄ value can't change as rA rises (what is the reason?). Repeat (d) and (e) for this case. Compare your answers with those in (f).
(h) Now suppose that instead of being located on a flat, featureless plain, the CBD is located on the ocean (where the coast is perfectly straight). This means that only a half-circle of land around the CBD is available for housing. How large must be the radius of this half-circle to fit the population of 200,000 residents? Using your answer, repeat (d) and (e), assuming that all parameters are back at their original values. Are people in this coastal city better or worse off than people in the inland city of (c) and (d)? (Assume unrealistically that people don't value the beach!) Can you give an intuitive explanation for your answer?
(i) Finally, focus again on the inland city, and suppose that the zoning authority imposes a building height restriction. This restriction limits housing square footage per block to 7,500, half the previous amount. The cost of building materials per square block falls from 90 to 43 (note that the cost is less than half as much because of diminishing returns). Find the new value of x̄ (compare the answer in (h)), and repeat (d) and (e). How does the height restriction affect the utility of urban residents? Explain intuitively why this effect emerges. Does the restriction seem to be a good policy?
1. In this exercise, you will analyze the supply-demand equilibrium of a city under some special...
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 dwellings must contain exactly 1500 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...
multi step problem. thank you! 1. Balancing Rent and Commuting Costs (6 points) Suppose that a household resides in an urban area at a distan of 8 miles from downtown. The household occupies a residential lot measuring 5000 square feet, and at this distance from downtown land rent is $2.00 per square foot per year. One of the members of the household must commute to downtown for work five days a week (50 weeks per year). The total cost of...
Consider a city that conforms to the assumptions of the basic monocentric city urban model studied in class, with one key difference. The difference is that the urban residents experience crime, which varies in intensity across the city. The level of crime, as measured by the probability of being robbed on the street, is highest at the CBD. The probability of being robbed falls gradually as distance from the CBD increases, and it reaches zero 5 miles out from the...
(C only please) Consider a city that conforms to the assumptions of the basic monocentric city urban model studied in class, with one key difference. The difference is that the urban residents experience crime, which varies in intensity across the city. The level of crime, as measured by the probability of being robbed on the street, is highest at the CBD. The probability of being robbed falls gradually as distance from the CBD increases, and it reaches zero 5 miles...
18 Suppose that the demand and supply schedules for rental apartments in the city of Gotham are as given in the table below. Instructions: Enter your answers as whole numbers. a. What is the market equilibrium rental price per month and the market equilibrium number of apartments demanded and supplied? Market equilibrium rental price is: Market equilibrium quantity is: b. If the local government can enforce a rent-control law that sets the maximum monthly rent at $1,500, will there be...
1. A self-employed woman marries the man she has been paying to do her accounting. After they marry they decide there is no point continuing to write a check to him since they are now one-household. What effect does this have on GDP? Select one: a. None, since only their legal status changes and the same amount of productive activity is being done. b. GDP decreases because his accounting services were an intermediate good and are now a final good....
1. When it comes to financial matters, the views of Aristotle can be stated as: a. usury is nature’s way of helping each other. b. the fact that money is barren makes it the ideal medium of exchange. c. charging interest is immoral because money is not productive. d. when you lend money, it grows more money. e. interest is too high if it can’t be paid back. 2. Since 2008, when the monetary base was about $800 billion,...