In: Economics
True or false: (False) When digital music cost $1 per song and digital movie rentals cost $4 each, an individual chose to purchase 9 songs and rent 4 movies per month. When the price of digital music increases to $1.25 per song, that individual now chooses to purchase 4 songs and rent 5 movies per month. Because their consumption of one good has increased and their consumption of the other good has decreased, this individual’s utility could be either higher or lower than it was before the price increase. [Hint: If you’re having trouble with this question, a graph showing the original situation and the new situation might be helpful.]
The digital music song is denoted as X and digital movie is denoted as Y.
In the original situation, cost of digital music (say p) is $1. Hence,
p=$1
And, rent of digital movie (say r) is $4. Hence,
r = $4
Now, the individual buys digital music (X) at price p=$1 per song and digital movies (Y) at price p=$2 per song.
If, his income is M, then the budget constraint is
p.X+r.Y = M
or, 1.X+4.Y = M
or, X + 4Y = M..........(1)
Now, it is given that, the individual chose to buy 9 songs and 4 movies in a month. Hence,
X=9 and Y=4. Putting X and Y in equation (1), we get
9 + 4×4 = M
or, M = $25
Hence, the income of the individual is $25. Putting this in equation (1) we get the Original Budget Line as,
X + 4Y = M
or, X + 4Y = 25..........B1
And, the individual chooses (X,Y) = (9,4)
Now, the price of digital music increases to $1.25 per song. Hence, the individual will buy songs X at price p' i.e. $1.25 per song.
Hence, p' = 1.25
Hence, in the new situation,
The individual buys songs (X) at price p'=$1.25 and movies (Y) at price r=$4. His income is M=$25. Hence, the new budget constraint is
p'.X+r.Y = M
or, 1.25.X + 4.Y = 25.........B2
This is the new budget line.
In this new situation, the individual buys 4 songs and rents 5 movies. Hence, (X,Y) = (4,5) in the new situation.
Now, let us assume that the individual has convex preferences and his indifference curves are downward sloping.
In the following diagram, we plot the two situations.
Original Situation:
Budget Line (B1): X+4Y = 25
Choice of (X,Y) = (9,4)
New Situation:
Budget Line (B2): 1.25X+4Y = 25
Choice of (X,Y) = (4,5)
We can see that, the consumption of songs has decreased and consumption of movies has increased.
We can also see that, the initial utility of the individual was U1 and final utility of the individual is U2. The U2 is the lower indifference curve than U1.
Hence, the utility definitely decreases in the new situation. The new utility is always lower.
The given statement is now true. It says the utility could be either higher or lower. But we can see that, the utility is always lower in this case.
Hence, the statement is FALSE.
The answer is: False
Hope the explanation is clear to you my friend.