The marginal propensity to save for a household is given by MPS = 0.5 + 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 + 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
a. The marginal propensity to save (MPS) is the change in savings due to a change in income. In this case, the MPS is given as 0.5. The saving function is given by the integral of the MPS, which is S = ∫MPS dy = ∫0.5 dy = 0.5y + C, where C is the constant of integration.
Given the initial condition f(400) = 1000, we can solve for C. Substituting y = 400 into the saving function gives 1000 = 0.5*400 + C, which simplifies to 1000 = 200 + C. Solving for C gives C = 800. Therefore, the saving function is S = 0.5y + 800.
To find the level of savings when y = 400, substitute y = 400 into the saving function to get S = 0.5*400 + 800 = 200 + 800 = 1000.
b. The consumption function is given by C = y - S, where C is consumption, y is income, and S is savings. Substituting the saving function into the consumption function gives C = y - (0.5y + 800) = 0.5y - 800. Therefore, the consumption function of the household is C = 0.5y - 800.
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