Money, price indices and purchasing power

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

2. Starting point

A monetary price is an amount per unit, while a quantity is a number of units. Multiplying the two gives expenditure on that item. Prices and budgets must use compatible units.

3. Words for this lesson

4. Money performs several related functions

Money can serve as a medium of exchange, a unit of account and a store of value. As a medium of exchange, it helps people make payments without arranging a direct exchange of exactly the goods each side wants. As a unit of account, it supplies a common language for prices and records. As a store of value, it can carry purchasing power from one time to another.

These functions are distinct. A shop can quote prices in a monetary unit, receive payment and record a balance. The same unit connects the actions, but quoting a price is not itself a payment and holding a balance is not the same as spending it. Clear examples identify which function is being illustrated rather than assuming every mention of money answers the same question.

Money's usefulness depends partly on shared acceptance and institutions. A token accepted only for one classroom activity has a narrower role than a widely accepted monetary system. The lesson uses fictional tokens for calculations so that the arithmetic is independent of current exchange rates or laws. It does not claim that every token, voucher or valuable object is money in every setting.

Avoid a simplified historical story in which all societies first used barter and then followed one identical path to money. Monetary arrangements have varied across places and times. We can explain how a medium of exchange works without asserting an unsupported universal history. The economic function is the focus of this lesson; historical claims require their own evidence.

Term	What it means
Medium of exchange	Something widely accepted in payment for goods, services or obligations.
Unit of account	A common unit for quoting prices and keeping monetary records.
Store of value	A way to carry purchasing power across time, although its real value may change.
Price index	A measure comparing a defined set of prices with a base period under a stated method.
Inflation	An increase in a broad price level over a period, rather than merely one relative price rising.
Purchasing power	The goods and services an amount of money can obtain at the relevant prices.

Another way: A payment method is not unlimited purchasing power

People can make monetary payments in different ways. Physical currency can be handed over, while a bank account can be used through a transfer or payment instruction. A card or application is a method for initiating a payment; it is not automatically a new source of resources. The underlying arrangement determines whether a balance is reduced or a debt is created.

For example, a payment from an existing account balance reduces the payer's claim and increases another account or transfers funds through the system. A credit arrangement can allow payment now while creating an obligation to repay under stated terms. These are different accounts. The next lesson examines banks and settlement more closely, while later lessons calculate borrowing costs.

Do not count a payment instrument and its underlying balance as two separate pots of spending power. If a card accesses a ten-token balance, the person does not have ten tokens in the account plus another ten merely because the card exists. Similarly, a receipt confirms a transaction; it is not normally another payment available to spend.

These distinctions prevent money arithmetic from drifting away from real constraints. A faster payment method can reduce time or inconvenience, but it does not by itself create additional goods. A larger nominal balance may allow more purchases at unchanged prices, yet the actual purchasing power depends on the prices and availability of the things the person wants to obtain.

Another way: One price change differs from a broad price-level change

Prices can change relative to one another. If notebook prices rise while other prices stay fixed, notebooks become more expensive relative to those other goods. This might reflect a supply disruption or changed demand in that market. It is not sufficient on its own to establish inflation across a broad range of goods and services.

Inflation describes an increase in a broad price level over a period. A price index combines information about a defined set of prices using a stated method. The result depends on what is included and how items are weighted. A classroom basket can illustrate the calculation, but a two-item basket is not a claim to measure an entire economy's inflation accurately.

A falling inflation rate does not necessarily mean prices are falling. If a broad price index rises from one hundred to one hundred ten, then to one hundred fifteen, prices rose in both intervals. The second increase is smaller relative to its starting level. Slower inflation is different from a decline in the price level, which would require the index itself to fall.

The period matters. A monthly percentage and an annual percentage are not interchangeable. Nor should percentage changes simply be added across successive periods when exact compounding is needed. This lesson uses one specified interval at a time. Later work will examine more detailed measures and the distinction between nominal and real economic quantities.

Another way: Build a fixed-basket price index

A fixed-basket index compares the cost of the same quantities in two periods. First choose the basket and calculate its cost using base-period prices. Then price those same quantities using comparison-period prices. Divide the comparison cost by the base cost and multiply by one hundred. The base-period index is one hundred by construction.

Suppose the basket contains two notebooks and three pencils. Base prices are four tokens per notebook and two per pencil. Base cost is two times four plus three times two, or fourteen. If later prices are five and three, the same basket costs ten plus nine, or nineteen. The index is nineteen divided by fourteen times one hundred. The fraction can be kept exact unless a rounding rule is requested.

Keeping quantities fixed isolates the effect of the included price changes on that basket's cost. If consumers buy fewer notebooks after their price rises, their actual spending basket changes. That behavior is important, but substituting new quantities into one side of the fixed-basket calculation would answer a different question. State the index method before comparing results.

Weights matter because items purchased in larger quantities contribute more to the basket cost. Averaging the two posted prices without regard to quantities would not reproduce the expenditure on the defined basket. The calculation must preserve both the units and the basket composition. In the practice cases, base and comparison costs are chosen to make the requested index and percentage change exact.

Another way: Translate a nominal amount into basket purchasing power

A nominal amount is measured in monetary units. Its purchasing power depends on prices. If a complete basket costs ten tokens, a twenty-token budget buys two such baskets. If the basket later costs twelve, the same budget buys twenty divided by twelve baskets, assuming the model permits fractional baskets. With indivisible baskets, the maximum whole number would instead be one.

