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

General demand equation format

Q = a - bP

Q = Quantity demanded.

b = Slope of the demand curve

a = Y-intercept

P = Price

Slope of the demand curve

b = $\frac{\triangle Q}{\triangle P} = \frac{Q_{2} - Q_{1} }{P_{2} - P_{1} }$

$Q_1$  = 30,000                  $P_1= 2$

$Q_2$  = 28,000                  $P_2= (\frac{10}{100}\times 2)+2= 2.2$

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

b = -10,000

Q = a – 10,000P

Derive a by plugging Q and P into the equation:

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