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+dRQ=a+bP+cM+dR

where QQ is the quantity demanded of the most popular product B.U. sells, PP is the price of that product, MM is income, and RR is the price of a related product. The regression results are:

Adjusted R2R2 0.7786

Independent Variables	Coefficients	Standard Error	t-statistic	P-value
Intercept	2193.39	86.935	25.230	1.09E-22
P	-4.36	1.045	-4.172	0.000215
M	0.0039	0.00132	2.998	0.005224
R	-2.53	1.310	-1.932	0.062276

.

Do you think these regression results will generate good sales estimates for B.U. LLC, rap?

Select one:

a. Yes, except that the adjusted R2R2 and the intercept coefficient are too low to be convincing. The rest of the results (p-values, expected signs) are satisfactory.

b. No; the estimated coefficient for adjusted R2R2 should be positive, not negative.

c. Yes; the parameter estimates have expected signs, the individual coefficients are statistically significant at the 10% level, and the adjusted R2R2 is high.

d. No; though the adjusted R2R2 is good and the variables have the expected signs, the estimated coefficients are not statistically significant at the 10% level.

Now assume that the income is $57,600, the price of the related good is $15, and B.U. chooses to set the price of its product at $13.50.

What is the estimated number of units sold given the data above? (Round to the nearest single unit; i.e., no decimals).

Question text

What are the values for the own-price (EE), income (EMEM), and cross-price (EXREXR) elasticities?

Select one:

a. E=−4.36E=−4.36, EM=0.0039EM=0.0039, EXR=−2.53EXR=−2.53

b. E=−0.025E=−0.025, EM=0.097EM=0.097, EXR=−0.016EXR=−0.016

c. E=−4.172E=−4.172, EM=2.998EM=2.998, EXR=−1.932EXR=−1.932

d. E=−0.644E=−0.644, EM=1.035EM=1.035, EXR=−0.088EXR=−0.088

Question text

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

Select one:

a. QQ increases by 4%×4.36=0.1744%4%×4.36=0.1744%

b. QQ decreases by 0.025%0.025%.

c. QQ decreases by 4%4%.

d. QQ changes by 4%×−0.025=−0.10%4%×−0.025=−0.10%

Question text

If MM increases by 3%, what would happen (in percentage terms) to quantity demanded?

Select one:

a. QQ increases by 3%×2.998=0.08994%3%×2.998=0.08994%.

b. QQ falls by 0.67%.

c. QQ changes by 3%×0.097=0.29%3%×0.097=0.29%.

d. QQ decreases by 3%×0.005224=0.0000156723%×0.005224=0.000015672.

Question text

If RR decreases by 5%, what would happen (in percentage terms) to quantity demanded?

Select one:

a. QQ increases by 1.310%.

b. QQ decreases by 0.036%.

c. QQ increases by 0.08%.

d. QQ falls by 5%×2193.39=109.6695%5%×2193.39=109.6695%.

Answer 1

1. (c) Since all the coefficients have a p-value less than 0.1, so the coefficients are statistically significant and hence the regression results will generate good estimate of sales as the parameter estimates have expected signs, the individual coefficients are statistically significant at the 10% level, and the adjusted R^2 is high.

2. The estimated sales = 2193.39+ (-4.36)*13.50+0.0039*57600+ (-2.53*15) = 2321

3. (b) Own price elasticty E=coefficient on P *(own price/sales)=-4.36*(13.50/2321)=-0.025

Income elasticty EM = coefficient on M *(income/sales)=0.0039*(57600/2321) = 0.097

Cross price elasticty EXR = coefficient on R *( price of related good/sales) = -2.53*(15/2321)=-0.16

4. (d) The coefficient on P shows the change in Q when P changes by 1 unit. So in percentage terms when, P increase by 4%, then Q changes by 4%*0.025=-0.10%

5. (c) If M increases by 3%, then the quantity Q increases by  by 3%×0.097=0.29%

6. (c) If R decreases by 5%, then the quantity Q  increases by 0.08%.