Unit 2: Economic Indicators and the Business Cycle

Students will look at how economic phenomena such as employment and inflation are measured.

Circular Flow and Gross Domestic Product (GDP)

Circular Flow Model

The circular flow shows how money and goods move between households and firms. Households supply factors of production to firms and receive income in return. Firms use those factors to produce goods and services that households buy with their income.
There are two core markets in the basic model. The product market is where goods and services are sold by firms to households. The factor market is where households sell labor, land, and capital services to firms.
Money flows in the direction opposite to real goods and services. Income flows from firms to households through wages, rent, interest, and profit. Spending flows from households to firms when they purchase output.
Leakages and injections connect the simple model to macro outcomes. Savings and taxes are leakages that reduce spending in the product market. Investment, government purchases, and exports are injections that add spending back into the circular flow.
In equilibrium, total spending equals total income and equals total output. This equality is the foundation for GDP accounting and for the expenditure and income approaches. A clear diagram with two loops helps students track these equalities.

What GDP Measures and What It Does Not

GDP is the market value of all final goods and services produced within a country’s borders in a given period. “Final” means the good is purchased by the end user, which avoids double counting of intermediate goods. The phrase “within a country’s borders” means production by foreign owned firms inside the country counts, while production by domestic firms abroad does not.
Use the word “market value” to capture the common money metric that adds apples and software without mixing units. Nonmarket production like household work and volunteer services is excluded, which means GDP understates total economic activity where unpaid work is large. Illegal markets and some cash transactions are also missing because they are not recorded.
GDP includes newly produced goods and services in the current period. Used goods sales are excluded because their value was counted in the year they were produced, and pure financial transactions like buying stocks do not represent current production. Government transfer payments like Social Security are also excluded since they are income redistribution, not new output.
Inventory changes are counted because producing goods that are not yet sold still represents current period production. If inventories rise, investment increases by that amount, and if inventories fall, investment decreases because goods produced earlier are being sold now. This rule keeps measured production aligned with when output is created, not when it is sold.
Diagram tip, sketch a simple circular flow with households supplying factors to firms and receiving income, then spending on goods and services. Show product market flows in one direction and factor market flows in the other so students see how income equals expenditure. Label leakages and injections like taxes, government spending, saving, and investment to connect GDP accounting to macro equilibrium.

Limitations of GDP (PIES)

$ \textbf{P:}\ $ Production that is nonmarket is not captured by GDP. Household work, caregiving, and volunteer services create real value but do not have market prices. Economies with large informal caregiving can look smaller than they truly are.

$ \textbf{I:}\ $ Illegal and informal activity is excluded or poorly measured. Underground transactions and unreported cash income do not enter official accounts. This omission can bias comparisons across places and time when informality differs.

$ \textbf{E:}\ $ Externalities and environmental costs are not netted out. Pollution and resource depletion can rise with output but are not subtracted from GDP. A higher GDP can coincide with lower well being when damages are large.

$ \textbf{S:}\ $ Social measures of well being are not in GDP. The distribution of income, leisure time, and health and safety conditions matter for welfare. GDP can rise while median living standards do not improve if gains are concentrated.

Exam tip, state the PIES letter and the concrete mechanism. Then explain how that limitation affects interpretation of growth or cross country comparisons. This structure earns full credit and keeps the answer concise and precise.

