Based on the graphical representation of Karim's preferences and constraints in Figure E3.3, the problem is to identify the utility-maximizing combination of free time and consumption, and from that, calculate the number of hours he chooses to work.

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This diagram illustrates Karim's initial utility-maximizing choice at his original wage. The graph is set up with daily free time on the horizontal axis, ranging from 8 to 24 hours, and daily consumption in euros on the vertical axis, ranging from 0 to 600. His budget constraint is represented by a straight line connecting the points (8, 480) and (24, 0). The optimal choice is at point E, with coordinates (17, 210), where a convex, downward-sloping indifference curve is tangent to the budget line, indicating the highest utility he can achieve given his constraints.

Graphical Representation of Karim's Initial Optimal Choice

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

This diagram illustrates how a wage increase affects Karim's choices and improves his living standards. The horizontal axis measures daily free time (ranging from 8 to 24 hours), and the vertical axis measures consumption in euros (ranging from 0 to 600). Coordinates are presented as (free time, consumption). The original budget constraint is a straight line connecting (8, 480) and (24, 0). The initial optimal choice, Point E (17, 210), is located where a downward-sloping, convex indifference curve is tangent to this line. A new, steeper budget constraint is shown connecting (8, 720) and (24, 0). The new optimal choice, Point F (17 and a third, 300), is found where another downward-sloping, convex indifference curve is tangent to this steeper line.

Figure 3.9 - The Effect of a Wage Increase on the Feasible Set

An individual's utility is maximized when the two primary trade-offs they face are perfectly balanced. This optimal combination of consumption and free time occurs at the specific point where the Marginal Rate of Transformation (MRT), representing the market trade-off, is exactly equal to the Marginal Rate of Substitution (MRS), which represents the individual's personal trade-off. For Karim, this condition is met at point E.

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