Question

Assume that LM curve equation as( M/P)=d1y-d2i . solve for equilibrium output.derive the multiplier

Answer 1

$( M/P)=d1y-d2i\\ (1-c_1-b_1)Y = c_0-c_1T+b_o-b_2 i +G\\ Multiplier = \frac{1}{1-c_1-b_1}$

Substituting for interest

$Y= \frac{1}{(1-c_1-b_1+b_2d_1)/d_2}[c_0-c_1T+b_0+ (\frac{b_2}{d_2})(\frac{M}{P})+G]$

Multiplier becomes

$\frac{1}{(1-c_1-b_1+b_2d_1)/d_2}$