The demand for good X is given by Q x d = 1200-0.5P x +0.25P y -8P z +0.1M Resea

Question

The demand for good X is given by

Qxd = 1200-0.5Px+0.25Py-8Pz +0.1M

Research shows that the prices of related goods are given by Py=$5900 and Pz = $90, while the average income of individuals consuming this product is M=$55,000

A) How many units of good X will be purchased at Px= 4,910?

B) What is the own price elasticity at Px= $4,910? Is demand elastic or inelastic at this point? What would happen to firm’s revenues if it decided to charge a price below $4,910?

C) What is the cross price elasticity of demand between good X and good Y? Are goods X and Y substitutes or complements?

D) What is the income elasticity of demand? By how much would income need to change to bring an increase of 5% in the quantity demanded of good X?

Explanation / Answer

Qxd = 1200-0.5Px+0.25Py-8Pz +0.1M

When Py = 5900, Pz = 90, M = 55000,

Qxd = 1200 - 0.5Px + (0.25 x 5900) - (8 x 90) + (0.1 x 55000)

Qxd = 7455 - 0.5Px

(A) When Px = 4910, Qxd = 7455 - (0.5 x 4910) = 5000

(B) Price elasticity, eP = (dqx / dPx) x (Px / qx)

= - 0.5 x (4910 / 5000) = - 0.491

Since absolute value of eP < 1, demand is inelastic.

When price is reduced, quantity demanded increases at a lower proportion, causing total revenue to decrease.

(C) Cross price elasticity = (dqx / Py) x (Py / qx)

= 0.25 x 5900 / 5000 = 0.295

A positive cross price elasticity means as price of one good decreases (increases), demand of the other good decreases (increases). So the goods are substitutes.

(D) Income elasticity = (dqx / dM) x (M / qx)

= 0.1 x (50000 / 5000)

= 1

So income needs to increase 5% in order to increase quantity demanded by 5%.

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