(a) What is the own-price elasticity of demand when PX = $140? Use the point elasticity formula. Show all calculations.

Qd = 1200 - 3Px - 0.1Pz

Given Pz = $300

Then Qd = 1200 - 3Px - (0.1* 300)

Qd = 1200 - 3Px - 30

Qd = 1170 - 3Px

 

When Px = $140, the quantity demanded Q = 1170 - (3*140) = 750

The point elasticity = (dQ/dP) * (P/Q)

The point elasticity = (-3) * (140/750) = -0.56

The absolute value of the own-price elasticity of demand when PX = $140 is 0.56, which is less than 1. Thus, the demand is inelastic.

 

(b) Is this a necessary or a luxury good? Explain.

When there is 1% increase in price, the quantity demanded of the product will decrease by 0.56%. This means that the demand is inelastic and thus, a necessary good.

 

(c) What will happen to the firm's revenue if it decided to charge a price below $140? Explain and show all calculations.

Because the price elasticity of demand is inelastic, the price effect (which lowers revenue) will outweight the quantity effect (which raises revenue). So when the firm charges a price below $140, the firm's revenue will decrease.

 

(d) What is the cross-price elasticity between Good X and Good Z when PX = $140 and PZ= $300? Are goods X and Z substitutes or complements?

ZEd = (dQx/dPz) * (Pz/Qx)

ZEd = (-0.1) * (300/750) = -0.04

This means that when there is 1% increase in the price of good Z, the quantity demanded of good X will decrease by 0.04%. Hence the X and Z are complements.