Question

Barbara has preferences over flowers (x 1) and vases (x 2) represented by u( x 1 , x 2 ) = x 1 x 2. Her income is m=100m = 100 and prices are initially p 1 = 1 and p 2 = 2. If the price of flowers increases to p 1 ′ = 5, the decrease in demand for vases attributed to the income effect is:

1. 0

2. 20

3. 50

4. 75

Answer 1

For income effect:

Change in x1= x1(at the new price and old income) - x1(at the new price and changed income)

u( x 1 , x 2 ) = x 1 x 2

MRS= MUx1/MUx2

MUx1= differentiation of U wrt x1= x2

MUx2= differentiation of U wrt x2= x1

MRS= x2/x1

m = 100 and p 1 = 1 and p 2 = 2

Budget line: x1+2 x2= 100

For the optimal solution: MRS= p1/p2

x2/x1=1/2

2 x2= x1

Use this in budget line:

x1+x1=100

2x1=100

x1= 50

Now the price of x1 rises to 5: p1'= 5

New budget line: 5x1+2x2=100

For the optimal solution:

x2/x1=5/2

2x2=5x1

Use this in the new budget line:

5x1+5x1=100

10x1=100

x1= 10 [x1(at the new price and old income)]

Now to make a person afford the initial bundle the change in income is required:

Change in income = Change in p1 x initial x1= 4 x 50= 200

New income= m'= 300

New budget line: 5x1+2x2=100

For the optimal solution:

x2/x1=5/2

2x2=5x1

Use this in the new budget line:

5x1+5x1=300

10x1=300

x1= 30 x1(at the new price and changed income)

Income effect: Change in x1= 10-30= -20

It implies a decrease of 20.

Option 2 is the correct answer.