Answer to Question #200104 in Macroeconomics for Abdul basit

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

b.     How the elasticity does estimates help in managerial decision making?  

Answer 1

Solution:

a.).  i.). Price elasticity of demand:

Ped = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

Ped = $\frac{\triangle Q}{\triangle P} \times \frac{P}{Q}$

From the demand function, we are only interested in the elasticity of quantity demanded with respect to Magnum’s ice cream price.

The demand function: Q = 70 – 10P + 4Px + 50I

Ped = $\frac{\triangle Q}{\triangle P} \times \frac{P}{Q}$

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

P = Rs 100

Substitute the figures given to derive Q:

Q = 70 – 10(100) + 4(120) + 50(25,000)

Q = 70 + 480 + 1,250,000 – 1000

Q = 1,249,550

Ped =$-10\times \frac{100}{1249550} = -10\times0.0000800288 = -0.000800288$

Price elasticity of demand (Ped) = -0.000800288

ii). Cross Price Elasticity of demand:

In the case of cross-price elasticity of demand, we are interested in the elasticity of quantity demand with respect to the price of Walls ice cream. Thus, we can use the following equation:

Cross-price elasticity of demand =$\frac{\triangle Q}{\triangle Px} \times \frac{Px}{Q}$

Q = 70 – 10P + 4Px + 50I

$\frac{\triangle Q}{\triangle Px} = 4$ ΔQ/ΔPx = 4

Q = 70 – 10(100) + 4(120) + 50(25,000)

Q = 70 + 480 + 1,250,000 – 1000

Q = 1,249,550

Px = Rs 120

Cross-price elasticity of demand = $4\times \frac{120}{1249550} = 4\times0.000096034572 = 0.00038413$

Cross-price elasticity of demand = 0.00038413

iii.). Income Elasticity of demand:

In the case of income elasticity of demand, we are interested in the elasticity of quantity demanded with respect to per capital income. Thus, we can use the following equation:

Income elasticity of demand = $\frac{\triangle Q}{\triangle I} \times \frac{I}{Q}$

Q = 70 – 10P + 4Px + 50I

$\frac{\triangle Q}{\triangle I} = 50$ ΔQ/ΔI = 50

Q = 70 – 10(100) + 4(120) + 50(25,000)

Q = 70 + 480 + 1,250,000 – 1000

Q = 1,249,550

I = Rs 25,000

Income elasticity of demand =$50\times \frac{25,000}{1249550} = 50\times0.0200072026 = 1.00036013$

Income elasticity of demand = 1.00036013

b.). The elasticity of demand, whether price, cross elasticity, and income elasticity of demand is critical to every manager when it comes to important decisions. The management takes into account the price elasticity of demand when they make decisions regarding the pricing of the goods. This is because the change in the price of a good will bring about a change in the quantity demanded depending upon the coefficient of price elasticity. Income elasticity of demand, on the other hand, helps managers to predict future demand of any products and services especially when they have knowledge of probable future income of the consumers. Your business decisions should be sensitive to the impact of income elasticity on your particular industry. Cross elasticity of demand is of significant importance in managerial decision-making for formulating proper price strategy between different products depending on their cross-elasticity coefficient.