A household earns $50,000 per year and receives an unexpected $2,000 tax rebate. They spend $1,600 of it and save $400. What is their MPC?
A0.032 — calculated as $1,600 divided by total annual income of $50,000
B0.80 — calculated as $1,600 spent divided by the $2,000 income change
C0.20 — calculated as the $400 saved divided by the $2,000 income change
DCannot be determined without knowing their total annual consumption
MPC = ΔC / ΔY_d = 1,600 / 2,000 = 0.80. The MPC is always calculated from the *change* in income and the resulting *change* in consumption — not from totals. Option A is the classic confusion with the average propensity to consume (APC), which uses total income in the denominator. Option C gives the marginal propensity to save (MPS = 0.20), which is the complement: MPC + MPS = 1.
Question 2 Multiple Choice
If the MPC is 0.8, a $100 increase in government spending leads to what total increase in GDP through the multiplier process?
A$80 — the direct consumption share of the initial spending
B$100 — the initial dollar of government spending only
C$500 — calculated as 1 / (1 − MPC) = 1 / 0.2 = 5, times the initial $100
D$180 — the initial dollar plus one round of re-spending (100 × 0.8)
The fiscal multiplier is 1 / (1 − MPC) = 1 / (1 − 0.8) = 1 / 0.2 = 5. The initial $100 becomes income for someone who spends $80, which becomes income for someone who spends $64, and so on. The total is the geometric series 1 + 0.8 + 0.64 + … = 1 / (1 − 0.8) = 5. Option D captures only the first round of re-spending and misses the cascading effect that defines the multiplier.
Question 3 True / False
Because every dollar of disposable income must be either consumed or saved, MPC and MPS must sum to exactly 1 by definition.
TTrue
FFalse
Answer: True
MPC + MPS = 1 is a definitional identity, not an empirical claim. If a household receives an extra dollar and spends 80 cents, it must save the remaining 20 cents — there is no third category. This means MPS = 1 − MPC, and knowing one immediately gives you the other. It also means MPC must be between 0 and 1 (exclusive): it cannot be negative (you can't un-consume) or greater than 1 (you can't spend more than you receive, on the margin, in this framework).
Question 4 True / False
The average propensity to consume (APC) and the marginal propensity to consume (MPC) measure the same household behavior — APC is just the MPC calculated at a specific income level.
TTrue
FFalse
Answer: False
APC (= C / Y_d) measures the fraction of *total* income spent on consumption. MPC (= ΔC / ΔY_d) measures the fraction of an *additional dollar* of income that is consumed. For the consumption function C = a + b·Y_d, MPC is the constant slope b, while APC = a/Y_d + b — a value that changes as income rises. A high-income household may have a lower APC than a low-income household even if their MPC is identical, because autonomous consumption a is a smaller fraction of their larger income.
Question 5 Short Answer
Why do lower-income households tend to have a higher MPC than higher-income households, and what are the macroeconomic implications for fiscal stimulus targeted at different income groups?
Think about your answer, then reveal below.
Model answer: Lower-income households are typically liquidity-constrained — they spend essentially all of each additional dollar because they have unmet consumption needs and little savings cushion. Higher-income households can afford to save a larger fraction of additional income. This means fiscal stimulus (tax cuts or transfers) targeted at lower-income households generates a larger multiplier effect: more of each dollar cycles back into consumption and GDP. The same total stimulus will have a larger aggregate demand impact if concentrated at the bottom of the income distribution than if distributed uniformly or toward higher earners.
This has direct policy implications: a $500 tax rebate to a lower-income household with MPC ≈ 0.95 generates roughly $10,000 in total GDP impact via the multiplier (1 / 0.05 = 20). The same rebate to a high-income household with MPC ≈ 0.50 generates only $1,000 (1 / 0.5 = 2). Economists debating stimulus design must account for the distribution of MPC across the income spectrum, not just the aggregate MPC.