Question

Assume that the City Council in Prescott, Arizona is considering implementing price ceilings on rental units based on the number of bedrooms in the unit. The demand function for rental units (on a single bedroom equivalent basis) is given by Q_D = 120 – 4P and the supply function is given by Q_S = 2P, where P is price and Q is quantity. The Council is considering imposing a ceiling price on rental units of P_max = 16.

1. Using the given functions, draw a corresponding demand curve and a supply curve. Properly label the equilibrium price and quantity. Then show what will happen to equilibrium if the City Council imposes a price ceiling at 16.

2. Create an Excel file with a price column, including prices from $1 to $30. Using the formulas, compute the quantity demanded at each price and quantity supplied for each price.

Answer 1

1) At equilibrium, demand = supply

120 - 4P = 2P

120 = 6P

P = 20

At this price, Q = 40

At price ceiling of $16, quantity demanded is 56 and quantity supplied is 32 units. It result in shortage of 56 - 32 = 24 units.

2)

Price	Demand	Supply
1	116	2
2	112	4
3	108	6
4	104	8
5	100	10
6	96	12
7	92	14
8	88	16
9	84	18
10	80	20
11	76	22
12	72	24
13	68	26
14	64	28
15	60	30
16	56	32
17	52	34
18	48	36
19	44	38
20	40	40
21	36	42
22	32	44
23	28	46
24	24	48
25	20	50
26	16	52
27	12	54
28	8	56
29	4	58
30	0	60