Question

I.          Multivariate Linear Demand Curve:                                                                

            Lorena Bob wishes to analyze demand for Cleavers, a new cutting device, dubbed product x, by estimating  

                                                 Qdx = a - b Px + c Py + d I + e AD

She creates a worksheet in EXCEL with 5 columns: Qdx, Px, Py, I, AD. Here Qd_x is the demand for x, P_x is the price of x, P_y is the average price in dollars of another product Y, and I is dollars of household income and AD is total advertising expenditure for x.

In a typical market, the Px is $ 100, Py is $ 50, average family income is $ 40,000, and AD equals $ 1,000.   A portion of the Excel output is reproduced below.

SUMMARY OUTPUT                                                                                  

Regression Statistics                                                                           

Multiple R                   0.97757806                                                                            

R Square                     0.9400000                                                                              

Adjusted R Square      0.930000                                                                                

Standard Error            40                                                                               

Observations               25                                                       

ANOVA                                                                                            

D             SS                   MS                    F                  Signific F                   

Regression       2          1.593277         0.796638         226.3004         6.19E-15        

Residual          23        0.0739257       0.00352                                                          

Total                25        1.6672026                                                                  

Coefficients    STD Error

Intercept        2000      1596.0

X Variable 1 -0.25       5          

X Variable 2   10          4             

X Variable 3   1.5          0.022            

X Variable 4   10           0.5

1. Write down the equation that was estimated in EXCEL

2. Evaluate the slope with respect to each independent variable. Provide an interpretation for these values. Perform an impact-analysis.

3. Given the initial values, predict the level of sales in this market. Derive a 95% confidence interval around this prediction.

4. Use the initial values to calculate and interpret the following entities:

a.         own price elasticity of demand for x: =

b.         cross price elasticity of demand between x and y: =

c.         income elasticity of demand for x: =

5. Is Px a significant variable in this model -- test at 95%.

The calculated t value =

The table value of t =

Can you reject the null hypothesis (of no significance) ? _______

6.         Is Py a significant variable in this model -- test at 95%.

The calculated t value =

The table value of t =

Can you reject the null hypothesis (of no significance) ? _______

7. Test at 99% whether x is a normal good

The calculated t value =

The table value of t =

Can you reject the null hypothesis (of “not a normal good”) ? _______

8. Provide a precise interpretation of R squared for this problem.

Answer 1

Qdx = a - b Px + c Py + d I + e AD

1. Qdx = 2000 - 0.25 Px + 10 Py + 1.5 I + 10 AD

2. slope with respect to each independent variable

d Qdx / d Px = -0.25

For a unit increase in Px, Qdx falls by 0.25

d Qdx / d Py = 10

For a unit increase in Py, Qdx rises by 10

d Qdx / d I = 1.5

For a unit increase in I, Qdx rises by 1.5

d Qdx / d AD = 10

For a unit increase in AD, Qdx rises by 10

3. level of sales in this market = 2000 - 0.25 *100 + 10*50 + 1.5*40000 + 10*1000

= 2000 - 25 + 500 + 60000 + 10000

= 72475

4.

a.         own price elasticity of demand for x: = (d Qdx / d Px) * (Px/Qdx)

= -0.25 * 100 / 72475

= -25/72475

= -0.00034

For a percentage increase in Px, Qdx falls by 0.00034 percent.

b.         cross price elasticity of demand between x and y: = (d Qdx / d Py) * (Py/Qdx)

= 10 * 50 / 72475

= 500/72475

= 0.0069

For a percentage increase in Py, Qdx rises by 0.0069 percent.

c.         income elasticity of demand for x: = (d Qdx / d I) * (I/Qdx)

= 1.50 * 40000 / 72475

= 60000/72475

= 0.83

For a percentage increase in I, Qdx rises by 0.83 percent.

Note: max. 4 parts