Answer to Question #202181 in Management for Kwabena

Question

In the economy of Queensland, two products (Sta and Star) are prominent due to their quality and durability. At the price of GHȼ 30 for Sta, 5,000 quantities of Sta are demanded. Stonewall, a banker lives in this economy and earns a weekly income of GHȼ 2,000. At this income level, Stonewall consumes 100 quantities of Star monthly. The price of Sta increases by 50%, now 4,000 quantities of Sta are demanded. At the initial price of Sta, 1000 quantities of Star were demanded but at the new price of Sta, 3,000 quantities of Star are demanded. Stonewall attains a professional qualification thus his weekly income increases by 20%, at the new income level; he consumes 200 quantities of Star monthly.

a)Determine the Own Price Elasticity of Demand for Sta and interpret your answer?

b)Determine the Cross Price Elasticity of Demand for both products and interpret the

relationship between the two products?

c)Determine the monthly Income Elasticity of Demand for Star and explain the nature

of Star to Stonewall?

Answer 1

Answers

a)Determine the Own Price Elasticity of Demand for Sta and interpret your answer?

We use the Mid-point method to calculate the own price elasticity.

Own Price Elasticity of Demand= percentage change in quantity demanded/percentage change in price

Let P1 be the initial price of Sta

Let P2 be the final price of Sta

Let Q1 be the initial demand of Sta

Let Q2 be the final demand of Sta

Own Price Elasticity of Demand= Q2-Q1/(Q2+Q1)/2×100/P2-P1/(P2+P1)/2×100

               =-22.22/40

               =0.55

The elasticity of demand is always taken as an absolute. The elasticity of demand is 0.55, which is less than one; hence the demand is inelastic. Since the elasticity of demand is inelastic, changes in prices will have a small effect on the demand. For instance, if prices change by 1%, the change in demand will be less than 1%.

b) Determine the Cross Price Elasticity of Demand for both products and interpret the

Relationship between the two products?

Let Q2 be the initial quantity of Star demanded

Let Q3 be the initial quantity of Sta demanded

Let P1 be initial Sta price

Let P2 be final Sta price

Cross Price Elasticity of Demand= percentage change in Star quantity/percentage change in Sta price

             =Q3-Q2/(Q2+Q3)/2×100/P2-P1/(P2+P1)/2×100

               =100/40

               =2.5

The cross price elasticity of demand is 2.5, which is greater than 0 thus, Star and Sta are substitutes. Increase in the prices of Star would lead to the increase of demand for Sta. In this scenario, when Sta prices increase to 45 from 30, the Star demand increases to 3000 from 1000.

c)Determine the monthly Income Elasticity of Demand for Star and explain the nature

of Star to Stonewall?

Income elasticity of demand for Star= percentage change in quantity demanded/percentage change in income

Let A1 be the initial income=2000

Let A2 be the final income=2400

Let Q1 be initial demand=100

Let Q2 be final demand=200

Q2-Q1/(Q2+Q1)/2×100/P2-P1/(P2+P1)/2×100

         =66.6/18.18

          =3.66

The income elasticity of demand is 3.66, which is greater than 0, indicating Star is a normal good. Normal goods have a positive income elasticity of deman, which means an increase in demand is directly proportional to an increase in income. For every 1% increase in Stonewall's income, his demand for Star increases by 3.66%.