Unit 8 Supply and demand: Markets with many buyers and sellers

8.13 Price controls

We know that total surplus is maximized at the market-clearing price. But governments may nevertheless decide to intervene in a market to change the price to achieve other objectives, such as fairness.

In some countries, local or national governments control housing rents. Sometimes this is to protect tenants, who may have little bargaining power in their relationships with landlords, or sometimes because urban rents would be too high for groups of workers who provide essential local services.

Figure 8.25 shows a situation in which the local government might decide to control the housing rent in a city. (Note that here we mean rent in the everyday sense of a payment from tenant to landlord for the use of accommodation.) Initially, the market is in equilibrium with 8,000 tenancies at a rent of €500. Now suppose that there is an increase in demand for tenancies. Rents will rise, because the supply of rental housing is inelastic, at least in the short run: it would take time to build new houses, so more tenancies can only be supplied immediately if some owner-occupiers decide to become landlords and live elsewhere themselves.

rent ceiling
The maximum legal price a landlord can charge for a rent.

Suppose that the city authorities are concerned that this rise would be unaffordable for many families, so they impose a rent ceiling at €500. Follow the steps in Figure 8.25 to analyse what happens.

Housing rents and economic rents.
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Figure 8.25 Housing rents and economic rents.

The market clears: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500).
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The market clears

Initially, the market clears with 8,000 tenancies at rent of €500.

An increase in demand: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). Another downward-sloping, straight line parallel to the original demand curve and above it at all points is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830.
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An increase in demand

Now suppose that there is an increase in demand for tenancies.

Rent increases: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). Another downward-sloping, straight line parallel to the original demand curve and above it at all points is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830.
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Rent increases

The supply of housing for rent is inelastic, at least in the short run. The new market-clearing rent, €830, is much higher.

A rent ceiling?: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). Another downward-sloping, straight line parallel to the original demand curve and above it at all points is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830. The horizontal distance between the new demand curve and point (8,000, 500) is excess demand.
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A rent ceiling?

Suppose the city authorities impose a rent ceiling at €500. Landlords will continue to supply 8,000 tenancies, so there is excess demand.

The short side of the market: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). £500 is the controlled rent. Another downward-sloping, straight line parallel to the original demand curve and above it at all points is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830, which is the market clearing rent. The horizontal distance between the new demand curve and point (8,000, 500) is excess demand.
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The short side of the market

When the price is below the market-clearing level, supply is less than demand. We say that the suppliers are on the short side of the market. They determine the number of tenancies.

Some people would pay much more: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). £500 is the controlled rent. Another downward-sloping, straight line parallel to the original demand curve and passing through points (8,000, 1,100) and (12,000, 500) is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830, which is the market clearing rent. The horizontal distance between the new demand curve and point (8,000, 500) is excess demand.
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Some people would pay much more

When the price is $500, there are 12,000 people on the long side of the market. Only 8,000 obtain tenancies. There are 8,000 people willing to pay €1,100 or more, but tenancies are not necessarily allocated to the people with highest willingness to pay.

Opportunities for rent-seeking: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). £500 is the controlled rent. Another downward-sloping, straight line parallel to the original demand curve and passing through points (8,000, 1,100) and (12,000, 500) is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830, which is the market clearing rent. The horizontal distance between the new demand curve and point (8,000, 500) is excess demand. The vertical distance between the new demand curve at point (8,000, 1,100) and the original demand curve at point (8,000, 500) is the economic rent.
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Opportunities for rent-seeking

If it were legal, some tenants could sublet their accommodation at €1,100, obtaining an economic rent of €600.

The long-run equilibrium: In this diagram, the horizontal axis displays the number of tenancies. The vertical axis displays the housing rent in euros. Coordinates are (tenancies, rent). A downward-sloping, straight line is the demand curve. An upward-sloping, straight line is the supply curve. They intersect at point (8,000, 500). £500 is the controlled rent. Another downward-sloping, straight line parallel to the original demand curve and passing through points (8,000, 1,100) and (12,000, 500) is the new demand curve. It intersects the supply curve at a higher number of tenancies than 8,000, corresponding to a rent of £830, which is the market clearing rent. Another upward-sloping, straight line, parallel to the original supply curve and passing through point (12,000, 500) is the new supply curve. The horizontal distance between the new demand curve and point (8,000, 500) is excess demand. The vertical distance between the new demand curve at point (8,000, 1,100) and the original demand curve at point (8,000, 500) is the economic rent.
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The long-run equilibrium

In the long run, the city authorities could make more tenancies available at a reasonable rent by encouraging housebuilding, to shift out the supply curve.

