Optimal choice

On the same graph depict the budget line of the consumer and its map of indifference curves.
Point with the most preferable of the marked points, but it lies above the budget line, and therefore a set of goods, defined it, is unattainable for the consumer. At point d income I the consumer is not fully used.

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Fig. 4.7. Consumer equilibrium

As the assumption is nonsatiated, the consumer will always make full use his income, and his choice will be based on the budget line. At the point a indifference curve intersects the budget line. In this situation, it is possible to move along the budget line to a higher indifference curve, for example, point b, as shown in Fig. 4.7.
Such movements in this direction can improve customer satisfaction, until he gets to the point of tangency e of the budget line and some indifference curve. Any shift from this point along the budget line transfers to a lower indifference curve, i.e. reduces the degree of satisfaction. Hence, the tangency point e is an equilibrium of the consumer and determines the optimal choice.
Since the point of contact e slope of the indifference curve - MRS is the slope of the budget line - then we must have
MRS = . (4.2)

This equation together with the budget constraint (4.1) allows to find an equilibrium set of goods X and Y.

Fig. 4.8. Corner solution

In the situation shown in Fig. 4.7, the equilibrium e defines a set that contains non-zero amounts of both goods X and Y. This so-called internal solution.
Map of indifference curves and price of the goods may be such that there is no touch of the budget line and any indifference curve (Fig. 4.8).
For example, the consumer likes to eat oranges more than cake, and the price of oranges is relatively low. Then he spends all his earnings to buy oranges.

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