Final answer:
The statement that the MPC must be 0.4 is false because the correct calculation of the multiplier from the change in aggregate expenditures and real GDP indicates that the MPC is actually 0.6.
Step-by-step explanation:
If aggregate expenditures rise by $200 billion and real GDP consequently rises by $500 billion, this indicates a certain level of responsiveness in the economy to increased expenditures. This responsiveness is quantified by the marginal propensity to consume (MPC), which measures how much of an additional dollar of income is spent.
According to the Keynesian expenditure multiplier formula, the multiplier is equal to 1/(1-MPC).
Given that the real GDP increased by $500 billion as a response to a $200 billion increase in aggregate expenditures, we can calculate the multiplier as $500 billion / $200 billion = 2.5.
Thus, we can solve for MPC using 1/(1-MPC) = 2.5, which gives us an MPC of 0.6, not 0.4.
Therefore, the statement that the MPC must be 0.4 is false.