Question

The weekly demand function for a product Z sold by a given supermarket is 30, 000 units when its price was birr 2. A10% rise in the price of product Z results in the weekly demand to fall by 2000 units. Then drive The demand function

Answer 1

Solution:

The demand equation:

Q = a + bP

Where: Q = Quantity demanded.

            b = Slope of the demand curve

            a = Y-intercept

            P = Price of the good

First, derive the slope of the demand curve:

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

Q₁ = 30,000                  P₁ = 2

Q₂ = 28,000                  P₂ = (10$\% \times$ 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:

30,000 = a – 10,000(2)

30,000 = a – 20,000

a = 30,000 + 20,000 = 50,000

Q = 50,000 – 10,000P

The demand equation: Q = 50,000 – 10,000P