Question

The demand function for Good X is defined as QX = 20 – 0.5PX + 1.2PY, where PY is the price of Good Y. Calculate the price elasticity of demand using the point formula for PX = 12 and PY = 10. Determine whether demand is elastic, inelastic, or unit elastic with respect to its own price and whether Good Y is a substitute or a complement with respect to Good X.

Answer 1

Answer:Good X is inelastic, Good Y is inelastic, The two goods were substitute

Step-by-step explanation:

Qx= 20-0.5PX+ 1.2PY

QX=20-0.5 (12)+1.2 (10)

QX=20-6 + 12

QX = 26

To calculate the price elasticity of demand

e = dX/dP*PX/X

e = -0.5 (13)/26

= 0.23 since e < 1 Good X is inelastic

e = dX/dP*PY/Y

e = 1.2 (10)/26

e = 12/26

= 0.46 since e < 1 Good Y is inelastic

To know whether Good Y is a substitute or a complement with respect to X, we calculate the cross elasticity of demand

eXT = dX/dPY*PY/X

1.2 (10)/26

= 12/26

= 0.46 ( since it is positive the two good X and Y are substitute)