Question

1. The table below shows Harmony’s preferences for the number of songs she downloads per month, holding the prices of all goods constant. Income ($) Optimal number of songs Income elasticity of demand for songs

20 2

30 5

40 10

50 10

60 10

a. Complete the income elasticity of demand column for the table above (using the midpoint method). Are songs ever an inferior good for Harmony? At what level(s) of income are songs a luxury? (6 points) b. Draw a smooth approximation of Harmony’s Engel curve for songs. (3 points)

Answer 1

Solution:-

Given that,

a)

Now For the income range of $20-$30:-

Percentage change income(m) =

Therefore,Percentage change income(m) =40.

And percentage change in quantity demanded for Songs

Now income elasticity of demand=

Therefore, income elasticity of demand=2.14

Now For the income range of $30-$40:-

Percentage change income(m) =

Therefore,Percentage change income(m) =28.57

And percentage change in quantity demanded for Songs

Now income elasticity of demand=

Therefore, income elasticity of demand=2.33

Now For the income range of $40-$50:-

Percentage change income(m) =

Therefore,Percentage change income(m) =22.22

And percentage change in quantity demanded for Songs

=0

Now income elasticity of demand=

Therefore, income elasticity of demand=0

Now For the income range of $50-$60:-

Percentage change income(m) =

Therefore,Percentage change income(m) =18.18

And percentage change in quantity demanded for Songs

=0

Now income elasticity of demand=

Therefore, income elasticity of demand=0

Now from the above values ,these are substitute in Given table

Income(thousands of $)	Optimal number of songs	Income elasticity of demand for songs
20	2	xxx
30	5	2.14
40	10	2.33
50	10	0
60	10	0

As value of income elasticity of demand is positive at all price,hence songs are never an interior good to Harmony's.

Now for luxury goods know that value of income elasticity of demand is greater than 1 always.From the table we can see that at income level of $40 and $50 value of income elasticity of demand is grater than 1.Hence songs are luxury goods at income levels of $40 and $50.

b)

Now we can draw Harmony's Engel Curve for songs placing income (m) on the vertical axis and quantity of Songs(q) on the Horizontal axis.