## The Budget Line

PfF+PcC=I

* table 3.2 • 'Market Baskets arid the Budget Line

Market Basket Food (F) Clothing (C)

Total Spending

0 20

40 60 80

40 30 20

10 0

Clothing (units per week)

Food

(units per week )

FIGURE 3.8 A Budget Line. The consumer's budget line describes the combinations of goods that can be purchased given the consumer's income and the prices of the goods. Line AG shows the budget associated with an income of $80, a price of food of Pf = $1 per unit, and a price of clothing of Pc = $2 per unit. The slope of the budget line is in Table 3.2. Because giving up a unit of clothing saves $2 and buying a unit of food costs $1, the amount of clothing given up for food along the budget line must be the same everywhere. As a result, the budget line is a straight line from point A to point G. In this particular case, the budget line is given by the equation F + 2C = $80.

The intercept of the budget line is represented by market basket A. As she moves along the line from market basket A to market basket G, the consumer spends less on clothing and more on food. It is easy to see that the extra clothing that must be given up to consume an additional unit of food is given by the ratio of the price of food to the price of clothing ($l/$2 = Since clothing costs $2 per unit, while food is only $1 per unit, a unit of clothing must be given up to get 1 unit of food. In Figure 3.8 the slope of the line, measures the relative cost of food and clothing.

Using equation (3.1), we can see how much of C must be given up to consume more of F by dividing both sides of the equation by Pc and then solving for C:

Equation (3.2) is the equation for a straight line; it has a vertical intercept of I/Pc and a slope of -(PF/Pc).

The slope of the budget line, -(Pf/Pc), is the negative of the ratio of the prices of the two goods. The magnitude of the slope tells us the rate at which the two goods can be substituted for each other without changing the total amount of money spent. The vertical intercept (I/Pc) represents the maximum amount of C that can be purchased with income I. Finally,the horizontal intercept (I/Pf) tells us how many units of F could be purchased if all income were spent on F.

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