Slutsky equation

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The Slutsky equation (or Slutsky identity) in economics, named after Eugen Slutsky (1880-1948), relates Marshallian demand and Hicksian demand. It demonstrates that demand changes due to price changes are a result of two effects:

  • a substitution effect, the result of a change in the exchange rate between two goods; and
  • an income effect, the effect of price results in a change of the consumer's purchasing power.

The actual equation is

D_p x(p, w) = D_p h(p, u)- D_w x(p, w) x(p, w)^\top,\,

where h(p,u) is the Hicksian demand and x(p,w) is the Marshallian demand. The first term represents the substitution effect, and the second term represents the income effect.

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