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Econ 431 Stratton

Notes on Labor Supply and Slutsky Equation

The Slutsky Equation is an equation which shows how the effect of any price change can be decomposed into 2 parts: an income effect (illustrated by a parallel shift in the budget line) and a substitution effect (illustrated as a movement along an indifference curve). The graphical representation below and the term Hicksian Decomposition may be more familiar to you (if you have had intermediate microeconomic theory).

General Case

A = Apples B = Books

PA = Price of A PB = Price of B

Y = Income Equation of budget constraint: A = Y/PA – (PB/PA)B

[pic]

In this example, the price of Books (PB) is unchanged. The price of Apples (PA), however, increases from PA to P’A thus causing the budget line to rotate in towards the origin. The optimal consumption bundle changes from F to H. Utility falls from U to U’.

The change in the consumption of either good can be split into an income effect and a substitution effect. Let’s take the change in consumption of A, from A* to A**, and decompose in into its separate effects. (A* - A**) is the total or net or uncompensated effect. It can be denoted: [pic]

• If you hold the individual’s utility constant at the post-price change level U’, and keep relative prices constant (PB/PA), you will observe the income effect associated with the price change. This is illustrated by the movement from A* to A’ (from F to G). The dashed line is parallel to the ‘old’ budget constraint but tangent to the ‘new’ indifference curve.

• Holding constant the post-price change utility at U’, and changing relative prices to reflect the change in PA, you will observe the substitution (or compensated) effect. This is reflected in the move from A’ to A** (from G to H). Thus, the movement from A’ to A** reflects the change in A resulting from a change in PA, holding utility constant at U’. This is denoted: [pic] (read “holding U...