Suppose a consumer wants to consume two goods which 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 t

Question

Suppose a consumer wants to consume two goods which 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 the consumer, identify those which cost her exactly Rs 40.

Accepted Answer

> [!TLDR]
> With income Rs 40 and both goods priced at Rs 10, the consumer can afford any bundle $(x_1, x_2)$ where $10x_1 + 10x_2 \leq 40$, i.e., $x_1 + x_2 \leq 4$ in non-negative integers. Bundles costing exactly Rs 40 satisfy $x_1 + x_2 = 4$.

## Understanding the Budget Constraint

A consumer's budget set consists of all commodity bundles she can afford given her income and the prices she faces. When goods come in integer units only, we're looking at discrete points rather than a continuous budget line.

The budget constraint here is straightforward. If good 1 costs Rs 10 per unit and good 2 also costs Rs 10 per unit, then a bundle $(x_1, x_2)$ costs $10x_1 + 10x_2$. The consumer can afford this bundle if and only if:

> [!FORMULA]
> $$10x_1 + 10x_2 \leq 40$$

Simplifying by dividing through by 10:

$$x_1 + x_2 \leq 4$$

Since goods are available only in integer units, both $x_1$ and $x_2$ must be non-negative integers (you can't buy $-1$ apples or $2.5$ oranges in this market).

## (i) All Available Bundles

We need every pair of non-negative integers $(x_1, x_2)$ such that $x_1 + x_2 \leq 4$.

Start systematically:

- When $x_1 = 0$: $x_2$ can be $0, 1, 2, 3, 4$ → bundles $(0,0), (0,1), (0,2), (0,3), (0,4)$
- When $x_1 = 1$: $x_2$ can be $0, 1, 2, 3$ → bundles $(1,0), (1,1), (1,2), (1,3)$
- When $x_1 = 2$: $x_2$ can be $0, 1, 2$ → bundles $(2,0), (2,1), (2,2)$
- When $x_1 = 3$: $x_2$ can be $0, 1$ → bundles $(3,0), (3,1)$
- When $x_1 = 4$: $x_2$ can be $0$ → bundle $(4,0)$

That gives us 15 bundles in total.

| $x_1$ | Available values of $x_2$ | Bundles |
|-------|---------------------------|---------|
| 0 | 0, 1, 2, 3, 4 | (0,0), (0,1), (0,2), (0,3), (0,4) |
| 1 | 0, 1, 2, 3 | (1,0), (1,1), (1,2), (1,3) |
| 2 | 0, 1, 2 | (2,0), (2,1), (2,2) |
| 3 | 0, 1 | (3,0), (3,1) |
| 4 | 0 | (4,0) | …

Q.Suppose a consumer wants to consume two goods which are available only in integer units. The two goods are equally priced at Rs 10 and the consumer's income is Rs 40.

Concept understanding — Budget Line Definition

The precise definition

Why it matters

What happens when things change?

Understanding the Budget Constraint

(i) All Available Bundles

Units of Good 1	Units of Good 2	Bundles
0	0, 1, 2, 3, 4	(0,0), (0,1), (0,2), (0,3), (0,4)
1	0, 1, 2, 3	(1,0), (1,1), (1,2), (1,3)
2	0, 1, 2	(2,0), (2,1), (2,2)
3	0, 1	(3,0), (3,1)
4	0	(4,0)

Q.Suppose a consumer wants to consume two goods which are available only in integer units. The two goods are equally priced at Rs 10 and the consumer's income is Rs 40.

Understanding the Budget Constraint

(i) All Available Bundles

🎓Unlock everything free for 14 days

Unlock everything free for 14 days