Worked example 1
The market for rented flats in a city has demand Qd = 9 000 − 5R and supply Qs = 1 000 + 5R, where R is the monthly rent in $ and Q is the number of flats.
(a) Calculate the equilibrium rent and the number of flats rented. (b) The city sets a maximum rent of $600. Calculate the shortage this creates. (c) Analyse one benefit and one problem of the maximum rent.
Show solution outline
Step 1 — Equilibrium (a): 9 000 − 5R = 1 000 + 5R → 8 000 = 10R → R = $800. Quantity = 9 000 − 5(800) = 5 000 flats.
Step 2 — At the maximum rent (b): Qd = 9 000 − 5(600) = 6 000; Qs = 1 000 + 5(600) = 4 000. Shortage = 6 000 − 4 000 = 2 000 flats. Note that 1 000 fewer flats are rented than at equilibrium: some landlords withdraw or sell up.
Step 3 — Benefit (c): the 4 000 tenants who do find a flat pay $600 instead of $800 — $200 a month more to spend on other things — so housing is more affordable for them.
Step 4 — Problem (c): 2 000 would-be tenants cannot find a flat at the legal rent. Waiting lists grow, landlords may let to whoever pays an illegal premium (a black market), and with lower returns landlords spend less on maintenance. The control is only effective because $600 is below the equilibrium of $800; a ceiling above $800 would change nothing.
Diagram: D and S crossing at (5 000, $800); a horizontal line at $600 with the shortage gap between Qs = 4 000 and Qd = 6 000.