University of Victoria

Economics 312 Urban Land Economics

Martin Farnham Problem Set #5 Note: Answer each question as clearly and concisely as possible. Use of diagrams, where appropriate, is strongly encouraged. Problem sets are ungraded. However, developing a careful understanding of the problems will, on average, dramatically improve your exam performance. True/False/Uncertain For each question, state clearly whether you find the statement to be true, false, or uncertain. Then provide a clear explanation. Answers without explanation will be given zero points. 1) Advocates for affordable housing in Victoria are likely to oppose restrictions on conversion of single-family homes to duplexes. True. Duplexing of homes increases the supply of housing. Increased supply should lower the price of housing, thereby making it more affordable. 2) Relative to the social optimum, individuals are likely to overinvest in locks for their homes. True. If locks just shift crime from one household to another, then when you buy a lock you take into account the benefit it offers you (in terms of added protection) and the cost to you (what you pay for the lock plus installation). You don’t take into account the fact that the lock increases the probability that your neighbor will be broken into. The shifting of crime is a negative externality. This means that people will tend to overinvest in locks relative to the socially optimal level of investment. 3) An increase in interest rates should cause equilibrium rents to rise. True. A landlord’s costs include capital costs. If a building costs $1 million dollars, then the cost of owning that building is whatever is foregone as a result of owning it. If you take $1 million out of your bank account and put it into a building, you forego the annual interest on that $1 million. That is the cost of owning the building. If you could earn 6% a year in some alternative investment, then the capital cost associated with a $1 million building is $60,000 per year. The higher interest rates are (that is, the more you could be making in some alternative investment) the higher your costs are. In equilibrium, we should expect rents to exactly equal landlord’s costs (capital costs, maintenance, depreciation, etc.). If interest rates rise, so that costs rise above market rents, then some

landlords will leave the market (convert their buildings to other uses). This will reduce the supply of housing units and drive up rents until, in equilibrium, rents equal costs. Therefore, an increase in the interest rate should increase rents in equilibrium. Note that owner costs should rise as well (because owners who live in their own units also experience an opportunity cost associated with tying up money in the house). 4) If a landlord experiences capital gains this year, her costs will be higher next year (holding everything else constant). True. We know that capital gains this year lower the landlord’s costs this year. But if landlords costs are V(i+d+m-g), and V goes up this year, then next year’s capital costs will be higher (assuming (i+d+m)>g). If your building was worth $1 million at the start of this year, but is worth $1.2 million by the end of this year, then your capital costs will rise from (1 million)*(i+d+m-g) this year to (1.2 million)*(i+d+m-g) next year. Short Answers 1) Using diagrams to illustrate your answer, explain why an increase in demand for rental housing would cause landlords to increase their maintenance activities. Landlords don’t perform maintenance out of kindness. They perform maintenance to improve the quality of their residences in order to be able to charge higher rent. They will perform maintenance up to the point where MB=MC. That is, they’ll raise the level of quality of the housing unit to the point where the marginal cost of an extra unit of quality is equal to the marginal extra rent the landlord gets from an extra unit of quality. In the diagram below, I assume that total willingness to pay for quality is linear, but that the total cost of quality is convex (meaning that given a unit of fixed size, eventually it becomes very costly to increase quality any further—you’d have to put a lot of maintenance into a 1-bedroom apartment on Hillside in order to raise the quality level to that of Buckingham Palace). Since the landlord is trying to maximize TR-TC, we can think of the problem as maximizing the distance between these two curves:

As demand for housing quality rises, the rents earned for each level of quality rise. This implies a steeper TR curve. With a steeper TR curve, the point where profits are maximized moves further to the right. For those who prefer thinking about setting derivatives equal, note that the point where TR’-TC is maximized is the point where MR=MC. That is, where the marginal extra rent earned from an incremental increase in quality is equal to the extra cost of an incremental increase in quality. An increase in demand for housing can be thought of as an increase in the marginal willingness to pay for an extra unit of quality. At this higher willingness to pay, landlord’s can afford to ramp up quality to a level where the marginal cost of providing quality (the slope of the TC curve) is a bit higher. 2) Consider the decision to commit a robbery. Using a simple marginal cost – marginal benefit diagram, illustrate the effect of each of the following policies (separately…don’t combine the policies) on the equilibrium level of crime in a city. a) Increased police presence on the street.

