Question

Jamal consumes only two goods, peaches and cream. His preferences are such that he treats these goods as perfect complements and consumes 2 peaches for every pint of cream. Suppose that initially the price of a peach is $2, the price of a pint of cream is $4 and Jamal has $56 to spend. Calculate the income effect of a change in the price of peaches from $2 each to $1.50 each.

Answer 1

Utility function is: U = min{P, 2C}

Initial budget line: 56 = 2P + 4C, or 28 = P + 2C

For a fixed-proportion utility function, Utility is maximized when P = 2C.

Substituting in budget line,

56 = 2C + 2C = 4C

C = 14

P = 2 x 14 = 28

After fall in price of peaches, new budget line:

56 = 1.5P + 4C

Substituting P = 2C,

56 = 1.5 x 2C + 4C

56 = 3C + 4C

56 = 7C

C = 8

P = 2 x 8 = 16

Total effect from price change for peaches = 28 - 16 = 12

For fixed-proportion utility function, substitution effect is zero and Total effect = Income effect

Income effect = 12