Baskets of Goods and the Budget Line

As a consumer, one can choose between several different goods and services. A certain combination of goods and services is called a basket of goods (a bundle of goods, or a market basket). The consumer’s problem can therefore be described as having to choose between different baskets, given the restrictions she faces, such that she maximizes her utility. We begin by looking at a simple case where we have just two goods, good 1 and 2, with prices p1 and p2. A basket that consists of the quantity q1 of good 1 and q2 of good 2 is written (q1,q2). For example, (4,3) means that we have 4 units (or kilos, liters, etc) of good 1 and 3 units of good 2. The price of the basket (q1,q2) is then:

                                                            p1 * q1 + p2 * q2

If we have a limited amount of money to buy these goods for, this will impose a restriction on how much we can buy of each good. Letting m denote the amount of money available, the price of the basket chosen must not exceed m. The different combinations of good 1 and 2 that cost exactly m can be written

                                                            p1 * q1 + p2 * q2 = m

Solving this expression for q2, we get the function of the budget line



This function is a straight line that intercepts the Y-axis at m/p2 and has the slope p1/p2 (see Figure 3.1). All the points on the budget line cost exactly m. The points in the grey area below the budget line cost less than m whereas the points above cost more than m. The baskets that a consumer with wealth m can buy are, consequently, the ones on and below the budget line. There is a simple strategy for finding the budget line: If we only buy good 2, the maximum quantity that we can buy is m/p2, whereas if we buy only good 1, the maximum quantity that we can buy is m/p1. Indicate the first point on the Y-axis and the second on the X-axis, and then draw a straight line between them. The line you have drawn is the budget line, and it will automatically have the slope -p1/p2.



The slope of the budget line is called the marginal rate of transformation (MRT). We consequently have that



Suppose, for instance, that the two goods are ice cream (price 10) and pizza (price 20). marginal rate of transformation (MRT) will then be -10/20 = -0.5. We can interpret this such that you have to give up half a pizza if you want to have one more ice cream (or, vice versa, that you have to give up two ice creams, -20/10, to get one more pizza). To transform your basket into another basket with one more ice cream, you have to give up half a pizza. Note that this means that the price of ice cream

If income or prices change, the budget line will also change. Look at Figure 3.2 and the budget line B1. If the price of good 1 rises from p1 to p'1, we can only buy a maximum of m/p'1 of that good, but we can still buy m/p2 of good 2. Consequently, the budget line rotates about the intercept with the Y-axis to B2.

If, instead, the price of good 2 rises from p2 to p'2, then B1 rotates about the intercept with the X-axis to B3. When a price changes, marginal rate of transformation (MRT) also changes since the slope of the budget line changes. If the price of ice cream rises from 10 to 20, marginal rate of transformation (MRT) will be -20/20 = -1. Now, you have to give up a whole pizza to get one more ice cream. Note that this also means that the pizza has become cheaper, relatively speaking: You can now get one more pizza for just one ice cream, even though the price of pizza is unchanged.

Assume now that the prices are p1 and p2, as they were originally, but that the income increases to m'. We can then buy a maximum of m'/p2 of good 2 and a maximum of m'/p1 of good 1. B1 consequently shifts to B4. Note that the slope of B4 is exactly the same as the slope of B1, since the prices are unchanged: You have more money, but you still have to give up half a pizza if you want to have one more ice cream.



If prices rise or if income falls, the area under the budget line becomes smaller. In the opposite cases, it becomes larger. The larger the area is, the more choices of consumption you have.