In: Economics
From mid-2003 to early 2009, Apple charged $0.99 for every song on its US iTunes website. In April of 2009, Apple revised their pricing strategy: $0.69 for older songs, $0.99 for most new songs and $1.29 for the most popular tracks.
In June 2015, Apple introduced a streaming audio service, Apple Music, for $9.99 per month. This service competes with traditional music download models.
Before Apple changed their pricing, they collected data from a number of focus group consisting of a random sample of music buyers in order to better predict the outcomes of their changes.
Assume the following information was collected from a focus group of 20 (when the price was fixed at $0.99 per song)
The question asked each participant, was ‘how many songs do you download now, and how many songs would you purchase at … (varying prices)’
The focus group responses were:
Price, $ per song |
Quantity, Songs per year |
1.49 |
441 |
1.29 |
493 |
1.19 |
502 |
1.09 |
536 |
0.99 |
615 |
0.89 |
643 |
0.79 |
740 |
0.69 |
757 |
0.49 |
810 |
a) estimate the linear demand function of song downloads on price.
b) interpret your results statistically
c) explain what the price coefficient means.
d) Using these results, determine how revenue varies with price.
e) BONUS: given only this information, can you speculate what price Apple would likely charge and why?
*We are supposed to do only four sub-parts. For solution to other parts please post as a different question.
I have used excel to estimate the demand equation. Use the regression option under the data tab.
SUMMARY OUTPUT | ||||||||||
Regression Statistics | ||||||||||
Multiple R | 0.978734 | |||||||||
R Square | 0.95792 | |||||||||
Adjusted R Square | 0.951908 | |||||||||
Standard Error | 28.8824 | |||||||||
Observations | 9 | |||||||||
ANOVA | ||||||||||
df | SS | MS | F | Significance F | ||||||
Regression | 1 | 132928.2 | 132928.2 | 159.3495 | 4.52E-06 | |||||
Residual | 7 | 5839.35 | 834.1929 | |||||||
Total | 8 | 138767.6 | ||||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||
Intercept | 1023.915 | 33.77697 | 30.31399 | 1.1E-08 | 944.0447 | 1103.784 | 944.0447 | 1103.784 | ||
Price | -412.821 | 32.70288 | -12.6234 | 4.52E-06 | -490.151 | -335.49 | -490.151 | -335.49 | ||
a) Demand: Songs = 1023.915 - 412.821*Price | ||||||||||
b) The t-value for the price is very large there the price variable is statistically significant from 0. | ||||||||||
c) The regression results: | ||||||||||
The slope coefficient of price tells that if the price of a song on average increases by one dollar | ||||||||||
the quantity of songs decreases by 413 songs. Thus, there is a negative relationship | ||||||||||
between the quantity of songs and the price. | ||||||||||
The R2 is 0.97 thus the independent variable price explains 97% of variation in the dependent variable quantity of songs. | ||||||||||
d) Since the demand is inelastic the revenue increases with increase in price. | ||||||||||