Inflation, CPI, and Interest Rates — Application Problems (通货膨胀、CPI 与利率应用题)
Question 1 — CPI Calculation (计算消费者物价指数)
In 2010, the cost of a market basket is 960.
Compute the CPI for 2020 (base year 2010).
2010 年的市场篮子成本为 960。计算以 2010 为基年的 2020 年 CPI。
📖 点击查看答案
CPI₍2020₎ = (960 / 800) × 100 = 120
📝 点击查看解析
CPI = (Current year expenditure / Base year expenditure) × 100。
CPI 表示价格相对基年的变动程度。
CPI = (960 ÷ 800) × 100 = 120 → 表示价格水平比基年上升 20%。
Question 2 — Inflation Rate (计算通货膨胀率)
If CPI in 2020 is 120 and CPI in 2021 is 126, calculate the inflation rate in 2021.
若 2020 年 CPI 为 120，2021 年为 126，求 2021 年的通胀率。
📖 点击查看答案
Inflation rate = (126 − 120) / 120 × 100 = 5%
📝 点击查看解析
通胀率 = [(本年 CPI − 上年 CPI) / 上年 CPI] × 100
= (126−120)/120×100 = 5%，即物价平均上涨 5%。
Question 3 — Adjusting Past Salaries (调整历史薪资)
Your mother earned $25,000 in 1993 when CPI was 144. CPI in 2018 is 251.
Find her equivalent salary in 2018 dollars.
你母亲 1993 年的年薪为 $25,000，当时 CPI 为 144，2018 年 CPI 为 251。求按 2018 年购买力计算的等价薪资。
📖 点击查看答案
25,000 × (251 / 144) = $43,576
📝 点击查看解析
等价薪资 = 历史薪资 × (当年 CPI / 基年 CPI)
= 25,000 × (251 ÷ 144) ≈ 43,576。
说明物价上升约 1.7 倍。
Question 4 — Real vs Nominal Interest (名义与实际利率)
If the nominal interest rate is 6% and inflation is 2%, what is the real interest rate?
名义利率为 6%，通胀率为 2%，求实际利率。
📖 点击查看答案
Real interest rate = 6 − 2 = 4%
📝 点击查看解析
实际利率 = 名义利率 − 通胀率。
在低通胀时该近似公式成立。通胀 2% 会削弱名义利率 6% 的购买力收益，实际收益仅 4%。
Question 5 — Real Return under Higher Inflation (高通胀下的实际回报)
A bank pays 5% nominal interest. If inflation unexpectedly rises to 7%, what is the real return?
银行名义利率为 5%，若通胀意外上升至 7%，求实际收益率。
📖 点击查看答案
Real interest rate = 5 − 7 = −2%
📝 点击查看解析
当通胀高于利率时，实际利率为负。借款人用贬值货币还债而获益，放贷人实际亏损。
Question 6 — Unexpected Inflation and Borrowers (意外通胀对借款人的影响)
Borrowers and lenders expected 3% inflation, but actual inflation was 5%. Who benefits?
借贷双方预期通胀 3%，实际为 5%。谁受益？
📖 点击查看答案
Borrowers benefit; lenders lose.
📝 点击查看解析
通胀高于预期时，债务用更不值钱的货币偿还，借款人支付的实际价值减少，放贷人受损。
Question 7 — CPI Basket Composition (CPI 商品篮子构成)
In the 2018 CPI market basket, housing is 42.2% and food 14.3%.
If housing prices increase by 10% and food by 5%, how much does CPI rise (assuming other items constant)?
2018 年 CPI 商品篮子中住房占 42.2%，食品占 14.3%。若住房涨 10%、食品涨 5%，其他不变，CPI 上升多少？
📖 点击查看答案
CPI increase = 0.422×10 + 0.143×5 = 5.635%
📝 点击查看解析
加权平均通胀率 = Σ(权重 × 各类涨幅)。
住房贡献 4.22%，食品贡献 0.715%，合计 5.635%。
Question 8 — Substitution Bias (替代偏差)
Explain why CPI tends to overstate inflation due to substitution bias.
说明为何替代偏差导致 CPI 高估通胀。
📖 点击查看答案
CPI assumes fixed quantities, ignoring consumers’ switch to cheaper goods, making it overstate price increases.
📝 点击查看解析
CPI 使用固定权重，不考虑消费者因价格变动转向更便宜商品，实际生活成本上升较慢，CPI 高估通胀。
Question 9 — Quality Bias (质量提升偏差)
Smartphones become more durable and faster, but their prices rise. How does this affect CPI?
智能手机更耐用、性能更快但价格上涨，这对 CPI 有何影响？
📖 点击查看答案
Part of the price rise reflects better quality, not inflation, but CPI may count all as inflation.
