Question

need as soon as possible please

Following table shows information about the demand for apples in the wholesale mar-

ket.

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?

Page 1 of 2

Answer 1

Demand For Apples In The Wholesale Market.
Price, P ($/lb)	Quantity, Qd (lbs)
10	0
8          (P1)	4          (Q1)
6          (P2)	8          (Q2)
4          (P*)	12        (Q*)
2	16

a)

b)

Qd= a+bP

a= Quantity intercept or x intercept. It is also called autonomous consumption that is quantity demanded when price is zero.

b= intercept of slope that is Change is quantity demanded divided by change in price.

Let’s find a and b,

a= Qd when price is zero, so to derive a we put value of any price (P*) and corresponding quantity demanded (Q*) in the above derived equation

The demand function :   

To derive the inverse demand function :

Inverse Demand Function :

c)

Qd=? when P=3

Supply For Apples In The Wholesale Market.
Price, P ($/lb)	Quantity, Qs (lbs)
0	0
2          (P1)	4          (Q1)
4          (P2)	8          (Q2)
6          (P*)	12        (Q*)
8	16

(i)

(ii)

Qs= c+dP

c= Quantity intercept of supply. It is always negative because no one sells when price is zero.

d= Inverse of the slope of supply curve. It is change in quantity supplied divided by changes in prices.

To find d :

TO FIND c , WE PUT ANY VALUE OF Qs AND CORRESPONDING PRICE in above equation,

Q* = c+2P*

Supply Function :

Inverse Supply Function :

(iii) Qs=? when P= 9

Qs=2(9)

Qs=18 lbs

( I )

Market Equilibrium is when Demand (Qd) = Supply (Qs)

Qd=Qs

20-2P=2P

4P=20

P=20/4

EQUILIBRIUM PRICE= $5/lb

THEREFORE, EQUILIBRIUM QUANTITY = 2(5) = 10lbs

(II)

CONSUMER SURPLUS is the area below tha demand curve but above the equilibrium price

Consumer Surplus = Area of the double shaded triangle = 0.5x5x10 = 25

PRODUCER SURPLUS is the area above supply curve but below the equilibrium price.

Producer surplus = Area of the single shaded triangle = 0.5x5x10 = 25

TOTAL SURPLUS = Consumer Surplus+Producer Surplus

Total Surplus = 25+25 = 50