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Stupid question: What do the phi and lambda from the equations above represent?

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The equations you have are equilibrium conditions, while derivation (of course) starts with the demand equation and sets demand equal to supply. Then:

  • $\varphi$ ($0<\varphi<1$) is the income elasticity of money demand - the responsiveness of demand with respect to income

  • $-\lambda$ ($-\lambda <0$) is the interest rate semi-elasticity of money demand - the responsiveness of demand to the change in interest rates.

Semi-elasticity means that we care how much Y changes in percentages when we increase $X$ by one (increase by one, not by one percentage point).

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To my understanding, $\phi$ and $\lambda$ are simply positive parameters in the Dornbusch model used to represent the linear (in logarithms) equilibrium condition in the money market.

$$ m - p = \phi y - \lambda i $$

is also known as the LM curve, in logarithms.

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