Question

A market is described by the following supply and demand curves:

Q^S = 2P

Q^D = 400 - 3P

Solve for the equilibrium price and quantity.

If the government imposes a price ceiling of $70, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?

If the government imposes a price floor of $70, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?

Instead of a price control, the government levies a tax on producers of $20. As a result, the new supply curve is:

Q^S = 2(P-20)

Does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus?

Answer 1

Equilibrium at point where Qs=Qd

2P = 400-3P

5P = 400

P = 80

Q = 2*80 = 160

Price Cieling of P = 70 will be binding as it is less than the equilibrium price.

Qs at P = 70, = 2*70 = 160

Qd at P = 70 = 400-3*70 = 190

Shortage = 190 - 160 = 30 units (Qd>Qs, Shortage = Qd-Qs)

Price floor of P= 70 will not be binding as the equilibrium price is already above ther price floor set.

New equilibrium after tax

2P-40 = 400 - 3P

5P = 440

P = 88

Q = 400-3*88 = 136

At P = 88, Qd = 136 and Qs = 2*88 = 176

Surplus as Qs>Qd = 176-136 = 40 units