Three Approaches to GDP and Component Breakdown

The expenditure approach adds spending by sector, $ \text{GDP} = C + I + G + X_n $. Consumption $C$ is household spending on goods and services, investment $I$ is business capital, new residential construction, and inventory change, government purchases $G$ are spending on goods and services, and net exports $X_n = X - M$ adjusts for foreign trade. Use this approach when you are given spending data by category.
The income approach adds incomes earned from production, $ \text{GDP} = w + r + i + \pi $, where $w$ is wages, $r$ is rent, $i$ is interest, and $ \pi $ is profit. Small adjustments like indirect taxes and depreciation reconcile income to expenditure because of measurement differences. This approach helps connect firm costs to household income in the circular flow.
The value added approach sums the additional value created at each stage of production. For each firm compute $ \text{value added} = \text{sales} - \text{intermediate inputs} $, then add across firms. This prevents double counting when supply chains are long or when you only have industry level data.
Component interpretation matters for policy questions. A rise in $I$ usually signals future productive capacity growth, while a rise in $C$ often reflects current demand strength, and changes in $X_n$ can reflect exchange rates or foreign growth. When $G$ increases, distinguish purchases of goods and services from transfers so you do not overstate demand.
Quick check, if you are missing one component you can solve for it with algebra. For example, if you know GDP, $C$, $G$, and $X_n$, then $ I = \text{GDP} - C - G - X_n $. Always verify that signs on $X_n$ are correct since imports enter with a negative sign.

Closed Economy

A closed economy does not trade with the rest of the world. In a closed economy, exports and imports are both zero. This removes net exports from the spending identity.
The general GDP identity is $ Y = C + I + G + (X - M) $. In a closed economy, the identity simplifies to $ Y = C + I + G $. In a private closed economy without government, it reduces further to $ Y = C + I $.
Working in a closed setting isolates core spending relationships. This makes it easier to see how consumption and investment determine output in the short run. Later, the model can be opened to add trade effects.
On AP questions, read carefully to see which version is assumed. Some prompts use a private closed economy for algebraic simplicity. Others include government but still exclude trade when they say closed.
When trade is excluded, changes in domestic saving and investment take on a larger role. Without external borrowing or lending, national saving must equal domestic investment. This identity helps explain why investment responds to saving behavior.

Consumers (Households)

Households are the owners of resources in the basic model. They supply labor, land, and capital services to firms through the factor market. They use the income they earn to buy goods and services in the product market.
Households allocate income to consumption, taxes, and saving. Consumption is spending on current goods and services that delivers utility. Saving is deferred consumption that funds future investment through financial markets.
In GDP accounting, most household purchases are counted in $ C $. Purchases of new homes are not in $ C $ and instead enter investment. Used goods and financial assets are not new production and are excluded.
Household behavior also shapes labor market measures. Participation decisions affect the labor force and the unemployment calculation. These choices can make the unemployment rate move differently from job availability.
Tips for problems, identify whether a household action changes consumption or saving. A change in saving shifts available funds for investment and can influence interest rates. A shift in consumption changes current aggregate demand directly.

Firms (Producers)

Firms hire inputs to produce output and sell it in the product market. They pay wages, rent, interest, and profit to households as income. These payments sum to the income side of GDP.
Firms undertake investment when they buy new capital, build structures, or add to inventories. Investment increases productive capacity over time and is a key driver of growth. In the short run, it also changes current spending and output.
When inventories rise, measured investment increases even if sales do not. This counts production that was not yet sold as current output. When inventories fall, investment is lower because sales exceed current production.
Pricing decisions affect measured nominal GDP through the price level. Cost changes seen in producer price indexes often pass into consumer prices later. Understanding this timing helps you connect firm costs to inflation.
Problem tip, separate a firm’s purchase of a used machine from a new one. A used machine does not add to current investment since it was counted when first produced. A new machine adds to $ I $ and therefore to current GDP.

Product Market

The product market is where final goods and services are exchanged. Firms supply output to this market and households demand it. Prices and quantities here determine the value of consumption in GDP.
Government is also a buyer in the product market. Its purchases of goods and services add to $ G $ in the spending identity. Transfers do not add to product market demand since they are not purchases of output.
Net exports reflect foreign demand for domestic goods minus domestic demand for foreign goods. A positive value means foreign buyers add to demand in the product market. A negative value means imports subtract from demand for domestic output.
Shifts in the product market can come from income changes, expectations, or policy. A rise in household wealth may increase $ C $ and shift demand outward. A rise in real interest rates can reduce $ C $ and $ I $ and shift demand inward.
Exam strategy, read each transaction and ask if it is a final purchase. If yes and it is new, it contributes to current product market sales. If it is an intermediate or used good, it does not add to current GDP.

