Port Alder Rent Control: Shortage, Elasticity and Time Horizon
Port Alder is a mid-sized city where the private rented housing market is in equilibrium at $1,800 per month and 40,000 tenancies. The city council, responding to complaints that nurses and teachers cannot afford rents, imposes a legal maximum rent of $1,200 per month. A housing consultancy estimates that at $1,200 landlords would offer 28,000 units, while tenants would demand 52,000. The consultancy also estimates a price elasticity of supply of 0.6 in the first year and 1.4 after five years; demand elasticity is -0.3 in the first year and -0.8 after five years. Landlords say they will convert flats to short-term holiday lets, which are outside the cap. The council has no plans to build social housing. Tenants' groups argue that the measure protects existing residents. The council wants to know whether the policy will still look successful after five years.
1. Calculate the shortage at $1,200 and explain why the elasticity estimates matter for the council.
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At the capped rent of $1,200, quantity demanded is 52,000 and quantity supplied is 28,000, so the shortage is 52,000 - 28,000 = 24,000 tenancies. This is not a small mismatch: it is 60% of the original 40,000 tenancies. The elasticity estimates matter because they predict how the shortage evolves. With supply elasticity 0.6 in year one and 1.4 after five years, landlords have more time to convert flats to holiday lets, sell property or delay maintenance, so supply becomes more responsive. Demand elasticity rises from -0.3 to -0.8 as tenants find substitutes such as sharing, moving away or living with family. The council should not read the first-year shortage as permanent. However, the direction is clear: a binding price ceiling below equilibrium creates excess demand unless supply is perfectly inelastic. The numerical shortage also understates the welfare loss because it does not count queuing, bribes, key money or reduced quality. The council needs to decide whether protecting sitting tenants is worth a persistent shortage that harms new entrants.
2. Using the elasticity data, assess how the shortage is likely to change over five years.
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The first-year shortage is 24,000. Over five years, supply elasticity rises to 1.4, meaning supply responds more to the price gap. Demand elasticity rises in absolute value to -0.8, meaning tenants are more able to adjust. These elasticities do not by themselves give the new quantities, but they imply that both curves become flatter around the controlled price. The supply response is likely to be dominated by exit: landlords converting to holiday lets, selling to owner-occupiers or reducing maintenance. That reduces the quantity supplied at every rent. The demand response is likely to be dominated by new household formation being discouraged and existing tenants staying put, which actually keeps measured demand high. So the shortage may not shrink; it may change form. A larger share of the shortage could appear as hidden demand - people not registering as tenants because they have given up. The council should therefore measure not only advertised vacancies but also overcrowding, commuting distances and homelessness. The policy may look better in the headline rent data while looking worse in housing outcomes.
3. Recommend whether Port Alder should keep the rent cap, and identify one complementary policy.
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A judgement is needed. Keeping the cap protects existing tenants from sudden rent increases, which is a real equity gain, especially for nurses and teachers. But the estimated 24,000 shortage, the rise in holiday lets and the five-year elasticity trends point to significant allocative inefficiency. The cap does not increase the number of affordable homes; it mainly redistributes existing scarcity. A better package would keep a targeted cap for sitting tenants for a limited period while increasing supply. One complementary policy is a vacancy tax or stricter licensing of short-term holiday lets, which would reduce the incentive to exit the long-term rental market. Another is publicly funded social housing, but the council has no plan for it. The recommendation should depend on weighing equity against efficiency: if the council values protecting current residents most, keep the cap but accept queuing and quality decay; if it wants a durable affordability solution, phase out the cap and use supply-side measures. The worst outcome is to keep the cap and do nothing about supply.