Advanced Application Problems — GDP, Inflation, and National Accounts

高阶应用题 —— GDP、通胀与国民核算专题

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Question 1 — Nominal vs Real GDP (名义 GDP 与实际 GDP)

A country produces only food and clothing.
下表给出该国 2019 与 2020 年的商品价格与数量：

Year	Price of Food (食物价格)	Quantity of Food (食物数量)	Price of Clothing (衣服价格)	Quantity of Clothing (衣服数量)
2019	$5	100	$10	50
2020	$6	120	$12	60

Using 2019 as the base year, calculate:
a) Nominal GDP in 2020
b) Real GDP in 2020
c) GDP deflator in 2020

📖 点击查看答案

a) Nominal GDP (2020) = (6×120) + (12×60) = $1,440\ast \ast .b)RealGDP(2020,base2019)=(5\times 120)+(10\times 60)=\ast \ast$1,200.
c) GDP Deflator = (1,440 ÷ 1,200) × 100 = 120.

📝 点击查看解析

Nominal GDP uses current-year prices, while Real GDP uses base-year prices to eliminate inflation.
名义 GDP 用当年价格计算，而实际 GDP 用基准年价格剔除通胀。
GDP 平减指数衡量价格水平变化：
$GDPDeflator=\frac{NominalGDP}{RealGDP}\times 100=120$
→ 说明 2020 年总体价格水平较 2019 年上涨了 20%。

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Question 2 — Growth and Inflation (经济增长与通胀率)

Real GDP grows from 100 to 110, while the GDP deflator increases from 120 to 126.
Compute:
a) Nominal GDP growth rate.
b) Inflation rate.

📖 点击查看答案

a) Nominal GDP growth = (110×126 − 100×120) / (100×120) ×100 = 15.5%.
b) Inflation = (126−120)/120 ×100 = 5%.

📝 点击查看解析

名义 GDP 同时受价格与产出影响。
$NominalGrowth=RealGrowth+Inflation+Interactionterm.$

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Question 3 — GDP Deflator Application (GDP 平减指数应用)

In 2021, nominal GDP = $24trillion,realGDP=$20 trillion (base 2015).
Find GDP deflator and interpret it.

📖 点击查看答案

Deflator = (24/20)×100 = 120.

📝 点击查看解析

平减指数 120 表明价格水平相较基期上涨 20%，即 2015–2021 年平均通胀约 3%/年。

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Question 4 — Depreciation and National Income (折旧与国民收入)

GDP = $21trillion;depreciation=$1.4 trillion.
Find national income (NI).

📖 点击查看答案

NI = GDP − Depreciation = $19.6 trillion.

📝 点击查看解析

国民收入代表实际可分配生产所得，折旧部分用于资本补偿，故应剔除。

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Question 5 — GNP vs GDP (GNP 与 GDP)

U.S. firms earn $200billionabroad;foreignfirmsearn$150 billion in the U.S.
GDP = $20,000 billion. Compute GNP.

📖 点击查看答案

GNP = GDP + (U.S. income abroad − foreign income in U.S.) = 20,000 + (200 − 150) = $20,050 billion.

📝 点击查看解析

GNP 包含本国居民在境外的生产收入，不含外国人在本国的生产。

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Question 6 — Personal and Disposable Income (个人收入与可支配收入)

National income = $19,500B;corporateretainedearnings=$200B; transfer payments = $300B;personaltaxes=$1,000B.
Find:
a) Personal income (PI).
b) Disposable personal income (DPI).

📖 点击查看答案

a) PI = 19,500 − 200 + 300 = 19,600.
b) DPI = 19,600 − 1,000 = $18,600B.

📝 点击查看解析

PI 调整企业留存收益与政府转移支付；DPI 表示家庭可支配消费或储蓄的收入。

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Question 7 — Inflation from Deflator (通胀率计算)

Deflator 2020 = 112, Deflator 2021 = 120.
Compute the inflation rate.

📖 点击查看答案

(120 − 112)/112 ×100 = 7.1%.

📝 点击查看解析

通胀率等于 GDP 平减指数的年增长率，反映总体物价水平变化。

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Question 8 — Real GDP Growth (实际 GDP 增长率)

Real GDP rises from $18Tto$19.26T. Compute the annual growth rate.

📖 点击查看答案

(19.26−18)/18 ×100 = 7%.

📝 点击查看解析

年增长率 = 实际产出变化 / 前一年产出 ×100%。

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Question 9 — Inflation and Nominal Growth (通胀与名义增长)

If nominal GDP grew 8% and real GDP grew 3%, approximate inflation rate = ?

📖 点击查看答案

Inflation ≈ 8 − 3 = 5%.

📝 点击查看解析

名义增长 ≈ 实际增长 + 通胀率。

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Question 10 — Price Stability Test (物价稳定性测试)

If GDP deflator remains constant but real GDP increases, what happens to nominal GDP?

📖 点击查看答案

Nominal GDP increases at the same rate as real GDP.

📝 点击查看解析

若价格不变（平减指数恒定），名义 GDP 增长仅由产量推动。

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Question 11 — Base Year Effect (基准年效应)

Changing base year alters:
a) Price index level?
b) Real GDP growth rate?

📖 点击查看答案

a) Yes. b) No.

📝 点击查看解析

平减指数绝对值随基准年变化而调整，但增长率（相对变化）不受影响。

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Question 12 — Comparing Countries (国家比较)

Country A: GDP $500B,population50M;CountryB:GDP$900B, population 150M.
Which has higher per capita GDP?

📖 点击查看答案

A: 500/50 = $10,000;B:900/150=$6,000 → Country A higher.

