BUDGET CONSTRAINT AND BUDGET LINE

A budget constraint shows the maximum combination of two goods that can be purchased by an individual given his current income level.

In other words, the budget constraint shows the plausible combination of two goods that is purchasable by an individual given his current income level.

The concept of the budget constraint is inherently based on the fact that consumers' consumption is limited by their income or capital at hand. 

Budget constraints hold two assumptions: the price of the two goods is fixed. Secondly, current consumer income is fixed.

Supposed in the world of two goods, a consumer has €200 to spend on two goods. And given that the price of the first and second goods is €20 and €10. The table exemplifies the consumer budget constraints

Good A(€20) each Good B (€10) each
10 0
9 2
8 4
7 6
6 8
5 10
4 12
3 14
216
118
0 20

As can be observed, Any quantities of the two goods that the consumer decides to buy will cost €200 in total.

The above information can be represented on a graph. This graph is called the budget line.

As you might imagine, a budget line is the graphical representation of the plausible combination of two goods purchasable by a consumer given his income. Here is the budget line for the above budget schedule.


Any combination that the consumers choose on the budget line will mean he is maximizing his income.

Slope Of a Budget Line: the relative price of two goods

The slope of budget lines has specific importance. This is because the absolute value of the slope of budge lines represents the relative price or price ratio. 

Returning to our earlier example, we see that the slope or $\frac{P_a}{P_b}$ is 2, indicating that the relative price of one unit of product A is 2 units of product B.

What changes the slope and position of the budget line?

So far, we have assumed that the price of the two goods and income are constant. However, and as everybody knows, price and income are never fixed.

What effect would a change in prices of goods have on the slope and position of the budget line?

Assuming there is a decrease in the price of good X so that the consumer can purchase more of product X with his current income. This means the budget line will shift outward

Now, think of what would happen if the price of good X increases? The consumer will be able to buy less of good X given his current income. Thus, the budget line shifts inward.

The effect of change in the price of good X is represented below

Do changes in price change cause changes in the slope of the budget line?

The slope of the budget line is derived by dividing the price of good X by the price of good Y.

Hence, changes in the price of either good X or good Y will affect the slope of the budget line, assuming the changes in the price of the goods are non-proportionally.

What effect would a change in consumer income have on the slope and position of the budget line?

When consumer income increases so that he can buy more of two goods, say, good X and good Y, the budget line will shift outward.

A decrease in income will mean the consumers can buy less of the two goods. Hence, the budget line shifts inward

The accompanying budget lines illustrate changes in income.


Does a change in income affect the slope of the budget line?

As earlier asserted, the slope of a budget curve is calculated by dividing the price of the good X divided by the price of Good Y.

Hence, a change in income will not cause a change in the slope of the budget line since income is not a component of the slope of the budget line.

In short, a change in income or price of the two goods would shift the budget line.

However, not all change is equal. A price change will change the slope of the budget line whereas, a change in income will not change the slope of the budget line.

It is vital to note here that a change in the prices of goods would affect the budget line only if the change is non-proportionally.

The slope of the budget line will not change if the change in the price of goods is proportional, that is, if the price of goods X and goods Y increased or decreased by the same proportion.
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