Question

supposed that, instead of a fixed level of taxes, we had an income tax so that t=ty where t is the income tax rate. drive an expression for multiplier. what is the expression equivalent to the autonomous expenditure multiplier (1/1-b) for this case of an income tax?

Answer 1

An expression for multilplier.

$$Tax _m = {-MPC\over1-MPC}×tax$$

$$Mpc = Y -ty$$

$$={-Y-ty\over1-Y-ty}×ty$$

$$m={ty(Y+ty)\over1-Y-ty}$$

Autonomous expenditure multplier.

${1\over1-b} income tax$

Expenditure multplier formula is

$$m ={1\over1-mpc}$$

$${1\over1-Y-ty}= {1\over1-b}$$