Question

2. Given a demand equation for goods X:
?? = 50 − 0.4?? + 0.02? + 0.1??
a. How much is the quantity demanded if price of goods x (PX) is RM50, income (Y) RM6000 and price of goods z (Pz) is RM60?
b. Calculate price elasticity of demand for good x when its price is RM50. Is the demand for good x sensitive to the change in its price?
c. Determine the cross elasticity of demand for good x when the price of z is RM60. What is the type of relationship between the two goods?
d. Calculate income elasticity of demand for good x when income level is RM6000. State the type of goods x.

Answer 1

2.

?? = 50 − 0.4?? + 0.02? + 0.1??

a.

if price of goods x (PX) is RM50, income (Y) RM6000 and price of goods z (Pz) is RM60:

?? = 50 − 0.4(50) + 0.02(6000) + 0.1(60)= 50-20+120+6= 156

b.

Price elasticity of demand for good x= (dQx/dPx) x (Px/Qx)

dQx/dPx= -0.4

Price elasticity of demand for good x= -0.4 x (50/156)= -0.128

Yes, demand for good x less sensitive to the change in its price

c.

Cross elasticity of demand for good x= (dQx/dPz) x (Pz/Qx)

dQx/dPz= 0.1

Cross elasticity of demand for good x= 0.1 x (60/156)= 0.038

There is a positive relationship between both the goods. They are substitute goods.

d.

Income elasticity of demand= (dQx/dY) x (Y/Qx)

dQx/dY= 0.02

Income elasticity of demand= (0.02)(6000/156)= 0.769

As income elasticity is positive which implies good is a normal good.