Question

The weekly demand function for a product Z sold by a given supermarket is 30, 000 units when its price was birr 2. A 10% rise in the price of product Z results in the weekly demand to fall by 2000 units. Then drive The demand function

Answer 1

Demand function

Q = a - bP

Q = Quantity demanded.

b = Slope/ gradient of the curve

a = Y-intercept

P = Price of the good

Slope of the demand curve

 $b= \frac{\Delta Q}{\Delta P}= \frac{Q_2-Q_1}{P_2-P_1}$

$Q_1=30,000$     $P_1= 2$

$Q_2=(30000-2000)= 28,000$         $P_2= (\frac{110}{100}\times 2)= 2.2$

= $\frac{28,000 - 30,000 }{2.2 - 2 } = \frac{-2,000 }{0.2 } = -10,000$

$b=-10,000$

$Q= a-10,000$

Plug in Q and P into the equation to obtain (a)

28,000 = a – 10,000(2.2)

28,000 = a – 22,000

a = 28,000 + 22,000 = 50,000

$\therefore Q= 50,000- 10,000P$