Chapter EMD, Problem 2FRQ

a)

To determine

The question requires us to draw the budget line.

Explanation of Solution

The budget line represents the limitations that a consumer faces during purchasing the consumption bundle. In the given case,

Consumer’s budget = $20

Charge for downloading songs = $2 per song

Charge for downloading movies = $5 per movie.

A person can download a maximum of 4 (= 20/5) movies if he uses his entire income on movies, considering the budget. So, the vertical intercept is equal to the 4. The horizontal intercept is 10, this means a person can download a maximum of 10 songs if he uses his entire income on songs.

Thus, the downward-sloping straight line represents the budget line in the following figure:

  

Here, the gray-colored downward-sloping straight line shows the budget line of the consumer.

b)

To determine

The question requires us to determine the combination of songs and movie downloads that maximizes her utility.

Explanation of Solution

A consumer can maximize his utility at the point where the indifference curve is tangent to the budget line.

The bundles given in the question 1, are not optimizing the utility as few of them are above the budget line (which means the sum of multiplications of their prices are higher than $20) while few of them exist below the budget line (as they are worth less than $20).

The consumer will download a bundle with 2 units of movies and 5 units of songs to maximize his utility.

Given,

Budget = $20

Charge for downloading songs = $2 per song

Charge for downloading movies = $5 per movie.

The budget constraint will be:

  $\begin{array}{l}M=P_X{Q}_X+P_Y{Q}_Y\\ 20=2Q_X+5Q_Y\end{array}$

When Kathleen downloads 2 units of movies and 5 units of songs, then she is utilizing her entire income and getting the highest utility as shown in the figure at point E.