Question

Question 12. You are the manager of a firm that sells a leading brand of alkaline batteries. A file named Q12.xls with data on the demand for your product is available online at www.mhhe.com/baye8e. Specifically, the file contains data on the natural logarithm of your quantity sold, price, and the average income of consumers in various regions around the world. Use this information to perform a log-linear regression, and then determine the likely impact of apercent decline in global income on the overall demand for your product.

Short answer

Answer

The elasticity of the requested quantity in relation to the income is 3%, by increasing the income by an average of 1%, the demanded quantity decreases by 7%.

Step-by-step solution

Do the regression analysis

As per the above data, the log-linear regression equation can be interpreted as:

By using the spreadsheet program, we will do the regression analysis. Its procedure is:

1. To start with, from the toolbar select "Data".
2. The "Data" menu shows.
3. After that, choose "Data Analysis".
4. The Data Analysis - Analysis Tools dialog is shown now.
5. Chose "Regression".
6. Click "OK".
7. After that, in the Regression dialog box, select the "InputRange" box and then choose the dependent variable data.
8. Select the "InputRange" box and then choose the independent variable data.
9. At last, to run the results, select "OK".

Check for elasticity of quality demand

After the procedure, check the values of the coefficients from the table. Then, obtain an estimate of the demand for the product through the equation:

$\ln \left(\text{Quantity}\right)=1.29-0.07\ln \left(\text{Price}\right)-0.03\ln \left(\text{Income}\right)$

The coefficients ofprice and income measures the elasticity of Quantity demanded with respect to Price and Income respectively.

The elasticity of the requested quantity in relation to the income is 3%.

This clearly shows by increasing the income by an average of 1%, the demanded quantity decreases by 7%.