Question

Sketch a Slutsky decomposition graph for a price increase of good y. Indicate the income effect and substitution effect for both good. Exact values do not matter.

Answer 1

Slutsky’s method of separating income effect and substitution effect. Figure 3 illustrates the Slutskian version of calculating income effect and substitution effect.

In figure 3, AB₁ is the initial budget line. The consumer’s original equilibrium point (before price effect takes place) is E₁, where indifference curve IC₁ is tangent to the budget line AB₁. Suppose the price of commodity X falls (price effect takes place) and other things remain the same. Now the consumer shifts to another equilibrium point E₂, where indifference curve IC₃ is tangent to the new budget line AB₂. Consumer’s movement from equilibrium point E₁ to E₂ implies that consumer’s purchase of commodity X increases by X₁X₂. This is the total price effect caused by the decline in price of commodity X.

Now the task before us is to isolate the substitution effect. In order to do so, Slutsky attributes that the consumer’s money income should be reduced in such a way that he returns to his original equilibrium point E₁ even after the price change. What we are doing here is that we make the consumer to purchase his original consumption bundle (i.e., OX₁ quantity of commodity X and E₁X₁ quantity of commodity Y) at the new price level.

In figure 3, this is illustrated by drawing a new budget line A₄B₄, which passes through original equilibrium point E₁ but is parallel to AB₂. This means that we have reduced the consumer’s money income by AA₄ or B₄B₂ to eliminate the income effect. Now the only possibility of price effect is the substitution effect. Because of this substitution effect, the consumer moves from equilibrium point E₁ to E₃, where indifference curve IC­₂ is tangent to the budget line A₄B₄. In Slutsky version, the substitution effect leads the consumer to a higher indifference curve.