Question

A car manufacturer producers two (2) core products: SUVs (product X) and sports cars (Product Y). Sports cars are selling at $20,000 per units, and SUVs have a selling price of $40,000 per unit. Due to changing consumer preferences, the price of sports cars increases by 50%; as a result, the demand for SUVs falls from 10,000 units to 5,000.

Using the "arc method," the cross price elasticity of demand for SUVs is:

	a.	-0.40
	b.	- 1.675
	c.	+1.675
	d.	0.67

The cross price elasticity of demand for product X  with respect to the price of product Y is 0.30

This means that

	a.	an increase in the price of Y by 10 percent gives rise to a decrease in the quantity demanded of X by 3 percent.
	b.	an increase in the price of X by 10 percent gives rise to an increase in quantity demanded of Y by 3 percent.
	c.	an increase in the price of Y by 10 percent gives rise to an increase in the quantity demanded of X by 3 percent.
	d.	an increase in the price of X by 10 percent gives rise to a decrease in the quantity demanded of Y by 3 percent.

Your analysis of the responsiveness of the quantity demanded of Good X to price changes reveals that the own price elasticity of demand for Good X is -1.5.

If your firm increases the price of Good X by 5%,

	a.	the quantity demanded of Good X will decrease by 7.5%.
	b.	the quantity demanded of Good X will increase by 5%.
	c.	the quantity demanded of Good X will decrease by 5%.
	d.	the quantity demanded of Good X will increase by 7.5%.

Answer 1

1....... b

Explanation:- good y — sports car, good x  — SUV

Px1= 20000 , px2 = 20000+ 20000×50/100= 30000   Px= 30000—20000= 10000  

Qy1 = 10000 , Qy2=5000 , Qy = —5000

Arc price elasticity of demand = (Qy/Px )×  {( Px1+Px2)/(Qy1+Qy2)} = (—5000/10000) × (50000/15000) = —25/15 = —1.67

( cross elasticity of compliments are negative, price of sports car and demand for SUV move in the opposite direction).

2. ...... a

Explanation:-  

Cross elasticity, Exy = % change in quantity demand for good x/%change in the price of good y

or, 0.3= %change in qd of good x/10  

or, % change in the qd of good x = 0.3×10 = 3

So , quantity demand of good x rises by 3%

3.........a

Explanation:- Ep = %change in q d of good x/%change in the price of good x , or —1.5 = % change in quantity demand of good x / 5 ,

or, % change in the quantity demand of good x = —1.5×5=—7.5

So, quantity demand of good x falls by 7.5%.