Use the indifference curves and the budget lines in Figure 19.3 to answer the indicated question. Assume the price of Y is $1 per unit. If the price per unit of good X is $3, the consumer would maximize utility by consuming

Question

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At point A on the budget line for $30 ($3 per unit of X), the consumer can afford to buy 10 units of X and 30 units of Y. At this point, the consumer's marginal rate of substitution (MRS) for X in terms of Y is steeper than the slope of the budget line. This indicates that the consumer can increase their utility by consuming more X and less Y.

Moving to the point where the budget line is tangent to the indifference curve (point B), the consumer maximizes their utility. At this point, the MRS for X in terms of Y is equal to the slope of the budget line, indicating that the consumer is consuming X and Y in the optimal proportions given their budget constraint.

Since the price of Y is $1 per unit, and the consumer is spending $30 on X and Y in total, they can afford to purchase 10 units of X ($3 per unit) and 20 units of Y ($1 per unit). Therefore, the consumer would maximize utility by consuming 20 units of Y and 10 units of X. Solving for the corresponding point on the graph, we see that the optimal bundle is at point B, where the indifference curve is tangent to the budget line for $30.

Use the Indifference Curves and the Budget Lines in Figure