Question

John really likes listening to music. His preferences for vintage records (?1) and music downloads (?2) can be represented by the utility function ? = ?1?2. Initially, the price of a vintage record was $10, but it increased to $20 due to a new trend toward collecting vinyl. The price of a music download is $4 and John’s income is $240.

1. How would you describe John’s preferences for vintage records and music downloads?

2. The increase in the price of vintage records will affect John’s consumption of vintage records. Let’s use the Slutsky equation to decompose the change in quantity demanded. First, by how much will John change his consumption of vintage records due to the substitution effect (i.e. change in relative prices)?

3. By how much will John change his consumption of vintage records due to the income effect (i.e. change in purchasing power)? Are vintage records a normal or inferior good? Explain in one sentence.

4. What is the total change in John’s consumption of vintage records as the price increased from $10 to $20? Are vintage records an ordinary or Giffen good? Explain in one sentence.

Answer 1

a) John has well-behaved or Cobb-Douglas preferences for vintage records and music downloads

b)

As on decreasing the income the quantity demanded falls, vintage record is a normal good.

Since price effect is positive, vintage records in an ordinary good.