Tutors on net
Tutors on NetTutors on Net

Elasticity Of Demand

 Income Elasticity of Demand

Illustration 19

If a customer’s daily income hikes from $1000 to $1200, his purchase of a commodity X enhances from 50 units per day to 70 units, determine the income elasticity of demand for X.

Solution

Change in demanded quantity ΔM = M2 – M1

                                    =          1200 – 1000    =          200

                        e1        =          Percentage change in demanded quantity
                                                            Percentage change in price

                        e1        =          ΔQ                   M2 + M1
                                                ΔM      *          Q2 + Q1

                        ΔQ       =          70 – 50            =          20

                                    =          20                    1200 + 1000
                                                70        *             50 + 70

                                    =          20                    2200
                                                70        *          120

Income Elasticity of Demand             =          5.23

Illustration 20

Presume demand for cars in Seattle as a function of income is given by the following equation: Q = 30000 + 15M, where Q is the quantity demanded, M is per capita level of income in dollars.

Determine the income elasticity of demand when per capita annual income in Seattle is $20000.

Solution

Income elasticity e1    =       ΔQ                   M
                                              ΔM      *          Q

With respect to procure income elasticity, we have to first ascertain quantity demanded Q at level of income of $20000. Therefore

                        Q         =          30000 + 15 * 20000 = 330000

It will be observed from the provided income demand function that co-efficient of income M is equal to 15. This entails that ΔQ = 15.
                                                                                                                                                                                                    ΔM

With this price of information we can calculate income elasticity.

                        e1        =         ΔQ                   M
                                                ΔM      *          Q

                                    =          15 * 20000
                                                       330000

                                    =          0.90

Illustration 21

The following demand function for apparels has been approximated, Q = 4000 + 40Y – 8.8 P. where Y is income in thousands of dollars, Q is the quantity demanded in units and P is the price per unit. When P = $400 and Y = 40 thousand dollars ascertain the following.

  1. Price Elasticity of Demand, Income Elasticity of Demand
  1. Ascertain what effect a rise in price would have on total revenue
  1. Asses how sales of trousers would change during a period of growing income

Solution

(1) Coefficient of P                 =          ΔQ       =          8.8
                                                            ΔP

Price elasticity of demand      =          ΔQ                   P
                                                            ΔP       *          Q

                                                =          8.8       *          400
                                                                                      Q

Now, let us first ascertain the demanded quantity which is Q at the provided income Y = 40 thousand dollars and given price P = 400 per unit. Substituting the values of income and price in the provided demand function, we procure,

                                    Q         =          4000 + 40Y – 8.8P

                                                =          4000 + (40 * 40) – (8.8 * 400)

                                                =          4000 + 1600 – 3520

                                                =          2080

Therefore,        ep        =        ΔQ                   P
                                                ΔP       *          Q

                                    =          8.8       *          400
                                                                        2080

                                    =          1.70

Income elasticity         =          ΔQ                   Y
                                                ΔY       *          Q

ΔQ = 40,         Q = 2080,        Y = 40 thousand dollars.
ΔY

                                    =          40        *          40      =          0.77
                                                                        2080

(2) Since price elasticity of demand for apparels is less than 1, hike in price would consequent enhancement in total revenue.

(3) As the income elasticity of demand for apparels is less than one, apparels are a requisite and hence the enhancement in income of the people will tend to less than a proportionate enhancement in their sales.

Illustration 22

From the following demand functions, ascertain whether demand is inelastic, elastic or unitary elastic at the provided price.

  1. Q = 200 – 2P and the provided P = $10
  1. P = 2000 – 30P and the provided P = $50
  1. P = 100 – 0.2Q and the provided P = $10

Solution

  1. Q = 200 – 2P where P = $10

In this demand function the derivative dQ    =          2
                                                              dP

Substituting the value of P in this demand function (1), we obtain
           
                        Q         =          200 – (2 * 10)  =          180

                        ep        =          dQ                   P         
                                                dP        *          Q

                                    =          2          *          20 / 180

                                    =          0.22

Since ep is less than 1, demand is inelastic.

  1. Q = 2000 – 30P, where P = 50

In this demand function equation, the derivative dQ / dP     =          30

Substituting the value of P in this demand function

                        Q         =          2000 - 30 * 50

                                    =          500

                        ep        =          30        *          1500 / 500      

                                    =          3

Since ep is >1, demand is elastic.

  1. P = – 0.2Q and the provided P = $10

Let us first express this demand function in terms of demanded quantity as a function of price.

                                    P          =          100 – 0.2Q

                                    0.2Q    =          100 – P

                                    Q         =          100 – P
                                                               0.2

                                                =          500 – 5P

Now price is given to be $10. substituting in the Q equation, we obtain the following.

                                    Q         =          500 – 5*10

                                                =          500 – 50          =          450

The derivative of dQ which is 500 – 5P is 5.
                             dP

                                    ep        =          dQ                   P
                                                            dP        *          Q

                                                =          5          *          10        =          0.11
                                                                                    450

Since ep = 0.11 and is less than 1, demand is inelastic.

Online Live Tutor Income Elasticity of Demand, Demand functions:

    We have the best tutors in Economics in the industry. Our tutors can break down a complex Income Elasticity of Demand, Demand functions problem into its sub parts and explain to you in detail how each step is performed. This approach of breaking down a problem has been appreciated by majority of our students for learning Income Elasticity of Demand, Demand functions concepts. You will get one-to-one personalized attention through our online tutoring which will make learning fun and easy. Our tutors are highly qualified and hold advanced degrees. Please do send us a request for Income Elasticity of Demand, Demand functions tutoring and experience the quality yourself.

Online Elasticity of Demand Help:

    If you are stuck with an Elasticity of Demand Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Elasticity of Demand help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Elasticity of Demand Homework Help. Please do send us the Elasticity of Demand problems on which you need help and we will forward then to our tutors for review.