Answer to Question #276716 in Microeconomics for cyah

Question

You have been presented with the following data and asked to fit statistical demand functions:

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

a.Linear Relationship

i.Use any multiple regression packages to estimate a linear relationship between the dependent variable and the independent variables.

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

iii.Discuss the economic implications of the various coefficients.

b.Non-linear relationship.

i.Select and estimate any form of non-linear relationship.

ii.Is the estimated demand function “good”? Why or why not? Compare with the linear form above. Elaborate.

Answer 1

Estimated regression equation:

Quantity = 205.86 - 12.24 $×$ Price + 1.41 $×$ Income - 3.34 $×$ Advertising

ii)

R² = 0.9729

It means that 97.29% of variation in the dependent variable can be explained by the model, so there is very high Goodness of fit.

iii)

Intercept is 205.86, which is the minimum possible quantity when all of the independent variables are set to 0.

Coefficient of price is -12.24, which means that as price rises (falls) by 1 unit, quantity falls (rises) by 12.24 units.

Coefficient of income is 1.41, which means that as income falls (rises) by 1 unit, quantity rises (falls) by 1.41 units.

Coefficient of advertising is -3.34, which means that as advertising rises (falls) by 1 unit, quantity falls (rises) by 3.34 units.

b)

In this case,there is no constant change in price and quantity which leads to a non- linear Demand curve.There is an inverse relationship between Price and Demand. The resulting curve has a downward sloping curve.

ii) The estimated demand curve is not good since there is no constant change in price and quantity demanded. None of the above function has a linear demand curve