Answer to Question #74272 in Microeconomics for zulfiqar

Question

Given the following demand equation for economics books
Qx = 5000 - 500Px + 0.011 + 250Pz
(a) Assuming I = $ 20,000 and Pz = $20 What is the price elasticity of x at Px = $16 ?
(b) Assuming Px = $20 and Pz = $20 what is the income elasticity at I = $20,000 ?
(c) Assuming Px = $22 and I = $20,000 Calculate the cross elasticity at Pz = $20 ?

Answer 1

Qx = 5000 - 500Px + 0.01I + 250Pz
(a) Assuming I = $ 20,000 and Pz = $20:
Qx = 10200 - 500Px.
If Px = $16, then Qx = 2200 units.
The price elasticity of x at Px = $16 is:
Ed = -500*16/2200 = -3.64, so demand is elastic.
(b) Assuming Px = $20 and Pz = $20 the income elasticity at I = $20,000 is:
Ei = 0.01*20,000/2200 = 0.09, so economic book is normal good.
(c) Assuming Px = $22 and I = $20,000:
Qd = 5000 - 500*22 + 200 + 250*20 = -800.
The cross elasticity at Pz = $20 is:
CrossEd = 250*20/(-800) = -6.25, so the goods are complements.