📝 点击查看解析

人均 GDP 衡量平均产出能力，而非总规模。

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Question 13 — Real vs Nominal Example (实际与名义示例)

Nominal GDP grew 10%, GDP deflator grew 6%.
Find real GDP growth.

📖 点击查看答案

Real growth ≈ 10 − 6 = 4%.

📝 点击查看解析

通过平减指数调整，剔除通胀影响，得实际增长率。

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Question 14 — Hidden Economy (隐形经济影响)

If underground economy = 15% of official GDP, and official GDP = $1 trillion, what is the true GDP?

📖 点击查看答案

True GDP = 1 × (1 + 0.15) = $1.15 trillion.

📝 点击查看解析

地下经济被遗漏，修正后产出上升 15%。

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Question 15 — Depreciation Ratio (折旧率)

GDP = $22T,NI=$20.5T. Compute depreciation rate.

📖 点击查看答案

Depreciation = 1.5T → 1.5/22 ×100 = 6.8%.

📝 点击查看解析

折旧占 GDP 的比例表征资本消耗强度。

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Question 16 — GDP vs Well-being (GDP 与福祉)

GDP per capita increased by 5%, but pollution doubled. What happens to well-being?

📖 点击查看答案

Likely decreases — GDP ignores environmental degradation.

📝 点击查看解析

GDP 未计入负外部性，产出上升不代表生活质量提升。

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Question 17 — Inflation Composition (通胀成分)

CPI inflation = 3%; GDP deflator inflation = 5%. What does this imply?

📖 点击查看答案

Broader inflation in investment goods/services beyond consumers.

📝 点击查看解析

CPI 仅反映消费者价格；平减指数包含政府与投资支出。

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Question 18 — GDP Identity (GDP 核算恒等式)

If C=60%, I=15%, G=20%, NX=5% of GDP, and GDP = $20T, find each component.

📖 点击查看答案

C=12T, I=3T, G=4T, NX=1T.

📝 点击查看解析

Y = C + I + G + NX 为支出法恒等式。

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Question 19 — Income Method (收入法计算)

If wages=70%, rent=10%, interest=10%, profit=10% of GDP $20T, compute national income distribution.

📖 点击查看答案

Wages 14T, rent 2T, interest 2T, profit 2T.

📝 点击查看解析

收入法分解产出来源。

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Question 20 — Inflation Adjustment (通胀调整)

Nominal GDP = $1,200B, Deflator = 150. Find real GDP.

📖 点击查看答案

1,200 / (150/100) = $800B.

📝 点击查看解析

实际 GDP 剔除通胀效应：Real = Nominal / (Deflator/100)。

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Question 21 — Chain-weighted GDP (链式加权 GDP)

Why is chain-weighted GDP preferred over fixed base-year GDP?

📖 点击查看答案

It accounts for changing relative prices over time.

📝 点击查看解析

链式权重动态调整价格权重，更准确反映长期结构变化。

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Question 22 — Inflation Erosion (通胀侵蚀)

If income grew 4% but prices 6%, what happens to real income?

📖 点击查看答案

Real income fell ≈ 2%.

📝 点击查看解析

$RealGrowth=NominalGrowth-Inflation.$

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Question 23 — Negative Real Growth (负增长)

If nominal growth 2%, inflation 4%, determine real growth.

📖 点击查看答案

2 − 4 = −2%.

📝 点击查看解析

价格上涨超过产出增长 → 实际萎缩。

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Question 24 — Government Spending and GDP (政府支出与 GDP)

Government builds $500B infrastructure financed domestically. Effect on GDP?

📖 点击查看答案

GDP increases by $500B (investment spending).

📝 点击查看解析

政府投资直接计入 G 项，提高当期产出。

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Question 25 — Net Exports Impact (净出口对 GDP 的影响)

Exports rise $50B;importsrise$70B. What is net effect on GDP?

📖 点击查看答案

ΔNX = 50 − 70 = **−$20B\ast \ast ,GDPdecreasesby$20B.

📝 点击查看解析

净出口为 GDP 的一部分，进口增加削减总产出。

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Question 26 — Inflation Rate from Multiple Years (多年度通胀计算)

Deflators: 2019=100, 2020=108, 2021=117.
Compute average annual inflation.

📖 点击查看答案

(117/100)^(1/2)−1 = 8.2% per year.

📝 点击查看解析

使用几何平均增长率计算复合年通胀率。

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Question 27 — Comparing Real Growth (跨国实际增长比较)

Country X: real GDP growth 5%, population growth 3%.
Compute per capita GDP growth.

📖 点击查看答案

5 − 3 = 2%.

📝 点击查看解析

人均增长率 = 实际 GDP 增长率 − 人口增长率。

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Question 28 — Inflation from Index Numbers (指数法通胀)

GDP deflator index: 2018=105, 2019=110, 2020=120.
Find cumulative inflation 2018–2020.

📖 点击查看答案

(120−105)/105 ×100 = 14.3%.

📝 点击查看解析

累计通胀 = 指数变化率。

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Question 29 — GDP per Capita Interpretation (人均 GDP 解读)

If real GDP grew 10% and population grew 10%, what happens to per capita real GDP?

📖 点击查看答案

No change (0%).

📝 点击查看解析

产出与人口同比增长 → 人均水平不变。

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Question 30 — Inflation and Policy (通胀与政策分析)

If deflator rises from 100 to 130 in five years, what is the implied annual inflation, and what policy might be needed?

📖 点击查看答案

Annual inflation = (130/100)^(1/5)−1 = 5.4%.
Policy: contractionary monetary policy.

📝 点击查看解析

持续通胀表明货币供给过快增长，应通过加息或紧缩支出控制物价。

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