Answer to Question #200124 in Microeconomics for aman

Question

PERIOD

QUANTITY

PRICE

INCOME

ADVERTISING

1

120

8.00

10

3

2

165

4.00

22

7

3

120

7.00

20

5

4

165

3.00

20

8

5

180

4.00

30

8

6

90

10.00

19

6

7

150

4.00

18

10.2

8

190

1.60

25

9.3

9

160

5.00

30

8

10

200

2.00

35

9.5

Linear Relationship

     a.         Use any multiple regression packages (eg. SPSS package) to estimate a linear relationship between the dependent variable and the independent variables.

     b.         Is the estimated demand function “good”? Why or why not?

     c.         Discuss the economic implications of the various coefficients.

     d.         Compute the price elasticity of demand and income elasticity of demand in period 10. Elaborate your answers.

Answer 1

Solution:

a.). See attached Multiple regression analysis:

b.). The estimated demand function is not good. This is because the adjusted R Square is below the R Square and the residuals of the model are not around zero.

 

c.). The regression coefficient tells you whether there is a positive or negative correlation between each independent variable and the dependent variable. A positive coefficient indicates that the value of the independent variable increases the mean of the dependent variable which tends to increase. A negative coefficient suggests that the independent variable increases, the dependent variable tends to decrease.

The period coefficient is positive which means that as quantity increases period also increases.

The advertisement coefficient is negative which means that as quantity increases advertisement decreases.

The price coefficient is negative which means that as quantity increases, the price decreases.

The income coefficient is positive which means that as income increases so do the quantity.

 

d.). Price elasticity of demand =$=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

% Change in qty demanded = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100$

$\frac{200 -160}{(200+160)/2 } \times 100 = \frac{40}{180} \times 100 = 22.22\%$

% Change in price = $\frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100$

$\frac{2 -5}{(2+5)/2 } \times 100 = \frac{-3}{3.5} \times 100 = -85.71\%$

Ped = $\frac{22.22\%}{-85.71\%} = -0.26$

Ped = 0.26

Ped is less than 1 which means it is price inelastic. The demand is less responsive to changes in price.

 

Income elasticity of demand = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

% Change in qty demanded = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100$

$\frac{200 -160}{(200+160)/2 } \times 100 = \frac{40}{180} \times 100 = 22.22\%$

% Change in Income = $=\frac{I_{2} -I_{1}}{(I_{2}+I_{1})/2 } \times 100$

$\frac{35 -30}{(35+30)/2 } \times 100 = \frac{5}{32.5} \times 100 = 15.38\%$

Income elasticity of demand = $\frac{22.22\%}{15.38\%} = 1.44$

Income elasticity of demand = 1.44

The income elasticity of demand is greater than 1 which means that it is the demand is elastic. It is highly responsive to changes in income levels.