Answer to Question #241803 in Microeconomics for Lidya

Question

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

QS = 2P

QD = 300 – P

a Solve for the equilibrium price and quantity.

b If the government imposes a price ceiling of $90, does a shortage or surplus (or neither) develop?What are the price, quantity supplied, quantity demanded and size of the shortage or surplus?

c If the government imposes a price floor of $90, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded and size of the shortage or surplus?

d Instead of a price control, the government levies a tax on producers of $30. As a result, the new supply curve is QS = 2(P – 30).

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

Demand represents the quantities of good a consumer is willing to purchase at alternative prices in a given period of time.

Supply represents the quantities of goods supplied at alternative prices in a given period of time.

Equilibrium is achieved where both the demand and supply curve intersect each other, i.e. where both and supply are equal.

a) Calculate the equilibrium price as follows:

Q^S=Q^D

2P=300 — P

2P + P=300

P=300/3=100$

Thus, the equilibrium price is100$.

Calculate the equilibrium quantity as follows:

Q^D=300-P

=300-100

=200

Thus, the equilibrium quantity is 200.

b)

If the price ceiling of $90 is imposed, which is less than the price is $100, then there will be a price binding.

The market price is 90$.

Calculate the quantity supplied as follows:

Q^S=2P

=2*90

=180

Thus, the quantity supplied is 180.

Calculate the quantity demanded as follows:

Q^D=300-P

=300-90

=210

Thus, the quantity demanded is 210.

Shortage occurs when demand is greater than the supply and surplus is when quantity supplied is greater than the quantity demanded.

Calculate the shortage as follows:

Shortage=Q^D — Q^S

=210-180

=30

Thus, the shortage is 30.

c)

If the price floor of $90 is imposed, which is less than the price is $100, then there will be a non-price binding.

The market price is 100$.

Calculate the quantity supplied as follows:

Q^S= 2P=2*100=200

Thus, the quantity supplied is 200.

Calculate the quantity demanded as follows:

Q^D =300-P=300-100=200

Thus, the quantity demanded is 200.

As the quantity demanded is equal to quantity supplied i.e. 200. Thus, there is neither shortage nor surplus.

c)

When a tax of $30 is imposed, the new supply curve is as follows:

Q^S=2(P-30)

Calculate the price as follows:

Q^S=Q^D

2(P-30)=300-P

2P-60=300-P

2P+P=300+60

3P=360

P=120

Thus, the price is 120$.

Calculate the quantity supplied as follows:

Q^S=2(P-30)

=2(120-30)

=240-60

180

Thus, the quantity supplied is 180.

Calculate the quantity demanded as follows:

Q^D=300-P

=300-120

=180

Thus, the quantity demanded is 180.

As the quantity demanded is equal to quantity supplied i.e. 180. Thus, there is neither shortage nor surplus.