Answer to Question #184333 in Microeconomics for myra

Question

Suppose you are the economic adviser of a company producing three brands of mobile phones; Nokia 10 , Samsung X and iPhone Z. Suppose further that, your company currently sells 120 units of iPhone Z at ¢800 per unit, 150 units of Samsung X at ¢800 per unit and 200 units of Nokia 10 at ¢100 per unit, but in a bid to maximize profit, the company’s managing director proposes an increase in price of Samsung X from ¢800 to ¢1000 per unit for which quantity demanded is anticipated to fall from 150 to 100 units; iPhone Z from ¢800 to ¢1200 per unit for which quantity demanded is anticipated to fall from 120 to 100 units; and Nokia 10 from

¢100 to ¢200 per unit for which quantity demanded is expected to fall from 200 to 100 units.

1.Using the mid-point formula, compute the price elasticity of demand for each brand.

2. From your answer in i, what is the type and economic interpretation of each brand’s value of elasticity.

Answer 1

I)

$P_{ed}=\frac{[\frac{(Q_1-Q_0}{(Q_1+Q_2)/2}]}{[\frac{P_!-P_o}{(P_1+P_o)/2}]}$

Here,

 Q₀ is the initial quantity demanded

Q₁ is the quantity demanded after a price change

P₀ is the initial price

P₁ is the new price​

a) price elasticity of demand for Nokia 10

Q₀ = 200 units, and Q₁ = 100 units

P₀ = 100 per unit, and P₁ = 200 per unit

 

$P_{ed}=\frac{[\frac{100-200}{(100+200)/2}}{\frac{200-100}{(200+100)/2}}$

$P_{ed}=\frac{-100}{150}\times\frac{150}{100}=1$

Therefore Price elasticity of demand for the Nokia 10, is 1.

b)price elasticity of demand for samsung X

Q₀ = 150 units, and Q₁ = 100 units

P₀ = 800 per unit, and P₁ = 1000 per unit

$P_{ed}=\frac{\frac{100-150}{(100+150)/2}}{\frac{1000-800}{(1000+800)/2}}$

$P_{ed}\frac{-50}{125}\times\frac{900}{200}=1.81$

Therefore Price elasticity of demand for Samsung X is 1.81.

c) price elasticity of demand for iphone z

Q₀ = 120 units, and Q₁ = 100 units

P₀ = 800 per unit, and P₁ = 1200 per unit

$P_{ed}=\frac{\frac{100-120}{(100+120)/2}}{\frac{1200-800}{(1200+800)/2}}$

$P_{ed}=\frac{-20}{100}\times{1000}{400}=0.45$

Therefore Price elasticity of demand for iPhone Z is 0.45.

 II)Type and Economic interpretation of each brand’s value of elasticity.

 

a) Nokia 10:

The elasticity of demand for Nokia 10 is 1.

Therefore Nokia 10 has a perfect elasticity of demand

 This means proportionate change in the price and quantity demanded is the same.

There is an inverse relationship between quantity demanded and price with an equal proportion of change in quantity and price.

 

b) Samsung X:

The price elasticity of demand for Samsung X is 1.81.

1.81 is greater than 1 hence the demand for samsung X is relatively elastic. A small change in price results to a relatively high change in quantity demanded. The negative sign shows that there is a negative relationship between quantity demanded and price.

 

c) iPhone Z:

 

The price elasticity of demand for iPhone Z is 0.45.

0.45 is less than 1 meaning iphone z has a relatively les elastic or relatively inelastic demand.

An increase in price will have minimal impact on quantity demanded. The negative sign shows negative relationship between quantity demanded and price.