The marginal propensity to save for a household is given by MPS = 0.5 + 0.2/ROOT OF y square 3 Find the saving function of the household and determine the level of savings when y = 400, using the initial condition of f (400) = 1000 b. Determine the consumption function of the household.
Question
The marginal propensity to save for a household is given by MPS = 0.5 + 0.2/ROOT OF y square 3 Find the saving function of the household and determine the level of savings when y = 400, using the initial condition of f (400) = 1000 b. Determine the consumption function of the household.
Solution
The given marginal propensity to save (MPS) function is MPS = 0.5 + 0.2/√y^3.
a. To find the saving function, we need to integrate the MPS function with respect to y.
∫(0.5 + 0.2/√y^3) dy
= 0.5y + 0.2∫y^(-3/2) dy
= 0.5y - 0.4y^(-1/2) + C
To find the constant of integration C, we use the initial condition f(400) = 1000.
1000 = 0.5(400) - 0.4(400)^(-1/2) + C
1000 = 200 - 0.4(20) + C
1000 = 200 - 8 + C
C = 1000 - 192 = 808
So, the saving function is S(y) = 0.5y - 0.4y^(-1/2) + 808.
b. The consumption function is given by C(y) = y - S(y).
So, C(y) = y - (0.5y - 0.4y^(-1/2) + 808)
= 0.5y + 0.4y^(-1/2) - 808.
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