Skip to main content
edited title
Link
EconJohn
  • 8.8k
  • 6
  • 33
  • 68

Income effect $-\frac{\partial x_i}{\partial p_im} x_i$ or $\frac{\partial x_i}{\partial p_im}x_i$?

Source Link
EconJohn
  • 8.8k
  • 6
  • 33
  • 68

Income effect $-\frac{\partial x_i}{\partial p_i} x_i$ or $\frac{\partial x_i}{\partial p_i}x_i$?

Recall that the slutsky equation is:

$$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$

I know $\frac{\partial h_i}{\partial p_i}$ defined as the substitution effect, the second part of the equation is the income effect.

My Question: is the income effect defined as $-\frac{\partial x_i}{\partial m}x_i$ or $\frac{\partial x_i}{\partial m}x_i$ (is the negative sign a defining characteristic?)