It is connected by the formula(consumption function) C =A+MD where
C = Consumer spending
A=Autonomous consumption
M=Marginal Propensity to consume
D=real disposable income
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MPS =0.401 mpc = 0.509
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If the full multiplier for G (i.e. ignoring crowding out effects) is = change in G/Multiplier Then the tax multiplier is = change in T x marginal propensity to consume/multiplier since the mpc is between 0 and 1 the tax multiplier is less. Intuitively it is not difficult to see why, the change tax enters spending decisions through consumption and consumption is dependant on the mpc. Whereas as G affects spending decisions directly - it is a injection into the economy that does not have to work through some indirect source to have an effect on the economy.
The graph is a region of the space on one side or another of the related function. If the inequality is strict then the related function itself is not part of the solution; otherwise it is.