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#economics
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#saving-function
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if the Marginal propensity to save MPS is s(y)=0.3-0.1y⁻⁰·⁵ the following function of income S is null when Income y is 81 find the saving function ?

Jul 1

economics

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Anonymous

Jul 3

To find the saving function, we can use the given marginal propensity to save (MPS) equation:
MPS = s(y) = 0.3 - 0.1y^(-0.5)
We are given that when income (y) is 81, the saving function (S) is null, meaning there is no saving at that income level.
Let's substitute y = 81 into the MPS equation and solve for the saving function:
0 = 0.3 - 0.1(81)^(-0.5)
First, let's simplify the exponent term:
(81)^(-0.5) = 1/sqrt(81) = 1/9 = 1/3^2 = 1/3^2 = 1/3^(2*0.5) = 1/3^1 = 1/3
Now substitute this value back into the equation:
0 = 0.3 - 0.1(1/3)
0 = 0.3 - 0.1/3
0 = 0.3 - 0.03333...
0 ≈ 0.26667...
Therefore, the saving function can be expressed as:
S(y) = 0.26667... * y
Please note that this is an approximation, as we rounded the decimal. The saving function is linear, and for every unit increase in income, the saving amount is approximately 0.26667 units.

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