Question

The following equations describe the market for Fitbits:

Demand equation: Q_d = 2000 - 5P; Supply equation: Q_s = 20 P

(a) Find the equilibrium quantity and price for Fitbits; (b) In an effort to encourage people to get healthy, the Government imposed a price ceiling of $50 on Fitbits. How many Fitbits are sold with the price ceiling?; (c) Is there excess demand or excess supply at $50? If so, how much?

Answer 1

a) For equilibrium:

Qd = Qs

2000 - 5P = 20P

25P = 2000

P = 2000 / 25 = $80

Q = 2000 - 5(80) = 1600

Thus, the equilibrium quantity is 1600 and equilibrium price is $80

b) At P = $50

Qs = 20P = 20(50) = 1000

Qd = 2000 - 5P = 2000 - 5(50) = 1750

Since at P = $0, Qs is 1000 , therefore, 1000 Fitbits are sold with the price ceiling.

c) As calculated above that at P = $50, Quantity demanded is more than quantity supplied, there ia an excess demand at $50.

Excess Demand = 1750 - 1000 = 750.