Question

Demand for Magnum Ice Cream is given by an equation as Q = 70 – 10P + 4 Px + 50 I  

Where, Q = Quantity of Magnum demanded, P = Price of Magnum Ice Cream, Px = Price of Walls Ice Cream, I = Per Capita Income

a.      Assume P = Rs 100, Px = Rs 120 and I = Rs 25 (Rs in thousands).  

Calculate        

(i)                Price Elasticity of Demand

(ii)             Cross Price Elasticity of Demand

(iii)           Income Elasticity of Demand 

How the elasticity does estimates help in managerial decision making?  

Answer 1

$Q=70-10p+4Px+50I$

where Q= Qty of magnum demanded

        P= Price of magnum

      Px= Price of walls

        I= Per Capita Income

a) Price elasticity of demand

$=\frac{\triangle Q}{\triangle P}* \frac{Q}{P}$

$Q= 70-10(100)+4(120)+5(25)$

$\frac{\triangle Q}{\triangle P}=-10$

Putting the values

$\frac{100}{800}=-10$

The price elasticity of demand is -1.25

Since the price elasticity is less than 1, It means demand per magnum is inelastic

b) Cross Price Elasticity of Demand

$E_c=\frac{\triangle Q}{\triangle P}*\frac{Px}{Q} \implies 4* \frac{120}{800}=0.6$

c) Income Elasticity of Demand

$=\frac{\triangle Q}{\triangle I}* \frac{I}{Q}$

$Q= 70-10p+4px+50I$

$50*25/800= 1.56$

Since the goods are substitutes, so management should not increase the price as it would lead to an increase in the quantity demanded of other goods.