In Figure 5.7, the feasible frontier is represented by a downward-sloping, concave curve. This curve is plotted on a graph where the horizontal axis shows Angela's hours of free time (ranging from 0 to 24), and the vertical axis displays the bushels of grain she can produce (ranging from 0 to 70). The frontier connects the specific points (0, 64), A (16, 46), and (24, 0), defining the maximum technically possible output for each level of free time.

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Figure 5.7 is a diagram presenting Angela's optimization problem. It plots her hours of free time (0-24) on the x-axis against bushels of grain (0-70) on the y-axis. The graph includes her feasible frontier, a downward-sloping, concave curve passing through points (0, 64), A (16, 46), and (24, 0). It also shows several parallel, convex indifference curves representing her preferences. The lowest of these, IC3, intersects the feasible frontier at two suboptimal points, including point B. The optimal allocation is at point A, where the feasible frontier is tangent to indifference curve IC-star, and the Marginal Rate of Substitution (MRS) equals the Marginal Rate of Transformation (MRT). Higher indifference curves, like IC5, lie entirely above the feasible frontier, representing unattainable outcomes. Point C, for instance, lies on IC5 at 16 hours of free time but with an unachievable quantity of grain.

Figure 5.7 - Angela's Optimal Choice as an Independent Farmer

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

CORE Econ - The Economy 2.0: Microeconomics

The Feasible Frontier in Figure 5.7

This activity involves finding the optimal combination of free time and grain for Angela, which represents the best possible outcome she can achieve given her production constraints. The objective is to identify the point on her feasible frontier that allows her to reach the highest attainable indifference curve, as depicted in Figure 5.7.

Activity: Determining the Best Angela Can Do

Angela's optimal choice, which maximizes her utility, is at point A, corresponding to 16 hours of free time and 46 bushels of grain. At this point, the two critical trade-offs she faces are perfectly balanced. The trade-off she is subjectively willing to make between grain and free time, her Marginal Rate of Substitution (MRS), becomes equal to the objective trade-off she is constrained to make by her production technology, the Marginal Rate of Transformation (MRT). This condition (MRS = MRT) signifies the point of tangency between her feasible frontier and the highest possible indifference curve, as depicted in Figure 5.7.

Angela's Optimal Choice (Point A) where MRS = MRT

This activity involves analyzing a diagram that displays Angela's feasible frontier alongside several of her indifference curves. The task is to use this graphical information to determine which of a given set of statements about her economic situation are correct.

Activity: Evaluating Statements on Angela's Choices Using a Graph

The indifference curve IC3 intersects the feasible frontier at two points, demonstrating suboptimal but feasible choices for Angela. One of these intersection points is labeled as point B. This point represents an allocation with fewer hours of free time and a larger amount of grain compared to the optimal point A. While feasible, any point on IC3 provides lower utility than point A, which lies on the higher indifference curve IC-star.

Point B and Suboptimal Choices on Indifference Curve IC3 (Figure 5.7)

Indifference curves located entirely above the feasible frontier, like IC5 in Figure 5.7, represent unattainable allocations. Point C is an example of such an allocation; it lies on IC5 and corresponds to 16 hours of free time. The amount of grain at point C is greater than at point B (a suboptimal but feasible point) and is beyond what Angela can produce with that amount of free time. Therefore, any allocation on IC5 is impossible for Angela to achieve.

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