Question

Given the demand data answer the following questions after estimating your regression model of demand for Good 1. Quantity demanded of Good 1 is given by Q1 and the price of Good 1 is given by P1. The price of Good 2 is given by P2. Use a linear-linear functional form (i.e., do not transform the variables in anyway, such as with natural logarithms). Many economists refer to this as a “lin-lin” functional form. Evaluate elasticities at the sample means of the data.

Q1	P1	P2	INCOME
81.70	1.78	1.11	25088
56.90	2.27	0.67	26561
64.10	2.21	0.83	25510
65.40	2.15	0.75	27158
64.10	2.26	1.06	27162
58.10	2.49	1.10	27583
61.70	2.52	1.09	28235
65.30	2.46	1.18	29413
57.80	2.54	0.88	28713
63.50	2.72	1.30	30000
65.90	2.60	1.17	30533
48.30	2.87	0.94	30373
55.60	3.00	0.91	31107
47.90	3.23	1.10	31126
57.00	3.11	1.50	32506
51.60	3.11	1.17	32408
54.20	3.09	1.18	33423
51.70	3.34	1.37	33904
55.90	3.31	1.52	34528
52.10	3.42	1.15	36019
52.50	3.61	1.39	34807
44.30	3.55	1.60	35943
57.70	3.72	1.73	37323
51.60	3.72	1.35	36682
53.80	3.70	1.37	38054
50.00	3.81	1.41	36707
46.30	3.86	1.62	38411
46.80	3.99	1.69	38823
51.70	3.89	1.71	38361

1. What is the change in Q1 given a change in P1? _________ 2. Is it statistically significant at the 95% level? _________ 3. What is the mean of Q1? _________ 4. What is the mean of P1? _________ 5. What is the price elasticity of demand for Good 1? _________ 6. Is the demand for Good 1 elastic or inelastic at the sample means of the data? _________ 7. To increase revenue, the firm selling Good 1 should raise or lower price? _________ 8. What is the change in Q1 given a change in P2? _________ 9. Is it statistically significant at the 95% level? _________ 10. What is the mean of P2? _________ 11. What is the cross price elasticity of demand of Good 1 given a change in the price of Good 2? _________ 12. Are Goods 1 and 2 substitutes or complements? _________ 13. What is the change in Q1 given a change in INCOME? _________ 14. Is it statistically significant at the 95% level? _________ 15. What is the mean of INCOME? _________ 16. What is the income elasticity of demand for Good 1? _________ 17. Is Good 1 a normal or inferior good? _________ If normal, what type? _________ 18. What is the adjusted R2 ? _________ 19. Given P1 = $3.75, P2 = $1.65, and INCOME = $38000 what is the forecasted value of Q1? _________ 20. Given P2 = $1.65 and INCOME = $38000 what is the revenue-maximizing level of Q1? _________ What is the corresponding level of P1 that maximizes revenue? _________

Answer 1

Q1-7

The develop a relationship between Q1 and P1, regression analysis is done in excel by using following steps;

Step 1: Write the data values of Q1 and P1 in excel.

Step 2: Select Data > Data Analysis > Regression > Ok. the screenshot is shown below,

Step 3: Input Y Range: Q1 column, Input X Range: P1 column and Confidence Interval = 95% then OK. The screenshot is show below,

The result is obtained. The screenshot is shown below,

1)

From the result, regression equation is,

For 1 unit change in P1, the Q1 will decrease 10.165

2)

From the result summary of regression analysis, p-value for slope of P1,

Hence it is statistically significant at 95% level

3)

The mean of Q1 is obtained using the excel function =AVERAGE()

4)

he mean of P1 is obtained using the excel function =AVERAGE()

5)

The price elasticity of demand for good 1

6)

At the sample mean elasticity is,

There is a large value of hence demand is elastic.

7)

The revenue is defined by Price*Quantity such that

Total Revenue for goods 1 = P1*Q1 = P1*(87.28-10.165 * P1) = 87.28 * P1 - 10.165 * P1^2

Hence if the price increase revenue will decrease because of the negative quadratic function

Q8-10

Similarly thre regression analysis is done for P2 and Q1, The screenshot of result summary is given below,

8)

The regression equation is,

For 1 unit change in P2 the Q1 will decrease 11.4734

9)

The p-value for slope,

Hence it is statistically significant

10)

The mean of P2 is,