Question
Your company, which specializes in running shoes for men who are growing increasingly follicly-challenged (BalderDash), has the following demand function: Q = a + bP
Your company, which specializes in running shoes for men who are growing increasingly follicly-challenged (BalderDash), has the following demand function:
Q = a + bP + cM + dR
where Q is the quantity demanded of BalderDash's most popular shoes, P is the price of that product, M is consumer income, and R is the price of a related product. The regression results are:
Q = 21055.04 - 83.912P + 0.0266M -16.6R
Adjusted R Square | 0.7796 | |||
Independent Variables | Coefficients | Standard Error | t Stat | P-value |
Intercept | 21,055.04 | 1428.27 | 14.74 | 8.1E-16 |
P - Price | -83.912 | 19.079 | -4.398 | 0.000 |
M - Income | 0.0266 | 0.013 | 2.064 | 0.047 |
R - Price Related Prod. | -16.6 | 10.664 | -1.556 | 0.129 |
- Discuss whether you think these regression results will generate good sales estimates for BalderDash.
The regression results indicate that the model has a reasonably high Adjusted R Square (0.7796), suggesting that around 77.96% of the variability in the quantity demanded is explained by the independent variables. The model seems to provide reasonably good sales estimates, but the non-significant coefficient for the price of the related product raises some concerns about the robustness of its impact
Now assume that the income is $69,100, the price of the related good is $39, and BalderDash chooses to set the price of its product at $54.
- What is the estimated number of units sold given the data above? (round to nearest unit; no decimals)
Q = 21055.04 - 83.912P + 0.0266M -16.6R
Q = 21055.04 - 83.912(54) + 0.0266(69100) - 16.6(39)
Q = 21055.04 - 4531.248 + 1838.06 - 647.4
Q = 17714.452
- What are the values for the own-price, income, and cross-price elasticities?
E = %change Q / %change P or = (change Q / average Q) / (change P / average P)
Em = %changeQd / %changeM and Exr = %change Qx/ %changePr
E =
EM =
ER =
- If P increases by 6%, what would happen (in percentage terms) to quantity demanded?
- If M increases by 2%, what would happen (in percentage terms) to quantity demanded?
f. If R decreases by 3%, what would happen (in percentage terms) to quantity demanded?
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