The substitution effect can be calculated by subtracting the income effect from the overall effect. This calculation is derived directly from the principle that the overall effect is the sum of its two components. The formula is: $$ \text{Substitution Effect} = \text{Overall Effect} - \text{Income Effect} $$

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The overall effect of a price or wage change on an individual's choice can be decomposed into two distinct components: the income effect and the substitution effect. This relationship is additive, meaning the overall effect is the algebraic sum of the income and substitution effects. Consequently, if the values for the overall effect and one of its components are known, the value of the other component can be deduced.

The Overall Effect as the Sum of Income and Substitution Effects

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

In the scenario depicted in Figure 3.13b, the overall effect of the wage rise is a decrease in free time. This outcome occurs because the substitution effect, which encourages less leisure due to its higher opportunity cost, is larger in magnitude than the income effect, which encourages more leisure. The sum of these two opposing forces results in a net reduction in free time chosen.

Dominance of the Substitution Effect in Figure 3.13b

Calculating the Substitution Effect from the Overall and Income Effects

In the historical context of the United States from 1900 to 2020, the significant rise in real wages resulted in an income effect that was more powerful than the substitution effect. This dominance is the causal reason for the observed outcome where workers chose to increase both their daily consumption of goods and their amount of free time.

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