Explain the distinguish between equation budget line and budget constraints
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To understand how households make decisions, economists look at what consumers can afford. To do this, we must chart the consumer’s budget constraint. In a budget constraint, the quantity of one good is measured on the horizontal axis and the quantity of the other good is measured on the vertical axis. The budget constraint shows the various combinations of the two goods that the consumer can afford. Consider the situation of José, as shown in Figure 6.1a. José likes to collect T-shirts and movies.
In Figure 6.1a, the number of T-shirts José will buy is on the horizontal axis, while the number of movies he will buy José is on the vertical axis. If José had unlimited income or if goods were free, then he could consume without limit. But José, like all of us, faces a budget constraint. José has a total of $56 to spend. T-shirts cost $14 and movies cost $7.
Plotting the budget constraint is a fairly simple process. Each point on the budget line has to exhaust all $56 of José’s budget. The easiest way to find these points is to plot the intercepts and connect the dots. Each intercept represents a case where José spends all of his budget on either T-shirts or movies.
If José spends all his money on movies, which cost $7, José can buy $56/$7, or 8 of them. This means the y-intercept is the point (0,8). Here, José buys 0 T-shirts and 8 movies.
If José spends all his money on T-shirts, which cost $14, José can buy only 4 of them ($56/$14). This means the x-intercept is the point (4,0). Here, José buys 4 T-shirts and 0 movies.
By connecting these two extremes, you can find every combination that José can afford along his budget line. For example, at point R, José buys 2 T-shirts and 4 movies. This costs him:
T-Shirts @ $14 x 2 = $28
Movies @ $7 x 4 = $28
Total = $24 + $28 = $56
This point indeed exhausts José’s budget.
Figure 6.1a
Budget Constraints
We now know that José must purchase at some point along the budget line, depending on his preferences. Note that any point within the budget line is feasible. José can spend less than $56, but this is not optimal as he can still buy more goods. Since T-shirts and movies are the only two goods, there is no ability in this model for José to save. This means that not spending his full budget is essentially wasted income. On the other hand, any point beyond the budget line is not feasible. If José only has $56, he cannot spend more than that. Notice that areas in the green zone are not necessarily more optimal than points along the budget line. The optimal point depends on José’s preferences, which we will explore when we discuss José’s indifference curve.
Figure 6.1b
Slope
Though we can easily just connect the X and Y intercepts to find the budget line representing all possible combinations that expend José’s entire budget, it is important to discuss what the slope of this line represents. Remember, the slope is the rate of change. In economics, the slope of the graph is often quite important. In this situation, the slope is QY/QX. If we want to represent slope in terms of prices it is equal to Px/PY. This can seem unintuitive at first, as we are used to seeing slope as Y/X., but the reason this is not true for prices is because the y-axis represents quantity, not price. As we saw above, as price doubles, the quantity the consumer could previously purchase is halved.
If José is making $56:
When the price of movies is $7, he can buy 8 of them
When the price of movies is $14, he can buy 4 of them
Since price and quantity have this inverse relationship, we can use either Px/PY or QY/QX to find the slope. Since price is often the information given, it is important to remember that the slope can be calculated either way.
In Figure 6.1a, the number of T-shirts José will buy is on the horizontal axis, while the number of movies he will buy José is on the vertical axis. If José had unlimited income or if goods were free, then he could consume without limit. But José, like all of us, faces a budget constraint. José has a total of $56 to spend. T-shirts cost $14 and movies cost $7.
Plotting the budget constraint is a fairly simple process. Each point on the budget line has to exhaust all $56 of José’s budget. The easiest way to find these points is to plot the intercepts and connect the dots. Each intercept represents a case where José spends all of his budget on either T-shirts or movies.
If José spends all his money on movies, which cost $7, José can buy $56/$7, or 8 of them. This means the y-intercept is the point (0,8). Here, José buys 0 T-shirts and 8 movies.
If José spends all his money on T-shirts, which cost $14, José can buy only 4 of them ($56/$14). This means the x-intercept is the point (4,0). Here, José buys 4 T-shirts and 0 movies.
By connecting these two extremes, you can find every combination that José can afford along his budget line. For example, at point R, José buys 2 T-shirts and 4 movies. This costs him:
T-Shirts @ $14 x 2 = $28
Movies @ $7 x 4 = $28
Total = $24 + $28 = $56
This point indeed exhausts José’s budget.
Figure 6.1a
Budget Constraints
We now know that José must purchase at some point along the budget line, depending on his preferences. Note that any point within the budget line is feasible. José can spend less than $56, but this is not optimal as he can still buy more goods. Since T-shirts and movies are the only two goods, there is no ability in this model for José to save. This means that not spending his full budget is essentially wasted income. On the other hand, any point beyond the budget line is not feasible. If José only has $56, he cannot spend more than that. Notice that areas in the green zone are not necessarily more optimal than points along the budget line. The optimal point depends on José’s preferences, which we will explore when we discuss José’s indifference curve.
Figure 6.1b
Slope
Though we can easily just connect the X and Y intercepts to find the budget line representing all possible combinations that expend José’s entire budget, it is important to discuss what the slope of this line represents. Remember, the slope is the rate of change. In economics, the slope of the graph is often quite important. In this situation, the slope is QY/QX. If we want to represent slope in terms of prices it is equal to Px/PY. This can seem unintuitive at first, as we are used to seeing slope as Y/X., but the reason this is not true for prices is because the y-axis represents quantity, not price. As we saw above, as price doubles, the quantity the consumer could previously purchase is halved.
If José is making $56:
When the price of movies is $7, he can buy 8 of them
When the price of movies is $14, he can buy 4 of them
Since price and quantity have this inverse relationship, we can use either Px/PY or QY/QX to find the slope. Since price is often the information given, it is important to remember that the slope can be calculated either way.
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