Question

Janet has just been laid off due to a market correction and now has no income. Before being laid off, she had an income of $900 per week and the prices of the two goods she purchased, x and y, were $2 and $3 respectively. Due to the market correction, prices of x and y have dropped to $1 and $2 respectively. Janet’s preferences are represented by: u(x,y) = xy

(a) Is the amount we need to compensate Janet likely to be $900? Why? Explain using economic arguments.

(b) Calculate the amount that we need to compensate Janet to get her back to the same indifference curve she was on before the market correction.

Answer 1

u = xy

(a) Before lay-off, Budget line: 900 = 2x + 3y

Utility is maximized when MUx / MUy = Px / Py

MUx = $\partial$ u / $\partial$ x = y

MUy = $\partial$ u / $\partial$ y = x

MUx / MUy = y / x = 2/3

2x = 3y

Substituting in budget line,

900 = 2x + 2x = 4x

x = 225

Again,

900 = 3y + 3y = 6y

y = 150

This bundle (x = 225, y = 150) will cost less after the lay-off.

Total cost = $1 x 225 + $2 x 150 = $225 + $300 = $525

Assuming Janet consumes the same bundle before and after lay-off, the amount we need to compensate is $525 which is less than $900.

(b) Before lay-off, when x = 225 and y = 150, u = 225 x 150 = 33,750

After lay-off, Px/Py = $1/$2 = 1/2

MUx / MUy = y / x = 1/2

x = 2y

To get her back to same indifference curve, we keep utility constant at 33,750 & substitute x = 2y in utility function:

2y.y = 33,750

2y² = 33,750

y² = 16,875

y = 129.90

x = 2 x 129.9 = 259.80

Total cost of this bundle at new prices = $1 x 259.80 + $2 x 129.90 = $259.80 + $259.80 = $519.60

Required compensation = $519.60