Question

1. [Market Equilibrium]

Following table shows information about the demand for apples in the wholesale market.

Price, P ($/lb) Quantity Qd (lbs)

10 0

8 4

6 8

4 12

2 16

(a) Draw a graph with Price (P) on the vertical axis and Quantity demanded (Qd) on the horizontal axis?

(b) Write the equation for this inverse demand function.

(c) What is the quantity demanded when P = $3/lb? Following table shows information about the supply of 20 lbs box of apples in the wholesale market.

Price, P ($/lb) Quantity Qs (lbs)

0 0

2 4

4 8

6 12

8 16

(i) Draw a graph with Price (P) on the vertical axis and Quantity supplied (Qs) on the horizontal axis?

(ii) Write the equation for this inverse supply function.

(iii) What is the quantity supplied when P = $9/lb? Next we determine the market equilibrium.

(I) Find out the equilibrium price and quantity.

(II) What are the consumers’ surplus, producers’ surplus and the total surplus?

(III) What is the shortage / surplus if the Government imposes a price floor of $7/lb in this market?

(IV) What is the shortage / surplus if the Government imposes a price ceiling of $4/lb in this market?

(V) What is the shortage / surplus if the Government imposes a price floor of $4.5/lb in this market?

Answer 1

1.

Given;

P	Qd
10	0
8	4
6	8
4	12
2	16

a) The demand curve with Price (P) on the vertical axis and Quantity demanded (Qd) on the horizontal axis will be;

The demand curve will be a downward sloping curve where when price falls, qunatity demanded decreases.

b) The equation for demand curve will be in the form;

Qd = a - bP

where;

b = Q₂ - Q₁ / P₂ - P₁

let us take, Q₂ = 8 , Q₁ = 4
P₂ = 6, P₁ = 8

b = 8-4 / 6-8
b = -4/2
b = -2

Qd = a - bP
Qd = a - 2P

Q = 8 , P = 6

8 = a - 2*6
8 + 12 = a
a = 20

So, the demand equation is;

Qd = 20 - 2P

Thus, the inverse demand equation is;

2P = 20 - Q
P = 10 - Q/2

c) When is ; P = 3, the quantity demanded will be;

Q = 20 - 2*3
Q = 20 - 6
Qd = 14

2.

Given;

P	Qs
0	0
2	4
4	8
6	12
8	16

1) The supply curve with Price (P) on the vertical axis and Quantity supplied (Qs) on the horizontal axis will be;

The supply curve will be an upward sloping curve where when price increases, qunatity supplied also increases.

2)

The equation for supply curve will be in the form;

Qs = c + dP

where;

d = Q₂ - Q₁ / P₂ - P₁

let us take, Q₂ = 8 , Q₁ = 4
P₂ = 4, P₁ = 2

d = 8-4 / 4-2
d = 4/2
d = 2

Qs = c + dP
Qs = c + 2P

Q = 8 , P = 4

8 = c + 2*4
8 - 8 = c
c = 0

So, the supply equation is;

Qs = 2P

Thus, the inverse supply equation is;

2P = Q
P = Q/2

3) When P = 9, quantity supplied will be'

Qs = 2P
Qs = 2*9
Qs = 18

4) The equilibrium price and quantity will be achieved when quantity demanded is equal to quantity supplied;

Qd = Qs
20 - 2P = 2P
20 = 4P
P = 5

Q = 2*5
Q = 10

5) Consumer surplus : Consumer surplus will be the area between the price line and the demand curve. It will be calculated as;

CS = 1/2 * 10 * (10-5)
CS = 1/2 * 10 * 5
CS = 25

Producer surplus : Producer surplus will be the area between the price line and the supply curve. It will be calculated as;

PS = 1/2 * 10 * 5
PS = 25

6) If the Government imposes a price floor of $7/lb in this market,

when P = 7, quantity demanded and quantity supplied will be;

Qd = 20 - 2P
Qd = 20 - 2*7
Qd = 20 - 14
Qd = 6

Qs = 2P
Qs = 2*7
Qs = 14

As we can see ;

Qs > Qd

Therefore, there will be excess supply, i.e surplus in the market;

Surplus = 14 - 6
Surplus = 8

7) If the Government imposes a price ceiling of $4/lb in this market,

when P = 4, quantity demanded and quantity supplied will be;

Qd = 20 - 2P
Qd = 20 - 2*4
Qd = 20 - 8
Qd = 12

Qs = 2P
Qs = 2*4
Qs = 7

As we can see ;

Qs < Qd

Therefore, there will be excess demand, i.e shortage in the market;

Shortage = 12 - 7
Shortage = 5

6) If the Government imposes a price floor of $4.5/lb in this market,

when P = 4.5, quantity demanded and quantity supplied will be;

Qd = 20 - 2P
Qd = 20 - 2*4.5
Qd = 20 - 9
Qd = 11

Qs = 2P
Qs = 2*4.5
Qs = 9

As we can see ;

Qs < Qd

Therefore, there will be excess demand, i.e shortage in the market;

Shortage = 11 - 9
Shortage = 2