Why is the weighted rate not a simple average?

Items carry different shares of household spending, so each change must be multiplied by its weight before adding.

How does the Fisher equation differ from plain subtraction?

Subtraction is only an approximation; with high rates use (1+i)/(1+pi) minus 1.

S4 Economics Inflation, Paper 2: weighted index and real interest

2026-11-02

Ten graded items on a weighted CPI, the real interest rate, purchasing power, accelerating inflation, cost-push inflation, real returns on a loan, menu cost and shoe-leather cost.

Focus　Multiply by the weight, always deflate instead of subtracting, and separate cost-push from demand-pull.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S4 Economics: Inflation
Level	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationThe consumer price index rises from 125 to 135. Find the inflation rate.
FoundationFood (weight 30%) rises 10%, housing (50%) rises 4% and other items (20%) are unchanged. Find the weighted inflation rate.
FoundationThe nominal interest rate is 6% and inflation is 4.5%. Find the real interest rate using the Fisher approximation.
FoundationPrices rise 21% over two years. What is $1 000 worth in old prices?
IntermediateThe index goes from 100 to 108 and then to 118.8. How does inflation in the second year compare?
IntermediateA salary rises 6% while prices rise 9%. Find the change in real purchasing power.
IntermediateAn oil price shock raises transport and production costs and eventually the general price level. Which type of inflation is this?
ChallengeA loan of $50 000 charges 5% nominal interest while inflation turns out to be 8%. How much purchasing power does the lender lose in a year?
ChallengeA restaurant keeps reprinting its menu while households make more bank trips to hold less cash. Name the two costs.
Error redoError repair: a student writes that a rising CPI means every price rises. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	8%	135 minus 125 is 10, and 10 over the base 125 is 8%.
2	5%	0.3 times 10 is 3 and 0.5 times 4 is 2, giving 5%.
3	1.5%	The real rate is roughly nominal minus inflation, so 6 minus 4.5 is 1.5%.
4	About $826.45	1 000 divided by 1.21 is 826.45 in old prices.
5	10% in year two, above 8% in year one	The first year is 8%; the second is 10.8 over 108, which is 10%, so inflation accelerates.
6	About 2.75% lower	1.06 over 1.09 minus 1 is minus 0.0275, so purchasing power falls about 2.75%.
7	Cost-push inflation	Rising costs push prices up from the supply side, which is cost-push; demand growth is demand-pull.
8	About $1 388.89	The real return is 1.05 over 1.08 minus 1, about minus 2.78%, which on 50 000 is 1 388.89.
9	Menu cost for reprinting, shoe-leather cost for the extra bank trips	The cost of changing price lists is menu cost; the time and hassle of holding less cash is shoe-leather cost.
10	The index is a weighted average, so individual prices can fall	The index is a weighted average of a basket, so individual items such as electronics can fall while the index rises.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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