Answer to Question #275421 in Accounting for Afra

Question

The demand equation for a good is given by the equation: 

Q = 700 – 2P + 0.02Y 

(Where P is the price and Y is the income). 

Determine the following:

(a). Price elasticity of demand when P = $25 and Y = $500. 

(b). Income elasticity of demand when P = $25 and Y = $500.

(c). Interpret the results obtained in (a) & (b) above.

Answer 1

Solution

Demand Equation: Q= 700 – 2P + 0.02Y 

When P = $25 and Y = $500, demand(Q) is:

$Q= 700 – 2(25) + 0.02(500) = 660$

(a)

Price elasticity (e) of demand when P = $25 and Y =$500

$e=(P/Q) *(dQ/dP)$

Derivative of Q with respect to P:

$dQ/dP=-2$

So, price elasticity(e) is

$e=(P/Q)∗(dQ/dP)=(25/660)*(-2)= -5/66=-0.076$

Thus, price elasticity is −0.076

(b)

Income elasticity (i) of demand when P = $25 and Y =$500

$i=(Y/Q) *(dQ/dY)$

Derivative of Q with respect to Y:

$dQ/dY=0.02$

So, Income elasticity(i) is

$i=(Y/Q)* (dQ/dY)= (500/660)*(0.02)=1/66=0.015$ Thus Income elasticity (i) is 0.015

(c)

From the results, it's clear that the price elasticity of demand (0.076) is less than 1, implying the demand for the good is inelastic. It's also clear that the Income elasticity of demand(0.015) is positive, implying that the good in question is a normal good.