Question #74272

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 ?

Expert's answer

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.

(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.

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