PRICE LINE

Suppose the price of commodity ‘x’ is RS. 100 and price of commodity ‘y’ is Rs. 50 and a consumer has Rs. 2000 to spend per month on goods x and goods y.

a) Sketch the consumers budget constraint

b) Assume that he splits his income equally between x and y. show whether the consumer ends up on the budget constraints.

c) Suppose that the income rises from Rs. 2000 to Rs. 4000. Sketch the new budget constraint.

d) Assume that he again splits total budget equally into two goods. Show where the consumer ends up on new budget constraint.

From the above information we have:

• The total Budget of the consumer (B ) = Rs. 2000
• Price of the commodity x (Px) = Rs 100
• Price of the commodity y (Py) = Rs 50

a) Computation of consumers budget constraints:

As we know,

Under Price Line :

B = Px x Qx + Py x Qy

Or, 2000 = 100X + 50Y……….(.i)

A)Suppose that consumer spends his entire budget in order to purchase commodity X (i.e Qy = 0)

Then the equation ( I ) becomes:

2000 = 100X + 50 x 0

Or, 100x = 2000

Or, x = 20 units.

This gives the coordinate (X, Y) as (20, 0)

Similarly,

Suppose that consumer spends his entire budget in order to purchase commodity Y (i.e Qx = 0)

Then the equation (I) becomes:

2000 = 100 x 0 + 50Y

Or, 50Y = 2000

Or, Y = 40 units

This gives the coordinate (X, Y) as (0, 40)

Plotting the coordinates of above graphically, we get the following:


b) Assuming that he splits his income equally between x and y then, Computation of whether the consumer ends up on the budget constraints or not :


As we know, if the consumer equally divides or splits his budget: (i.e Rs. 1000 in goods x and Rs. 1000 in goods y )

Qx = B/ Px = 1000 / 100 = 10 units.

This gives the coordinate (X,Y ) as (10, 0)

Similarly,

Qy = B / Py = 1000 / 50 = 20 units.

This gives the coordinate (X,Y ) as (0,20)

Therefore, the new budget equation becomes:

10 Px + 20 Py = 2000

Plotting the coordinates of above graphically, we get the following:


C ) Sketching of the new budget constraint when the income rises from Rs. 2000 to Rs. 4000:

The new Budget (B ) = Rs. 4000

Suppose that consumer spends his entire budget in order to purchase commodity X (i.e Qy = 0)

We know, Qx = B/ Px = 4000 / 100 = 40 units.

This gives the coordinate (X,Y ) as (40, 0)

Suppose that consumer spends his entire budget in order to purchase commodity y (i.e Qx = 0)

We know, Qy = B/ Py = 4000 / 50 = 80 units.

This gives the coordinate (X,Y ) as (0, 80)

Therefore, the new budget equation becomes:

40 Px + 80 Py = 4000

Plotting the coordinates of above graphically, we get the following:



D ) If he again splits total budget equally into two goods, then computation of the consumer ending up on new budget constraint:


As we know, if the consumer equally divides or splits his budget: (i.e Rs. 2000 in goods x and Rs. 2000 in goods y )

Qx = B/ Px = 2000 / 100 = 20 units.

This gives the coordinate (X,Y ) as (20, 0)

Similarly,

Qy = B / Py = 2000 / 50 = 40 units.

This gives the coordinate (X, Y) as (0, 40)

Therefore, the new budget equation becomes:

20 Px + 40 Py = 4000

Plotting the coordinates of above graphically, we get the following: