Equilibrium Income and Autonomous Investment

Explanation

The expenditure multiplier is found by M = 1/(1-MPC). Thus, here M = 1/(1-3/4) = 4. Therefore $20 billion increase in aggregate expenditures is magnified four times to $80 billion.

To determine the effect of a $20 billion increase in autonomous investment on equilibrium income, we need to understand the relationship between aggregate expenditure (AE) and equilibrium income.

Aggregate expenditure (AE) is the sum of consumption (C) and investment (I). In this case, autonomous investment refers to investment that is independent of income or the level of economic activity.

The marginal propensity to consume (MPC) represents the proportion of an increase in income that is spent on consumption. In this case, the MPC is given as 3/4 or 0.75. This means that for every additional dollar of income, 75 cents are spent on consumption.

When an economy operates well below its full-employment capacity, it means that there is unused or idle productive capacity. This implies that any increase in aggregate expenditure will have a multiplier effect on income, leading to a larger increase in equilibrium income.

To calculate the change in equilibrium income resulting from the $20 billion increase in autonomous investment, we need to use the multiplier formula:

Multiplier = 1 / (1 - MPC)

In this case, the MPC is 0.75, so the multiplier is:

Multiplier = 1 / (1 - 0.75) = 1 / 0.25 = 4

The multiplier of 4 indicates that a change in autonomous expenditure will have four times the effect on equilibrium income.

Now, let's calculate the change in equilibrium income:

Change in equilibrium income = Multiplier * Change in autonomous investment

Change in equilibrium income = 4 * $20 billion = $80 billion

Therefore, the correct answer is A. $80 billion. The $20 billion increase in autonomous investment will cause the equilibrium income to rise by $80 billion.