Question

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

1. Draw a graph with Price (P) on the vertical axis and Quantity demanded (Q_d) on the horizontal axis?
2. Write the equation for this inverse demand function.
3. 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

1. Draw a graph with Price (P) on the vertical axis and Quantity supplied (Q_s) on the horizontal axis?
2. Write the equation for this inverse supply function.
3. What is the quantity supplied when P=$9/lb?

Next we determine the market equilibrium.

1. Find out the equilibrium price and quantity.
2. What are the consumers’ surplus, producers’ surplus and the total surplus?
3. What is the shortage / surplus if the Government imposes a price floor of $7/lb in this market?
4. What is the shortage / surplus if the Government imposes a price ceiling of $4/lb in this market?
5. What is the shortage / surplus if the Government imposes a price floor of $4.5/lb in this market?

Answer 1

a)

b) General demand equation: Q = a - bP

where a is intercept and b is slope

When Q = 0, P = 10

0 = a - 10b .... (1)

When Q = 4, P = 8

4 = a - 8b .... (2)

Solving (1) and (2)

Q = 20 - 2P

c) When P = 3, Qd = 14

i)

ii) General supply equation: Q = a + bP

When Q = 4, P = 2

4 = a + 2b ....(1)

When Q = 8, P = 4

8 = a + 4b .... (2)

Solving (1) and (2)

a = 0, b = 2

Supply equation: Q = 2P

iii) When price is 9, Qs = 18

I) Equilibrium occur when demand = supply

20 - 2P = 2P

P = 5

At this P, Q = 10

II) Consumer surplus is (1/2) * (10 - 5) * (10 - 0) = 25

Produxer surplus is (1/2) * (5 - 0) * (10 - 0) = 25

III) At a price of 7, there is demand of 6 while supply of 14 which result in surplus of 14 - 7 = 7 units.

IV) At a price of 4, there is demand of 12 while supply of 4 which result in shortage of 12 - 4 = 8

V) At a price of 4.5, there is demand of 11 while supply of 9 which result in shortage of 11 - 9 = 2 units.