Question

Q: Mike consumes only two goods: x and y. His Utility function is given by

U(x,y) = 2x+2y

Mike has an income of $200. The price of good y is $2. Suppose the price of good x changes from $1 to $2.

1. Find the compensating variation and explain your answer. Show the CV in a diagram.

2. Find the equivalent variation and explain your answer. Show the EV in a diagram.

Answer 1

1) Compensating variation refers to Minimum change in nominal income required to achieve same level of utility as before the price change, with new prices.

Because preference is perfect substitues,so lower price of x than y will make CONSUMERs to use all his money to buy X.

X=200/1=200, and U=2*200=400

Initially, Px=py=2, so CONSUMER was indifferent in consuming x and y and spending all his money on either x or y or half on each .

X=200/2=100, or y=200/2=100

In each case ,U=2*(100)=200

With new price to achieve initial utility level, x=200/2=100, required income =1*100=100

So compensating variation=200-100=100$.

B) Equivalent variation refers to change in nominal income so that CONSUMERs can get same utility as now, with initial prices.

New utility=400

To get this utility with initial prices px=Py=2,

Required income=400

So equivalent variation=400-200=200$