📝 点击查看解析
质量提升使价格上升部分为真实价值增加而非物价上涨，若 CPI 未能调整，通胀被高估。
Question 10 — New Product Bias (新产品偏差)
Why did the CPI underestimate consumer welfare improvements from smartphones in the 1990s?
为什么 1990 年代 CPI 未能反映智能手机对消费者福利的改善？
📖 点击查看答案
Because new products were included years after introduction, missing early price declines and quality gains.
📝 点击查看解析
CPI 每十年更新一次，新产品纳入滞后，未记录其初期降价和性能提升，导致通胀被高估、实际福利被低估。
Question 11 — Outlet Bias (销售渠道偏差)
How did the rise of online shopping affect CPI accuracy?
网购兴起对 CPI 准确性有何影响？
📖 点击查看答案
CPI overstated prices because it didn’t capture lower online and discount store prices.
📝 点击查看解析
CPI 传统取样于实体零售店，未计入电商与折扣店较低价格，导致通胀测算偏高。
Question 12 — Producer Price Index (生产者物价指数)
If the PPI increases by 8%, what likely happens to the CPI in the next period?
若 PPI 上涨 8%，CPI 下一期可能出现什么变化？
📖 点击查看答案
CPI will likely increase as higher production costs pass to consumers.
📝 点击查看解析
PPI 反映生产成本上升，企业通常转嫁成本至零售端，CPI 通常随后上升。
Question 13 — Nominal vs Real Variable (名义与实际变量)
A country’s nominal GDP grows 10% while inflation is 6%. What is the real GDP growth?
某国名义 GDP 增长 10%，通胀率 6%，求实际 GDP 增长率。
📖 点击查看答案
Real GDP growth = 10 − 6 = 4%
📝 点击查看解析
实际增长率 ≈ 名义增长率 − 通胀率。
通胀剔除后经济实际扩张约 4%。
Question 14 — Inflation Redistribution (通胀再分配)
Who loses most from unanticipated inflation?
非预期通胀中谁受损最严重？
📖 点击查看答案
Fixed-income earners and lenders.
📝 点击查看解析
固定收入者（如退休金领取者）与放贷人无法随通胀调整收入，其实际购买力下降最严重。
Question 15 — Shoe-leather Cost (皮鞋成本)
Explain why inflation increases “shoe-leather costs”.
说明通胀为何提高“皮鞋成本”。
📖 点击查看答案
People make more trips to withdraw smaller amounts of cash to avoid holding depreciating money.
📝 点击查看解析
通胀降低现金价值，人们频繁取现、减少现金余额，导致额外时间与手续费支出，形象地称为“皮鞋成本”。
Question 16 — Menu Cost (调价成本)
A restaurant reprints menus every time prices rise due to inflation. What type of cost is this?
一家餐馆每次通胀都重印菜单，这是何种成本？
📖 点击查看答案
Menu cost.
📝 点击查看解析
企业因通胀频繁修改标价所产生的额外支出即为“菜单成本”。
Question 17 — Tax Distortion (税收扭曲)
If investors are taxed on nominal interest income of 10% while inflation is 5%, what is the real after-tax return (tax rate 20%)?
若投资者名义利息 10%，通胀 5%，税率 20%，求税后实际收益。
📖 点击查看答案
After-tax nominal = 10 × (1−0.2)=8%; Real = 8 − 5 = 3%
📝 点击查看解析
税后名义收益 = 名义利率 × (1−税率) = 8%。
扣除通胀后实际收益 3%，显示通胀与税收共同削弱真实回报。
Question 18 — Anticipated Inflation Effects (预期通胀影响)
If inflation is fully anticipated at 5%, how do lenders, workers, and firms react?
若通胀完全可预期为 5%，放贷人、工人及企业会如何应对？
📖 点击查看答案
Lenders raise nominal rates by 5%; workers demand 5% wage rise; firms raise prices similarly.
📝 点击查看解析
各方会调整名义数值以抵消通胀：加息、加薪、提价。实际购买力与利润保持稳定。
Question 19 — Unanticipated Inflation Effects (非预期通胀影响)
Inflation was expected to be 2% but turned out 8%.
Explain how this affects debtors and creditors.
原预计通胀 2%，实际为 8%。说明对债务人和债权人的影响。
📖 点击查看答案
Debtors gain (repay with cheaper dollars); creditors lose (receive less valuable money).
📝 点击查看解析
通胀超出预期时，货币贬值，债务偿还的实际价值下降，借款人获益、放贷人受损。
Question 20 — Policy Implication (政策启示)
Why do central banks target low and stable inflation (e.g., 2%)?
为什么央行通常设定 2% 的低通胀目标？
📖 点击查看答案
To maintain price stability, protect real incomes, and prevent unfair redistribution from unanticipated inflation.
📝 点击查看解析
稳定低通胀能维护购买力与收入公平，防止通胀波动造成经济不确定性与财富随机再分配。