In general, a controlled price will not clear the market, and trade will then take place on the short side of the market: that is, the quantity traded will be whichever is lower of the quantities supplied and demanded. In Figure 8.25, the price is low and suppliers are on the short side.

When the rent is €500, the number of tenancies will be 8,000. Of the 12,000 people on the long side of the market, 8,000 would pay €1,100 or more, but tenancies are not allocated to those with highest willingness to pay. Those lucky enough to obtain tenancies may be anywhere on the new demand curve above €500.

In this brief article, economist Rebecca Diamond summarizes the research evidence from the US on the positive and negative effects of rent controls. Here, the Economics Observatory assesses the lessons from economic analysis for a recent proposal to implement nationwide rent controls in Scotland.

The rent control policy puts more weight on maintaining a rent that is seen to be fair and affordable (by existing tenants who might otherwise be forced to move out), than it does on Pareto efficiency. The scarcity of rental accommodation gives rise to a potential economic rent: if it were legal (it usually isn’t), some tenants could sublet their accommodation for €1,100, obtaining an economic rent of €600.

If the increase in demand proves to be permanent, the long-run solution for the city authorities may be policies that encourage housebuilding, which shifts out the supply curve so that more tenancies are available at a reasonable rent.

Question 8.14 Choose the correct answer(s)

Figure 8.25 illustrates the rental housing market. Initially, the market clears at €500 with 8,000 tenancies. Then, there is an outward shift in the demand curve, as shown in the diagram. In response, the city authority imposes a rent ceiling of €500 and prohibits subletting. Based on this information, read the following statements and choose the correct option(s).

  • There are 4,000 potential tenants who are left unhoused.
  • The market would clear at €1,100.
  • If subletting was possible, then those renting could earn an economic rent of €330.
  • Excess demand could be eliminated in the long run by building more houses.
  • At €500, 12,000 people want tenancies, but there are only 8,000 available.
  • The market would clear at €830.
  • Those subletting would be able to charge a rent of €1,100 under the new demand curve, obtaining economic rent of €600.
  • If enough houses were built, the supply curve would shift outwards and the market would again clear at €500.

Exercise 8.14 The distributional impact of rent control

The diagram shows the rental market before rent control, where in equilibrium (G), X0 apartments are rented at the price, P0. Suppose rent control lowers the price to PR and the number of apartments supplied to XR.

In this diagram, the horizontal axis shows the number of apartments, and the vertical axis shows the rental price per month, denoted p. Coordinates are (number of apartments, price). A straight, upward-sloping curve is the supply curve. A straight, downward-sloping curve is the demand curve. They intersect at point G (x0, p0). Point (xR, pR) lies on the supply curve. pR is the rent control price.
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  1. Under the usual assumption that apartments are allocated according to willingness to pay, draw a copy of this diagram and indicate the following areas:
    • Renter surplus after rent control
    • Landlord surplus after rent control
    • Landlord surplus transferred to renters
    • Renter surplus lost
    • Landlord surplus lost.
  2. Use your answer to the previous question to explain the effect of rent control on renters, landlords, and total surplus. Discuss some factors that affect the magnitude of gains or losses experienced by either party.
  3. Suppose that renters could vote to remove rent control, but they would only be willing to do so if the landlords made a suitable transfer as compensation. Use your diagram to explain how this arrangement could leave both renters and landlords at least as well off as under rent control.

Exercise 8.15 The price of a ticket

For sporting events, there can be excess demand for tickets. For example, the London 2012 Olympic Games received 22 million applications for 7 million tickets. Suppose the demand curve for tickets to one Olympic event is given as P = 425 – (1/250)Q, where the stadium can fit 50,000 spectators.

  1. Draw a supply and demand diagram to illustrate this situation. What ticket price would clear the market?
  2. Suppose that, instead, the Olympic organizing committee chose to sell all tickets at a price of £100. Illustrate this situation in your diagram. What would the excess demand be at this price?
  3. Given the excess demand at the current ticket price, some people who obtain tickets may be tempted to sell them rather than attend the event, creating a secondary market for tickets. Use your diagram to explain how sellers in the secondary market gain economic rents from doing so.
  4. Use the criteria of fairness and Pareto efficiency to evaluate the following methods of allocating tickets:
    1. Selling the tickets to whoever buys them first. Tickets may be transferable (for example, via secondary markets).
    2. Setting the ticket price below the market-clearing price and using a lottery to decide who gets the tickets. Tickets are non-transferable.