Budget Constraint Graph

You probably know that you shouldn't overspend on one particular thing which you currently so desire to buy but is not a necessity to you. You are making a conscious rational choice not to spend on that particular thing because you know that you will not have enough money to spend on what is actually necessary for you. But did you know that these choices can be drawn on a budget constraint graph? If this has got you interested, then let's explore further!

Consumer Budget Constraint Graph

Consumer budget constraint graph shows the combinations of goods that can be purchased by a consumer with a given level of income and given a certain set of prices. Let's take a look at Figure 1 below.

Fig. 1 - Consumer budget constraint graph

Figure 1 above shows a consumer budget constraint graph. For a given level of income \(B_1\), a consumer can purchase any combination of goods \(Q_x\) or \(Q_y\) that lie on the green budget constraint. For example, a bundle \((Q_1, Q_2)\) is attainable as a point with these coordinates lies on the budget line. This point is marked in pink in the graph above. Note that consumer spends all their income on purchasing a bundle of these two goods.

Points that lie to the right of the budget constraint are unattainable as the consumer's budget is insufficient to purchase higher quantities of both goods. Points to the left of the budget constraint are all feasible. However, as it is assumed that a consumer wants to maximize their utility, we infer that they would choose a point that lies on the budget line as they would spend all of their income and therefore get the most utility out of their budget allocation.

What happens if consumer budget changes? If consumer budget increases, then a budget constraint graph will shift in parallel to the right. If consumer budget decreases, then a budget constraint graph will shift in parallel to the left. It is more tricky to consider what happens if the prices of the two goods change. If one good becomes much cheaper, then indirectly, a consumer will be better off, even if their income is unchanged, as they will be able to consume more of this particular good.

Let's explore further with the help of Figure 2 below!

Fig. 2 - Changes in consumer budget constraint

Figure 2 above shows changes in consumer budget constraint. In particular, it shows a pivotal shift in consumer budget from \(B_1\) to \(B_2\). The shift is occurring due to a decrease in the price of the good \(Q_x\). Note that a new bundle \((Q_3,Q_2)\) is now attainable.

Budget Constraint and Indifference Curve

Budget constraint and indifference curves are always analyzed together. Budget constraint shows the limitation that is imposed on consumer due to their limited budget. Indifference curves represent consumer preferences. Let's take a look at Figure 3 below.

Fig. 3 - Budget constraint and indifference curve

Figure 3 shows a budget constraint and indifference curve. Note that the bundle of choice \((Q_1, Q_2)\) lies on the budget line exactly where the indifference curve \(IC_1\) is tangent to it. The utility given a budget constraint \(B_1\) is maximized at this point. Points that lie on higher indifference curves are unattainable. Points that lie on lower indifference curves would yield lower levels of utility or satisfaction. Thus, the utility is maximized at point \((Q_1, Q_2)\). The indifference curve shows a combination of goods \(Q_x\) and \(Q_y\) that yield the same level of utility. This set of choices holds due to the axioms of revealed preference.

Budget Constraint Graph Example

Let's go through an example of a budget constraint graph. Let's take a look at Figure 4 below.

Fig. 4 - Budget constraint graph example

Figure 4 above shows a budget constraint graph example. Imagine you can consume only two goods - hamburgers or pizzas. All your budget has to be allocated between these two particular goods. You have $90 to spend, and a pizza costs $10, while a hamburger costs $3.

If you spend all your budget on hamburgers, then you can buy 30 in total. If you spend all your budget on pizzas, then you can buy only 9. This implies that pizzas are relatively more expensive than hamburgers. However, neither of these two choices would yield a higher level of utility than the bundle that lies on \(IC_1\) as they would lie on lower indifference curves. Given your budget \(B_1\), the highest indifference curve that is attainable for you is \(IC_1\).

Thus, your choice is maximized at a point \((5,15)\), as shown in the graph above. In this consumption scenario, your chosen bundle consists of 5 pizzas and 15 hamburgers.

Budget Constraint Slope

Let's continue our example of pizzas and hamburgers, but take a look at how your consumption would change if the slope of your budget constraint changed. Let's take a look at Figure 5 below.

Fig. 5 - Budget constraint slope example

Figure 5 above shows a budget constraint slope example. Imagine that there is a price change, and now a pizza costs $5 instead of $10. The price of the hamburger is still at $3. This means that, with a budget of $90, you can now get 18 pizzas. So your maximum possible consumption level of pizza increased from 9 to 18. This causes the budget constraint to pivot as its slope changes. Note that there is no change to the point \((0,30)\) as the maximum amount of hamburgers you can purchase did not change.

With your new budget line \(B_2\), a higher level of utility that lies on the \(IC_2\) indifference curve is now attainable. You can now consume a bundle at a point \((8,18)\), as shown in the graph above. In this consumption scenario, your chosen bundle consists of 8 pizzas and 18 hamburgers. How these changes between the bundles happen is guided by the income and substitution effects.

The slope of the budget line is the ratio of the prices of the two goods. The general equation for it is as follows:

\(Slope=-\frac{P_1}{P_2}\).

Difference between Budget Constraint and Budget Line

What is the difference between budget constraint and budget line? Roughly speaking, they are the same thing. But if you really want to differentiate between the two, then there is a way!

You can think of a budget constraint as an inequality. This inequality must hold because you can strictly spend the amount that is less than or equal to your budget.

The budget constraint inequality is, therefore:

\(P_1 \times Q_1 + P_2 \times Q_2 \leqslant I\).

As for the budget line, you can think of it as a graphical representation of the budget constraint inequality. The budget line would show where this inequality is binding. Inside the budget line, there will be a budget set.

The general formula for the budget line:\(P_1 \times Q_1 + P_2 \times Q_2 = I\).