Question

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?

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9787
R Square	0.9579
Adjusted R Square	0.9519
Standard Error	28.8824
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	132928.2051	132928.2051	159.3495	0.0000
Residual	7	5839.3504	834.1929
Total	8	138767.5556
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1023.9145	33.7770	30.3140	0.0000	944.0447	1103.7844
Price, $ per song	-412.8205	32.7029	-12.6234	0.0000	-490.1505	-335.4905

a) Linear demand function = 1023.92-412.82*Price per song

b) As the P-value of price coefficient is less than 0.05 or 0.01, the price has significant effect on Quantity of Songs per year

c) The price coefficient of value -412.82 means for one dollar increase in price the sales decreases by 412.82 songs

d) As the price is inversely related with Quantity of Songs per year, the total revenue decreases with the increase in price

e) As the revenue is maximum at a price of $1.49, the speculated price it would charge is $1.49

Price, $ per song	Quantity, Songs per year	Total Revenue = P*Q
1.49	441	657.09
1.29	493	635.97
1.19	502	597.38
1.09	536	584.24
0.99	615	608.85
0.89	643	572.27
0.79	740	584.6
0.69	757	522.33
0.49	810	396.9