Question

Bob’s Underground, a limited liability corporation specializing in new rap artists (B.U. LLC, rap) has the following demand function:

Q = a + bP + cM + dR

where Q is the quantity demanded of the most popular product B.U. sells, P is the price of that product, M is income, and R is the price of a related product. The regression results are:

Adjusted R Square	0.8257
Independent Variables	Coefficients	Standard Error	t Stat	P-value
Intercept	9998.24	72.84	137.26	6.54E-46
P	-5.557	2.066	-2.689	0.011
M	0.0039	0.001	3.258	0.003
R	4.92	1.018	4.829	3.27E-05

1. Discuss whether you think these regression results will generate good sales estimates for B.U. LLC, rap.

Now assume that the income is $52,477, the price of the related good is $16.25, and B.U. chooses to set the price of its product at $14.95.

b.   What is the estimated number of units sold given the data above? (round to nearest unit; no decimals)

c.   What are the values for the own-price, income, and cross-price elasticities?

d.   If P increases by 4%, what would happen (in percentage terms) to quantity demanded?

e.   If M decreases by 3%, what would happen (in percentage terms) to quantity demanded?

f.    If R increases by 6%, what would happen (in percentage terms) to quantity demanded?

Answer 1

(a) Yes, the above regression results would provide a good estimate for B.U. LLC. Because, all of the factors considered here (such as own price, related price and income), show significant impact individually. This is evident from the individual p-values, which are very low. Also, these three factors collectively explain 82.57% of total variations in sales. Hence, this model will help the B.U. LLC to get a good estimate of their demand.

(b) Given the values of M, P and R, the demand can be estimated as:

(c) The elasticities can be calulated as follows: