4. Bob’s Underground, a limited liability corporation specializing in new rap ar
ID: 1103712 • Letter: 4
Question
4. 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 + dPR
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 PR is the price of a related product. The regression results are:
Adjusted R Square
0.8222
Independent Variables
Coefficients
Standard Error
t Stat
P-value
Intercept
-32.32
65.77
-0.491
0.626
P
-2.46
1.38
-1.813
0.079
M
0.008
0.001
6.045
9.53E-07
PR
-2.56
1.26
-2.025
0.051
Discuss whether you think these regression results will generate good sales estimates for B.U. LLC, rap.
Now assume that the income is $35,000, the price of the related good is $24, and B.U. chooses to set the price of its product at $21.
b. What is the estimated number of units sold given the data above?
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 increases by 3%, what would happen (in percentage terms) to quantity demanded?
f. If PR decreases by 5%, what would happen (in percentage terms) to quantity demanded?
Adjusted R Square
0.8222
Independent Variables
Coefficients
Standard Error
t Stat
P-value
Intercept
-32.32
65.77
-0.491
0.626
P
-2.46
1.38
-1.813
0.079
M
0.008
0.001
6.045
9.53E-07
PR
-2.56
1.26
-2.025
0.051
Explanation / Answer
Answer:
Here the R- square value is 0.8222. That tell that 82.22% of variation is expressed by the independent variables P, M and PR. Here as we see the P - value for individual independent varaible. Only Variableis significant here. But, other two variable like P and PR are not significant here. But, overall the model is significant here.
(b) HEre M = $ 35,000
PR = $ 24 and P = $ 21
Q = -32.32 -2.46P + 0.008M -2.56PR
Q = -32.32 - 2.46 * 21 + 0.008 * 35000 - 2.56 * 24 = 134.58
(d) Here the values for the elasticities of
(i) Own -price = (dQ/Q)/ (dP/P) = (dQ/dP) * (P/Q) = (-2.46) * (21/134.58) = -0.3838
(ii) Income = (dQ/Q)/ (dM/M) = (dQ/dM) * (M/Q) = 0.008* (35000/134.58) = 2.08
(iii) Cross - Price = (dQ/Q)/ (dPr/Pr) = (dQ/dPr) * (Pr/Q) = (-2.56) * (24/134.58) = -0.4565
(d) If P increase 4 %, the qunatity demanded will decrease
the New Pnew = 21 * 1.04 = $ 21.84
Qnew = -32.32 -2.46P + 0.008M -2.56PR
Qnew = -32.32 -2.46 * 21.84 + 0.008 * 35000 -2.56 * 24 = 132.5136
Change in Q = (132.5136 - 134.58) * 100/ 134.58 = -1.535 %
(e) If M increase 3% , the quantity demanded will increase
the New Pnew = 35000 * 1.03 = $ 36050
Qnew = -32.32 -2.46P + 0.008M -2.56PR
Qnew = -32.32 -2.46 * 21 + 0.008 * 36050 -2.56 * 24 = 142.98
Change in Q = (142.98 - 134.58) * 100/ 134.58 = 6.24 % increase
(f) if Pr increase 5%, the quantity demanded will decrease
the New Pnew = 24 * 1.05 = $ 25.2
Qnew = -32.32 -2.46P + 0.008M -2.56PR
Qnew = -32.32 -2.46 * 21 + 0.008 * 35000 -2.56 * 25.2 = 131.508
Change in Q = (131.508 - 134.58) * 100/ 134.58 = -2.28 % increase
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