Equilibrium Income in the Keynesian Model

C

The expenditure multiplier is found by M = 1/(1-MPC). Thus, here M = 1/(1-3/4) = 4. Therefore the $10 billion decrease in aggregate expenditures is magnified four times to $40 billion.

In the Keynesian model, the marginal propensity to consume (MPC) represents the proportion of an additional unit of income that individuals choose to spend rather than save. In this case, the MPC is given as 0.75, which means that for every additional dollar of income, individuals spend 75 cents and save the remaining 25 cents.

Now, let's analyze the situation described in the question. It states that there is an independent decline in investment of $10 billion. Investment is one of the components of aggregate expenditure (AE) in the Keynesian model. The equation for AE is:

AE = C + I + G + (X - M),

where: C = Consumption I = Investment G = Government spending (X - M) = Net exports (exports minus imports)

In this case, we are only concerned with the impact of the decline in investment (I) on equilibrium income. The multiplier effect in the Keynesian model helps us determine the change in equilibrium income resulting from a change in autonomous expenditure (in this case, investment).

The formula for the multiplier effect is: Multiplier = 1 / (1 - MPC)

Substituting the given MPC of 0.75 into the formula, we get: Multiplier = 1 / (1 - 0.75) = 1 / 0.25 = 4

This means that a $1 change in autonomous expenditure will lead to a $4 change in equilibrium income.

Since there is an independent decline in investment of $10 billion, we can apply the multiplier to calculate the change in equilibrium income: Change in income = Multiplier * Change in autonomous expenditure

Change in income = 4 * (-$10 billion) = -$40 billion

The negative sign indicates a decline in equilibrium income. Therefore, the correct answer is A. $40 billion. The independent decline in investment of $10 billion would cause equilibrium income to decline by $40 billion in the Keynesian model.