TR TC

Q*(TR’))

Q*(TR) quality

$ TR’

Increased police presence makes the probability of capture rise. This raises the expected cost of each crime committed to the criminal. This can be viewed as a shifting up of the marginal cost of crime curve, which should lead to a decline in the equilibrium number of crimes committed. b) Cutting of resources to prosecutors so that conviction rates fall.

Cutting resources to prosecutors should cause the conviction rate to fall. Presumably with less help doing research and less good quality prosecuting attorneys, fewer criminals will go to jail. We can think of this as shifting down the marginal cost curve (since the expected punishment for committing a crime falls when the probability of being convicted falls). This should cause the equilibrium number of crimes to rise. c) Rules that make it illegal to leave valuables in parked cars.

Public campaigns to reduce targets for criminals are common. I have often had notices placed on my window when parking in the Yates Street Parkade. The notices warn me to place valuables in the car out of view of potential thieves. The hopes is that if enough people comply with such notices, criminals will move their activities elsewhere. If people do comply and stop leaving valuables in cars, the marginal benefit associated with breaking into a car will decline, and we would expect the equilibrium number of break-ins to decline. d) Subsidies for deadbolts that make houses more difficult to break into. The picture for this case would be the same as the picture for (c). The probability of success, and therefore the expected loot collected in a robbery, declines as a result of more doors being impassable. This makes crime less worth committing. Note that it may also cause crime to shift to jurisdictions that don’t offer the deadbolt subsidy. 3) Consider the filtering model of housing. Suppose a local government institutes a “luxury tax” surcharge on local property taxes so homes greater than $500,000 in value

are subject to double the property tax rate of lesser-value homes. How will this affect the middle-income segment of the housing market? In the filtering model the housing market is segmented into different sub-markets (for high, medium, low quality housing). These markets are interrelated due to substitutability across markets and due to the effect that prices in one market have on the rate at which housing “filters down” to other markets. The luxury tax reduces the willingness to pay for high-end housing. This reduces the incentive for landlords to maintain a high level of quality, which leads the high-end housing stock to deteriorate more quickly. This increases the rate at which it filters down to the middle-quality segment of the housing market. So the supply of medium quality housing rises over time. At the same time, the demand for medium quality housing rises, as some people substitute away from the high-end housing. So both supply and demand for medium quality housing rise. This means quantity rises, and rents either rise or fall (depending on whether the supply shift or demand shift dominates). Depending on whether rents rise or fall in the medium-quality segment of the housing market, incentives to maintain medium-quality properties will either rise or fall. If they rise, then housing will filter down to the low-end of the market at a slower rate, reducing the supply of low-end housing and raising rents. On the other hand, if rents in the medium-quality segment of the market fall, then maintenance in that segment will decline and housing stock will filter down at a faster rate, thus increasing the supply of low-quality housing. Note that this process takes time. While a luxury tax will have immediate impacts on demand for housing on the medium-quality segment of the market, the supply-side effects take much longer. Housing doesn’t deteriorate overnight. So keep in mind long-run vs. short-run effects of such a policy shift. In this case, a short run increase in rents (from demanders substituting away from the high end of the market) will be followed by a longer-term increase in supply (due to filtering down) that will cause rents to fall back to some extent. 4) Discuss the pros and cons of three programs for providing housing to the poor. One basic thing to keep in mind is that the justification for a policy intervention on efficiency grounds can only be made if there is some market failure associated with homelessness. I would argue that market failures do exist. First, there are negative externalities associated with homelessness. Kids of the homeless suffer, people don’t like seeing homeless in the street, and there may be impacts on public health (or at least on the taxpayer if being homeless leads to higher medical bills paid for by the public health system in Canada). Second, the homeless may face credit constraints that don’t allow them to make the security deposit needed to get into a cheap apartment. Banks won’t lend to the homeless due to problems of asymmetric information (and the inability of the homeless to provide collateral for the loan). This too can be thought of as a market failure that justifies government intervention (because it can be social-welfare-enhancing).

a) Housing vouchers. b) A low-income housing subsidy. c) Rent-control.