Question

QUESTION 16 Suppose that price for Compact Disks (CDs) is $15 each. Suppose the price for downloading tracks of music legally is $1 for each song. Suppose Sophia has $30 to spend each month on music. 1. Draw the budget constraint on a graph with CDs on the horizontal axis. (1 points) 2. Suppose the price of CDs falls to $10. Draw the new budget line. (1 point) 3. Show using indifference curves the beginning and ending utility maximizing choices and the substitution and income effect given that CDs are inferior but not Giffen good. Label the substitution effect SE and the income effect IE on the graph. (4 points)

Answer 1

Question 16 Suppose that price for compact Disk (CDs) s $15 each ie Pen = $15 Price for downloading tracks of music illegally (6) . : Pd = $1 for each song. Total budget I = $30 each month ... 1 Sophie's budget liver I= CO PCD + D Pd. =) 30=1500 +D Now, horizontal infncept of the budget line, [ substitute D=07 will but : 30= 15 eo to => cD=2 Vatical intercept of the budget line [substitute CD=0] will be 30= (15x0) +D=> 0 = 30 Now by Joining horizontal and intical intercept, we get, the budget line : (MN.) Scanned, with CamScanner

700 Scanned with CamScanner 2 N 30

2 suppose puce of cos falls to $ 10 ie. Péo = $10, PO = $1; I = 30 Now budget constant is I .. =P Cot Pd. D = Pepco =) 30 - 2000 to Now horizontal in Ancept of the budg it line [ substitute D=07 will be's. 30 = 100D to -> C023 vertical in Ancept of the budget line will be? Tsubstitute Co=07 30= (1080) +D =) D=30 Scanned with CamScanner

and in tical Now, by Joining cs Scanes docept we get horizontal the bridgit line mo CS CamScanner

Man Ilzi - N Q, Q3 Q 22 substitution effect Income effect Total estect CS Scanned with CamScanner

3. Here the initial budget line is MN which is tangent to the initial indifference curve IC1 at point A with respect to which the initial consumption of CD is Q1. Now as the price of CD falls from $15 to $10, the budget line rotates outward from MN to MO which becomes tangent to the indifference curve IC2 at point E with respect to which the final quantity of CD is Q3. Now the total increase in the amount of CD sold from Q1 to Q3 can be decomposed into a substitution effect and an income effect.
Now to understand the substitution effect, we will hold consumer's real income constant. Hence the consumer will stay on the same indifference curve, but as the price of CD falls, the price ratio Pcd/Pd changes. Hence the consumer will stay on the budget line with the slope of the new budget line. Hence we draw a hypothetical budget line TU which is tangent to the initial indifference curve IC1 at point B with respect to which the quantity of CD sold is Q2. Hence the movement from point A to point B with respect to which the quantity of CD sold increases from Q1 to Q2 is due to the substitution effect.
  Now to understand the income effect, we will consider real income as variable. Now here as CDs are inferior goods, this means that increase in income will result in decline in the quantity of CD sold. Hence here as price of CD falls, budget line shifts rightward from TU to MO which becomes tangent to the new indifference curve IC2 at point E with respect to which the quantity of CD sold is Q3. Hence here as price of CDs fall, consumer feels richer as their purchasing power increases and as CDs are inferior goods, this increase in income will cause in lower quantity of CDs being sold. Hence the movement from point B to point E with respect to which the quantity of CDs sold falls from Q2 to Q3 is due to the income effect.