Question

For the following set of demand and supply equations do the following,

1. Determine which equation is demand equation and which one is supply equation. explain how?
2. Find the equilibrium price and equilibrium quantity for each set of equations.
3. Draw each set of equations in a clearly labeled graph and show the equilibrium P and Q.
4. Impose any price floor and determine the new Qd, Qs.
5. Based on a find out whether there is a surplus or a shortage and indicate how large it is?
6. Impose any price ceiling and determine the new Qd, Qs.
7. Based on b find out whether there is a surplus or a shortage and indicate how large it is?

Equations

P=100-2Q P=80+0.5Q           Equation Set 1

P=50-0.5Q P=20+0.5Q           Equation Set 2

Answer 1

Set 1:

P=100-2Q

P=80+0.5Q

a) P = 100 - 2Q is demand equation as there is negative relationship between price and quantity demanded which is shown by negative sign in front of 2Q

P = 80 + 0.5Q is supply equation as there is positive relationship between price and quantity supplied which is shown by positive sign in front of 0.5Q

b) Equlibrium occurs when demand equals supply

100 - 2Q = 80 + 0.5Q

Q = 8

At Q = 8, P = 84

c) It can be seen in below diagram.

d) Price floor is effective when it is set above equilibrium price. At price floor of $90, there is quantity demanded of 5 units and quantity supplied is 20 units.

e) There is surplus of 20 - 5 = 15 units

f) Price ceiling is effective when it is set below equilibrium price. Price ceiling is imposed at $82. New quantity demanded is 9 units while new quantity supplied is 4 units.

g)  After price ceiling, there is shortage of = 9 - 4 = 5 units

Set 2:

P=50-0.5Q

P=20+0.5Q

a) P = 50 - 0.5Q is demand equation as there is negative relationship between price and quantity demanded which is shown by negative sign in front of 0.5Q

P = 20 + 0.5Q is supply equation as there is positive relationship between price and quantity supplied which is shown by positive sign in front of 0.5Q

b) Equlibrium occurs when demand equals supply

50 - 0.5Q = 20 + 0.5Q

Q = 30

At Q = 30, P = 35

c)

d) Price floor is effective when it is set above equilibrium price. At price floor of $42, new quantity demanded is 16 units while quantity supplied is 44 units.

e) There is surplus of 44 - 16 = 28 units

f) Price ceiling is effective when it is set below equilibrium price. At price ceiling of $30, there is quantity demand of 40 units while quantity supply of 20 units.

g) There is shortage of 40 - 20 = 20 units.

100 -Supply -Price floor Setl - Ilemend 20 so Puentity Surplus at 890

Price a 100 Supply 841 Print Ceiling 11 Demand 4 89 250 Shortage at $82 Quantity

We were unable to transcribe this image

Supply e brice floor - - 35 - - T - - - - 20 1 1 16 30 Quentiti surplus at $42

Set 2. erine Ceiling - - Demand 20 30 4o 100 Quentity Shortage at $30

100 -Supply -Price floor Setl - Ilemend 20 so Puentity Surplus at 890

Price a 100 Supply 841 Print Ceiling 11 Demand 4 89 250 Shortage at $82 Quantity

We were unable to transcribe this image

Supply e brice floor - - 35 - - T - - - - 20 1 1 16 30 Quentiti surplus at $42

Set 2. erine Ceiling - - Demand 20 30 4o 100 Quentity Shortage at $30