Question

"Assume these are the normal supply and demand equations for inflatable Halloween decorations in October:

Demand: P = 72 – 0.3Q

Supply: P = 2 + 0.5Q

This year, due to COVID-19, the supply and demand equations have changed to:

Demand: P = 37 – 0.3Q

Supply: P = 1 + 0.5Q

"

a) Calculate the equilibrium price during normal years.

Enter as a value.

b) Calculate the equilibrium price during this year's Covid situation.

Enter as a value.

c) In an effort to boost sales of these Halloween inflatables during COVID, the local government puts a price ceiling on these goods with a maximum price of $16.  

True or False: this price ceiling will increase suppliers' willingness to produce Halloween inflatables.

d) The price ceiling of $16 will result in a shortage of how many units?

Enter as a value.

e) Calculate the deadweight created from the price ceiling.

Answer 1

A) A Equilibrium, D=S

72-0.3Q = 2+0.5Q

72-2 = 0.5Q+0.3Q

70 = 0.8Q

Q = 70/0.8 = 87.5

P = 72-0.3*87.5 = 45.75

B) 37-0.3Q = 1+0.5Q

37-1 = 0.5Q+0.3Q

36 = 0.8Q

Q= 36/0.8 = 45

P = 37-0.3*45 = 23.5

C) Fasle, as the price ceiling is imposed below the equilibrium price, the producers willingness to supply would decrease

D) Demand: 16 = 37-0.3Q, 0.3Q = 37-16, Q= 21/0.3 = 70

Supply: 16 = 1+0.5Q, 16-1 = 0.5Q, Q = 15/0.5 = 30

Shortage = 70-30 = 40 units

E) Deadweight loss: when P=16, The quantity exchanged would fall to QS = 30 at which the consumers are willing to pay 37-0.3*30 = 28

so, DWL = 0.5*(45-30)*(28-16) = 90