Consumer Choice

Given preferences and budget constraints, we can now determine how individual consumers choose how much of each good to buy. We assume that consumers make this choice in a rational way-that they choose goods to maximize the satisfaction they can achieve, given the limited budget available to them.

The maximizing market basket must satisfy two conditions. First, it must be located on the budget line. To see why, note that any market basket to the left of and below the. budget line leaves some income unallocated, which if spent could increase the consumer's satisfaction. Of course, consumers can-and sometimes do-save some of their incomes for future consumption. But this means that the choice is not just between food and clothing, but between consuming food or clothing now and consuming food or clothing in the future. At this point we will keep things simple by assuming that all income is spent now. Note also that any market basket to the right of and above the budget line cannot be purchased with available income. Thus, the only rational and feasible choice is a market basket on the budget line.

The second condition is that the maximizing market basket must give the consumer the most preferred combination of goods and services. These two conditions reduce the problem of maximizing consumer satisfaction to one of picking an appropriate point on the budget line.

In our food and clothing example, as with any two goods, we can graphically illustrate the solution to the consumer's choice problem. Figure 3.11

Maximizing Consumer Satisfaction

20 40 80 Food

(units per week)

FIGURE 3.11 Maximizing Consumer Satisfaction. Consumers maximize their satisfaction by choosing market basket A. At this point the budget line and indifference curve Ih are tangent, and no higher level of satisfaction can be attained. At A, the point of maximization, the marginal rate of substitution between the two goods equals the price ratio. At B, however, the marginal rate of substitution (1) is greater than the price ratio (J4), and maximization does not occur.

20 40 80 Food

(units per week)

FIGURE 3.11 Maximizing Consumer Satisfaction. Consumers maximize their satisfaction by choosing market basket A. At this point the budget line and indifference curve Ih are tangent, and no higher level of satisfaction can be attained. At A, the point of maximization, the marginal rate of substitution between the two goods equals the price ratio. At B, however, the marginal rate of substitution (1) is greater than the price ratio (J4), and maximization does not occur.

shows how the problem is solved. Here, three indifference curves describe a consumer's preferences for food and clothing. Remember that of the three curves, the outermost curve U3 yields the greatest amount of satisfaction, the curve U2 yields the next greatest amount, and the curve Ui yields the least.

First, note that point B on indifference curve Ui is not the most preferred choice, because a reallocation of income in which more is spent on food and less on clothing can increase the consumer's satisfaction. In particular, by moving to point A, the consumer spends the same amount of money and achieves the increased level of satisfaction associated with indifference curve Ui. Second, note that market baskets to the right and above indifference curve Ui, like the market basket associated with D on indifference curve U3, achieve a higher level of satisfaction but cannot be purchased with the available income. Therefore, A maximizes the consumer's satisfaction.

We see from this that the market basket that maximizes satisfaction must lie on the highest indifference curve that touches the budget line. Point A is the point of tangency between indifference curve U2 and the budget line. At A the slope of the budget line is exactly equal to the slope of the indifference curve. Because the MRS is the negative of the slope of the indifference curve, we can say that satisfaction is maximized (given the budget constraint) at the point where

This is an important result: Satisfaction is maximized when the marginal rate of substitution (of F for C)is equal to the ratio of the prices (ofF to C). Thus, the consumer can obtain maximum satisfaction by adjusting his consumption of goods F and C, so that the MRS equals the price ratio.

The condition given in equation (3.3) is an example of the kinds of optimization conditions that arise in economics. In this instance, maximization is achieved when the marginal benefit, that is, the benefit associated with the consumption of one additional unit of food, is equal to the marginal cost The marginal benefit is measured by the MRS. At point A it equals l/i (the magnitude of the slope of the indifference curve), which implies that the consumer is willing to give up Yi unit of clothing to obtain 1 unit of food. At the same point, the marginal cost is measured by the value of the slope of the budget line; it also equals l/i because the cost of getting one unit of food is to give up unit of clothing (Pf = 1 and Pc = 2 on the budget line).

If the MRS is less or greater than the price ratio, the consumers satisfaction has not been maximized. For example, compare point B in Figure 3.11 to point A. At point B, the consumer is purchasing 20 units of food and 30 units of clothing. The price ratio (or marginal cost) is equal to l/i because food costs $1 and clothing costs $2. However, the MRS (or marginal benefit) is greater than y2>. (It is approximately 1.) As a result, the consumer is willing to substitute one unit of food for one unit of clothing without loss of satisfaction. Because food is cheaper than clothing, it is in his interest to buy more food and less clothing. If the consumer purchases one less unit of clothing, for example, that $2 can be allocated to two units of food, when only one unit is needed to maintain his level of satisfaction.4

The reallocation of the budget continues in this manner (moving along the budget line), until we reach point A, because at A the price ratio of Vi just equals the MRS of H, which implies that the consumer is willing to trade one unit of clothing for two units of food. Only when the condition MRS = l/% = Pf/Pc holds is he maximizing his satisfaction.

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Responses

  • tekle
    Does consumer maximizes satisfaction where mrs = price ratio?
    6 years ago

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