Question

Suppose a consumer wants to consume two goods that are available only in integer units. The two goods are equally priced at Rs 10 and the consumer’s income is Rs 40.
(i) Write down all the bundles that are available to the consumer.
(ii) Among the bundles that are available to a consumer, identify those that cost will him/her exactly Rs 40. 

Answer 1

(i) P₁ = Rs 10

P₂ = Rs 10

M = Rs 40

Budget set ⇒ P₁x₁ + P₂x₂ ≤ M

10x₁ + 10x₂ ≤ 40

The bundles that are available to the consumer should cost less than or equal to Rs 40.

Horizontal intercept  ` = M_2/P_1 = 40/10 = 4`

Vertical intercept  ` = M_2/P_2 = 40/10 = 4`

Slope ` = (-P_1)/P_2 = (-10)/10 = -1`

The bundles in the shaded region (ΔAOB) are all available to the consumer, including the bundles lying on the line AB. 

(0,0)	(0, 1)	(0, 2)	(0, 3)	(0, 4)
(1, 0)	(1, 1)	(1, 2)	(1, 3)	(1, 4)
(2, 0)	(2, 1)	(2, 2)	(2, 3)	(2, 4)
(3, 0)	(3, 1)	(3, 2)	(3, 3)	(3, 4)
(4, 0)	(4, 1)	(4, 2)	(4, 3)	(4, 4)

(ii) The coordinates that lie on the line AB cost exactly the same as the income of the consumer. The bundles are as follows:

(0, 4), (1, 3), (2, 2), (3, 1), (4, 0)