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# Determining and interpreting elasticities of demand

In Qx = 3-0.5 in Px - 2.5 In Py + lnM + 2lnA

ln being natural log

Where
Px = \$10
Py = \$4
M = \$20,000
A - \$250

a) Determine the own price elasticity of demand and state whether demand is elastic, inelastic or unitary elastic
b) Determine the cross price elasticity of demand between good X and good Y and state whether these two goods are substitutes or compliments
c) Determine the income elasticity of demand state whether good X is normal or inferior
d) Determine the own advertising elasticity of demand

#### Solution Preview

Solution:

a) Determine the own price elasticity of demand and state whether demand is elastic, inelastic or unitary elastic

In Qx = 3-0.5 in Px - 2.5 In Py + lnM + 2lnA
Differentiating with respect to Px both sides we get
(1/Qx) *d(Qx)/dPx=-0.5*(1/Px)
dQx/dPx=-0.5*Qx/Px

We Know, Own price elasticity of demand=(dQx/dPx)*(Px/Qx)
=-0.5*(Qx/Px)*(Px/Qx)=-0.5
Absolute value of own ...

#### Solution Summary

Solution describes the steps for calculating own price elasticity, cross price elasticity, income elasticity and advertising elasticity of demand for a given natural logarithm function. It also predicts the nature of related good and nature of given demand based upon elasticities.

\$2.19