Answer to Question #114908 in Economics of Enterprise for Kassahun

Question

1. The demand for petrol rises from 500 to 600 Barrels when the price of a particular scooter is reduced from Birr. 25000 to Birr.22000. Find out the cross elasticity of demand for the two. What is the nature of their relationship?
A company has the following demand equation
Q= 1000–3000P+10A
Q = Quantity demanded
P = Product Price
A = Advertisement expenditure
Assume that P = 3 and A = 2000
2. Suppose the firm drops the price to Birr. 2.50 would this bebeneficial.
3. Suppose the firm raises the price to Birr. 4.00 While increasingits advertisement expenditure by 100 would this be beneficial? Explain

Answer 1

QUESTION 1:

The cross-price elasticity of demand is computed as:

$$E_{XY} = \dfrac{\text{\% Change in the demand for good X}}{\text{\% Change in the price of good Y}}$$

Let petrol be good X and scooter be good Y.

If the demand for petrol increases from 500 to 600 barrels, then:

$$\text{\% Change in the demand for good X}= \dfrac{600 - 500}{500}\times 100 = 20\%$$

If this increase in the demand for petrol is caused by a decrease in the price of scooters from Birr. 25000 to Birr. 22000, then:

$$\text{\% Change in the price of good Y} = \dfrac{22000 - 25000}{25000}\times 100 = -12\%$$

Therefore:

$$E_{XY} = \dfrac{20\%}{-12\%} = -1.67$$

The two goods are complements since the cross-price elasticity of demand is negative.

QUESTION 2:

Q= 1000–3000P+10A

Q = Quantity demanded

P = Product Price

A = Advertisement expenditure

Assume that P = 3 and A = 2000

2. Suppose the firm drops the price to Birr. 2.50 would this be beneficial.

The price elasticity of demand is computed as:

$$E_d = \dfrac{\Delta Q}{\Delta P}\cdot \dfrac{\bar P}{\bar Q}$$

We have the demand equation as:

$$Q = 1000 - 3000P + 10A$$

From the demand curve, we have:

$$\dfrac{\Delta Q}{\Delta P} = -3000$$

At P = 3 and A = 2000, the quantity demanded is:

$$Q_1 = 1000 - 3000(3) + 10(2000) = 12000$$

If the price is reduced to Birr. 2.50, the quantity demed changes to:

$$Q_2 = 1000 - 3000(2.50) + 10(2000) = 12600$$

Therefore:

$$E_d = -3000\cdot \dfrac{(3 + 2.5)/2}{(12000 + 12600)/2} = -0.67$$

The demand is inelastic. Therefore, reducing the price to Birr. 2.50 will not be beneficial since it will reduce the firm's revenue.

QUESTION

When the price is raised to Birr. 4.00 while increasing its advertisement expenditure by 100, the new quantity demanded will be:

$$Q_2= 1000–3000(4) + 10(2100) = 20800$$

Therefore:

$$E_d = -3000\cdot \dfrac{(3 + 4)/2}{(12000 + 20800)/2} =-0.64$$

This activity will be beneficial since the demand is inelastic and the revenue will increase.