A. The marginal propensity to consume (MPC) is the change in consumption divided by the change in income. In this case, the saving function is given as S = -400 + 0.2Y, where Y represents income. To find the MPC, we need to find the change in consumption. Since consumption is the opposite of saving, we can rewrite the equation as C = Y - S. By substituting the saving function into the equation, we get C = Y - (-400 + 0.2Y). Simplifying further, C = 1.2Y + 400. The change in consumption (∆C) is 1.2Y + 400 - Y, which simplifies to 0.2Y + 400. Therefore, the MPC is 0.2.
B. The marginal propensity to save (MPS) is the change in saving divided by the change in income. MPS is the opposite of MPC, so the MPS in this case is 1 - MPC, which is 1 - 0.2 = 0.8.
C. The expenditure multiplier (k) is calculated as 1 / MPS. In this case, the expenditure multiplier is 1 / 0.8 = 1.25.
D. The equation for consumption is C = Y - S, which we found to be C = 1.2Y + 400.
E. The equation for aggregate autonomous expenditures is the sum of investment and government expenditures, which is $500 billion + $550 billion = $1050 billion.
F. The equation for aggregate induced expenditures is the product of consumption and the expenditure multiplier. In this case, it is 1.25 * (1.2Y + 400).
G. Autonomous consumption refers to the consumption that does not depend on income. In this case, the autonomous consumption is 400.
H. Induced consumption refers to the consumption that depends on income. In this case, it is 0.2Y.
I. The equation for induced saving is the difference between induced consumption and income. In this case, it is 0.2Y - Y, which simplifies to -0.8Y.
J. Equilibrium aggregate expenditures occur when aggregate induced expenditures equal aggregate autonomous expenditures. Setting 1.25 * (1.2Y + 400) = $1050 billion and solving for Y gives Y = $4000 billion.
K. Equilibrium real GDP (Y) is the same as the income at equilibrium aggregate expenditures, which is $4000 billion.
L. Autonomous aggregate expenditures at equilibrium RGDP are the aggregate autonomous expenditures, which is $1050 billion.
M. If RGDP = $8000, it indicates that the economy is experiencing an inflationary gap or overheating. This means that the economy is producing above its long-run potential and may face inflationary pressures.
N. If RGDP = $5000, it indicates that the economy is experiencing a recessionary gap or an output gap. This means that the economy is producing below its long-run potential and is not utilizing its resources efficiently.
O. To solve the problem in (N), the government should increase government spending to stimulate aggregate demand. The amount of the increase would depend on the desired impact on equilibrium RGDP and the magnitude of the expenditure multiplier.