Find an expression for the savings function if the marginal propensity to save is given by MPS = 0.4 – 0.1Y −1/2 and savings are zero when income is 100.

Step-by-step explanation:

We are given the following equations from the Keynesian Model, find the autonomous consumption

level, marginal propensity to consume (MPC) and marginal propensity to save (MPS). Find the savings

function with respect to disposable income, and then use the given information about net taxes to find the

consumption and savings function with respect to real output. If the consumption function with respect to

disposable income is not given, find that first!

Note: Remember when we have the consumption function in the form C = a + b(Y – T) that autonomous

consumption is a and the marginal propensity to consume is b.

To solve for the consumption and savings functions with respect to real output rather than disposable

income we need to enter the value of net taxes.

The savings function with respect to disposable income is S = -a + (1 – b) (Y – T)

(a) C = 125 + 0.75(Y-T) Net Taxes = 100

Autonomous Consumption Level : a = 125

MPC : b = 0.75

MPS : MPS = 1-MPC = 0.25

Savings Function w/ respect to DI : S = - a + MPS(Y – T) = -125 + 0.25(Y – T)

Consumption Function w/ respect to Y : C = 125 + 0.75(Y – 100) = 50 + 0.75Y

Savings Function w/ respect to Y : S = -125 + 0.25(Y – 100) = -150 + 0.25Y

(b) C = 0.80(300-T+Y) Net Taxes = 50

= 240 – 0.8(T – Y) = 240 + 0.8(Y – T)

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Step-by-step explanation:

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step-by-step explanation:

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