MATHEMATICAL APPROACH TO DEMAND AND SUPPLY FUNCTIONS

Demand and supply functions can be discussed with the aid of mathematical equation as a MATHEMATICAL APPROACH TO DEMAND AND SUPPLY FUNCTIONS

Linear id simultaneous (by elimination and substitution) equations are used to solve the problems associated with demand and supply functions.

### MATHEMATICAL APPROACH TO DEMAND AND SUPPLY FUNCTIONS

Given that quantity demanded per period of time is a function of price and that the relation is pressed as Q = 60 – 7P, where Q is the quantity demanded and P is the price, i) Find the quantity demanded when the price

is:

- 630.00
- 6210.00
- 60.00
- Comment of (a)(ii) above

- Suppose the relation is now expressed

as P = 6(180 -3Q);

find P when

- Q = 0
- Q = 60;
- Q = 59

Solution

1(a) Q = 60 – BP

- When price is 630, Q = 60 – 7(30)

= 60 – 19

Q = 50

- When price is 6210.00,

Q = 60 – 7(210)

60 – 70 – -10

- When price is 60, Q = 60 – 7(0)

= 60 – 0

= 60

- In (a)(ii) above, the law of demand of comes into play here. The law of demand states that “The higher the price, the lower the quantity demanded.” This explains why the prices is as high as 6 210, and consumers are not willing to buy more as a MATHEMATICAL APPROACH TO DEMAND AND SUPPLY FUNCTIONS

(c)(i) P = 6(180 – 3Q)

When Q = 0

P = 6(180 – 2(0))

= 6180 – 0

= 6180

(ii) When Q = 60

P = 6(180 – 3(60))

P = 6(180 – 180)

= 60

(iii) When Q = 59

P = 6(180 -3(59)

P = 6(180 – 177)

P = 63

#### The demand and supply functions of commodity

The demand and supply functions of the commodity are given as follows: Quantity demanded (Qd) = 20 – 2P. Quantity supplied (QS) = 6P – 12, where P = price in naira

- Determine the equilibrium price and quantity bought and sold at that price.
- If the price of the commodity is fixed at 6 6.00, what is the magnitude of the excess supply?

Solution

Qd = 20 – 2P

QS = 6P – 12

- Qd = QS

20 – 2P = 6P – 12

-2P – 6P = -20 – 12

-8P = -32

8P = 32

P = 32

8

P = 4

Qd = 20 – 2P

= 20 – 2 (4)

= 20 – 8

= 12

Qs = 6P – 12

= 6(4) – 12

= 24 – 12

= 12

- Qs = 6P – 12

= 6(6) – 12

= 36 – 12

= 24

The magnitude of the excess supply will be 24 – 12=12.

Given the demand function for commodity **X**,

Qd = 12 – 2P, where Qd is the quantity demanded and P is the price of the commodity,

- Use the demand function to complete the table below:

P | 6 | 5 | 4 | 3 | 2 | 1 | 0 |

Qd |

- Draw the individual demand curve (the use of graph paper is essential).
- What is the maximum quantity the individual can buy of commodity X per unit of time?
- What is the relationship between quantity demanded and price in the function Qd = f(P)?

**Solution** 2 MATHEMATICAL APPROACH TO DEMAND AND SUPPLY FUNCTIONS

With demand function Qd = 12 – 2P, the table is completed as follows:

P | 6 | 5 | 4 | 3 | 2 | 1 | 0 |

Qd | 0 | 2 | 4 | 6 | 8 | 10 | 12 |

Qd = 12 – 2P

When P = 6

Qd = 12 – 2 (6)

= 12 – 12

= 0

When P = 5

Qd = 12 – 2 (5)

= 12 – 10

= 2

When P = 4

Qd = 12 – 2(4)

= 12 – 8

= 4

When P = 3

Qd = 12 – 2 (3)

= 12 – 6

= 6

When P = 2

Qd = 12 – 2(2)

= 12 – 4

= 8

When P = 1

Qd = 12 – 2 (1)

= 12 – 2

= 10

When P = 0

Qd = 12 – 2 (0)

= 12 – 0

= 12

- The maximum quantity is 12.
- There is an inverse relationship between quantity demanded and price, i.e. the higher the price, the lower the quantity demanded or the lower the price, the higher the quantity demanded.

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