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Utility maximization

Now let us have a situation when there are two products and the consumer has to choose between two goods, X and Y, which have prices Px and Py. The rational decision of a consumer is to maximize his total utility within the limits of his income. The consumer can maximize it when he allocates his income in such a way that the utility from the consumption of one extra rouble’s worth of X is equal to the utility from the consumption of one extra rouble’s worth of Y. In other words, when the marginal utility per rouble of X is equal to the marginal utility of extra rouble’s worth of Y.
2. The ordinalist theory was developed in the 1930s by such economists as Hicks and Allen, who were influenced by the earlier works of Pareto and Slutsky. They suggested an idea that an individual can rank goods in order of preference, for example, potatoes could be first and rice could be second in terms of utility although ‘first, second…’ say nothing about the absolute difference between utilities. Indifference curves and budget lines are the means of illustrating this ordinalist approach to demand theory.
Indifference curves can simplify the analysis of the ordinal utility approach graphically in two dimensions. An indifference map (Figure 9.1) shows consumer’s preferences for X and Y using 3 indifference curves. An indifference curve joins together all the different combinations of the two goods which have the same utility for the consumer in question. Consider the consumer’s choice between two goods X and Y in Figure 9.1.

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  Every point on the graph represents a combination of X and Y.
  
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  Point A represents very small quantities of both goods X and Y.
  
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  Points B, C, D represent larger quantities.
  
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  Since combinations B (10 units of Y and 2 units of X) and C (5 units of Y and 4 units of X) are on the same indifference curve, the consumer is said to be indifferent between them, i.e. both combinations mean the same utility to him.
  
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  Combination D is on a higher indifference curve, which implies that he prefers D to both B and C; and E to B, C, and D.
  

Figure 9.1 An indifference map (field of choice)

Quantity of good X

Indifference curves do not tell us which combinations of the two goods will be chosen by a consumer. In addition to the consumer’s preferences, we need to know his income and the prices of the two goods. Then we can determine the combination of X and Y that the consumer will choose.

As an example, suppose the price of X is 10 money units and the price of Y is 20 money units, and the consumer’s income is 100 money units. Table 9.1 shows the combinations of X and Y that he can just afford to buy. Plotting these points on the same graph (Figure 9.2) as the indifference map, we obtain what is called the budget line.