# Tutorial Sheet 3.

## MATH105 - Worksheet 3

1. Suppose that the weekly demand for a product is 100 units when the price is R63 per unit and that when the price drops to R58 per unit, the demand rises to 200 units per week. Find the demand function in the form

Q D

=

· · ·

.

2. The demand and supply curves for a commodity are

Q D

= 250

12

p

and

Q S

= 8

p

+ 170.

(a) Find the market equilibrium and the quantity exchanged at equilibrium.

(b) What is the slope of the demand curve?

3. When the price of a certain commodity is 20 the demand is 50 and the quantity supplied is 20. When the price rises to 50, the demand falls to 20, while the supply rises to 90.

(a) Find the supply and demand curves

Q S

and

Q D

.

(b) Find the price at market equilibrium and the quantity supplied then.

(c) Find the demand if the product is given away free.

4. When the price of a certain commodity is 20 the demand is 320 and the quantity supplied is 120. If the price rises to 40 then the quantity supplied rises to 360, but the demand drops to 160.

(a) Find the supply and demand curves (assume they are linear).

(b) Find the market equilibrium price and the quantities demanded and supplied there.

(c) Sketch the supply and demand curves.

5. For a certain commodity, when the price is 30 the demand is 10 and the quantity supplied is 40, but when the price is 15, the demand is 25 and the quantity supplied is 10.

(a) Find the supply and demand functions

Q S

(b) Find the supply and demand functions

Q S

and and

Q Q D D

in the form in the form (c) Find the market equilibrium price and the quantity supplied.

p

=

· · · Q

=

· · ·

(d) What will the demand be if the commodity is free?

(e) What is the maximum price anybody is prepared to pay?

6. For a certain commodity, when the price is 30 the demand is 45 and the quantity supplied is 15, but when the price is 54 the demand is 9 and the quantity supplied is 51.

(a) Find the supply and demand functions

Q S

(b) If

p

and

Q D

.

= 30 which is bigger, supply or demand? What will happen to

p

?

(c) If

p

= 48 which is bigger, supply or demand? What will happen to

p

?

1 .

Q D

= 1360

20

p

.

2 . (a)

p

= 4,

Q

= 202 (b)

1

/

12.

3 . (a)

Q D

= 70

− p

,

Q S

= (7

p −

80)

/

3o (b)

p

= 13,

Q

= 57 (c) 70.

4 . (a)

Q D

= 480

8

p

,

Q S

= 12

p −

120 (b)

p

= 30,

Q

= 240 5 . (a)

p

= 40

− Q D

,

p

=

Q S

(d)

Q D

= 40 (e)

p

= 40

/

2 + 10 (b)

Q D

= 40

− p

,

Q S

= 2

p −

20 (c)

p

= 20,

Q

= 20 6 . (a)

Q D

= 45

2

p/

3,

Q S

= 3

p/

2

30 (b) Demand. Price increases (c) Supply. Price decreases.