Always check divisibility. A measure of purchasing power can use fractional basket equivalents as an analytical comparison, even when a household cannot literally buy part of every item. A shopping feasibility question about whole packages needs integer quantities and possibly leftover money. The prompt should say which interpretation is intended.

Nominal income growth can coexist with reduced purchasing power. If income rises by ten percent while the relevant basket cost rises by twenty percent, the ratio of income to basket cost falls. Subtracting the rates gives an approximation to the real change, but the exact proportional comparison divides the new nominal factor by the new price factor. This lesson emphasizes the direct budget-divided-by-cost method.

Different households buy different baskets. A common index can be useful for a broad comparison without matching every person's experience. Someone spending more on an item with a large price rise may face a different change in their own basket cost. The index's scope should therefore be stated rather than presenting one average as an exact description of everyone's situation.

Another way: Interpret an index with its limitations visible

A price index is a measurement tool with assumptions, not a complete description of living standards. Quality changes, new products, substitutions and differences in access can affect interpretation. A fixed basket deliberately holds quantities constant, which makes the arithmetic transparent but can miss changes in what people actually choose or can obtain.

The base year is a reference point. If the index is one hundred twenty, the defined basket costs twenty percent more than in the base period under this method. It does not mean every individual price rose twenty percent. Some may have risen more, some less and some fallen. The aggregate result combines their weighted effects.

When comparing two non-base index values, calculate the percentage change relative to the earlier index. A rise from one hundred twenty to one hundred thirty-two is ten percent, because the increase of twelve is divided by one hundred twenty. It is not twelve percent merely because the index rose twelve points. Index points and percentage changes are different measurements.

An effective answer gives the basket, periods, calculation and bounded interpretation. 'This fixed basket costs twenty percent more than in the base period' is supported by an index of one hundred twenty. 'Everyone is twenty percent worse off' is not: incomes, other resources, different baskets and many nonmonetary conditions also matter. Precise measurement supports better reasoning by making clear what the number does and does not represent.

5. Comparing the cost of an activity basket

A fictional activity group uses the same supply basket each month: four notebooks and six pencils. In the base month, notebooks cost three tokens and pencils two, so the basket costs twelve plus twelve, or twenty-four. In the comparison month, notebooks cost six and pencils two, so the basket costs twenty-four plus twelve, or thirty-six.

The fixed-basket index is thirty-six divided by twenty-four times one hundred, or one hundred fifty. The basket cost has risen fifty percent from the base month. This does not mean every price rose fifty percent: notebook prices doubled while pencil prices stayed unchanged. The basket weights combine those different changes into one expenditure comparison.

The group has a budget of seventy-two tokens in each month. That buys three complete baskets in the base month and two in the comparison month. The nominal budget is unchanged, but its purchasing power over this particular basket has fallen. Because both divisions are exact, no issue of fractional baskets arises in this case.

The group might respond by reusing notebooks, changing the activity or obtaining supplies through another arrangement. Those are meaningful choices, but they would change the basket or its acquisition conditions. The fixed-basket calculation remains a comparison of the original quantities at the two sets of prices. It is a useful planning input, not a complete measure of the group's welfare or a forecast of future prices. Naming that boundary keeps a precise index from becoming a broader unsupported claim.

6. A tempting mistake

An index-point increase is not always the same percentage increase, and slower inflation is not necessarily falling prices. A fixed basket measures its own price change, not every person's complete living standard.

7. Read money's functions

8. Calculate a basket index

9. Compare purchasing power

10. Complete an index comparison

11. Guided practice

A fixed basket contains 2 units of A and 2 of B. Base prices are A=3, B=2 tokens. New prices are A=4, B=2. A budget is 36 tokens. Compute base basket cost, new basket cost, the new index (base=100), and whole new-price baskets affordable. No other costs apply.

12. Guided practice

A fixed basket costs twenty in the base period and twenty-five now. Complete the index, then interpret its difference from the base.

13. Guided practice

14. Practice

A fixed basket contains 2 units of A and 4 of B. Base prices are A=4, B=3 tokens. New prices are A=2, B=3. A budget is 48 tokens. Compute base basket cost, new basket cost, the new index (base=100), and whole new-price baskets affordable. No other costs apply.

15. Practice

A fixed basket contains 3 units of A and 2 of B. Base prices are A=2, B=3 tokens. New prices are A=4, B=0. A budget is 36 tokens. Compute base basket cost, new basket cost, the new index (base=100), and whole new-price baskets affordable. No other costs apply.

16. Somewhere new

A fixed basket contains 4 units of A and 6 of B. Base prices are A=3, B=2 tokens. New prices are A=6, B=2. A budget is 72 tokens. Compute base basket cost, new basket cost, the new index (base=100), and whole new-price baskets affordable. No other costs apply.

17. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

18. Test question

A fixed basket contains 2 units of A and 3 of B. Base prices are A=3, B=2 tokens. New prices are A=6, B=2. A budget is 54 tokens. Compute base basket cost, new basket cost, the new index (base=100), and whole new-price baskets affordable. No other costs apply.

19. What you can do now

Explain how to calculate a fixed-basket price index and interpret purchasing power. Show a fresh example and check its result.

	Your result
Base basket cost
New basket cost
New price index
New-price baskets affordable

	A relative price change alone	Inflation for that broad measure and period	A ten-percent increase, or twelve index points
One notebook's price rises while other prices are unchanged
A defined broad price index rises during the year
An index rises from 120 to 132

	Your result
Base basket cost
New basket cost
New price index
New-price baskets affordable

	Your result
Base basket cost
New basket cost
New price index
New-price baskets affordable