Factor Market

The factor market is where households sell resources and firms buy them. The main factor is labor, but land and capital services matter as well. Income generated here forms the basis for the income approach to GDP.
Wages are the price of labor services and are the largest share of income. Rent pays for land services and interest pays for capital. Profit is the residual income to firm owners after costs.
Unemployment is observed in this market when willing workers cannot find jobs. Movements in hiring change both employment and total income. These changes feed back into product market demand through consumption.
Minimum wages and union contracts are factor market institutions. They influence wage levels and sometimes employment outcomes. Questions may ask you to predict how changes in wage rates affect costs and prices.
Tip for diagrams, draw factor services flowing from households to firms. Draw income payments flowing back to households. Then connect income to consumption in the product market to close the loop.

Aggregate Spending: Consumer Spending and Investment Spending

Aggregate spending is the total planned expenditure on final goods and services. In a private closed setting, the focus is on $ C $ and $ I $. In a broader setting, government purchases and net exports are added as well.
Consumption $ C $ depends on disposable income and expectations. A common linear form is $ C = a + bY_d $ where $ a $ is autonomous consumption and $ b $ is the marginal propensity to consume. A higher $ b $ means each extra dollar of income leads to more spending.
Investment $ I $ is guided by expected profitability and the real interest rate. When real rates rise, some projects are not profitable and planned investment falls. When optimism about future sales increases, firms plan more investment.
Unplanned inventory change signals that actual spending differs from planned spending. If inventories rise unexpectedly, actual spending is below planned production and output may slow. If inventories fall unexpectedly, actual spending is above planned production and output may rise.
Exam tip, when asked how a shock affects GDP through spending, track $ C $ and $ I $ step by step. A cut in real interest rates raises $ I $ and often raises $ C $ for durable goods. This shifts aggregate expenditure upward and raises equilibrium output in the short run.

Aggregate Income and the Value-Added Approach

Aggregate income sums payments to factors of production. The core categories are wages, rent, interest, and profit. These payments are earned when firms produce output and sell it.
In a closed accounting system, total income equals total spending and equals total output. This equality holds because each dollar spent on a final good becomes income to someone. The circular flow diagram makes this equality visible.
The value added approach avoids double counting in long production chains. For each firm, compute $ \text{value added} = \text{sales} - \text{intermediate inputs} $. Summing value added across firms yields GDP without counting the same inputs twice.
Example, a mill sells flour to a bakery and the bakery sells bread to consumers. The mill’s value added is the price of flour minus the cost of wheat. The bakery’s value added is the price of bread minus the cost of flour, and the sum equals the final bread price.
Tip, if a question gives only sales and input costs at each stage, choose the value added method. If it gives factor payments, choose the income approach. If it gives category spending, choose the expenditure approach.

Unemployment

Measuring the Labor Market

The labor force consists of people who are employed or actively seeking work. The unemployment rate is $ u = \frac{\text{unemployed}}{\text{labor force}} \times 100\% $, and the labor force participation rate is $ \text{LFPR} = \frac{\text{labor force}}{\text{adult civilian population}} \times 100\% $. These ratios let you separate joblessness from participation changes, which often move differently.
Discouraged workers are not counted as unemployed because they are not actively looking for work. When many people stop searching, the unemployment rate can fall even though the job market is weak. Check LFPR to avoid misreading a falling unemployment rate as good news when participation is dropping.
Underemployment includes part time workers who want full time jobs and workers employed below their skill level. The headline unemployment rate does not capture this margin, which is why broader measures exist in practice. In exam questions, state clearly which measure you are using to justify your conclusion.
Worked identification, if a person has no job and looked for work in the last four weeks, they are unemployed. If they have a job, even a temporary or part time one, they are employed. If they stopped looking last month after many months of searching, they are not in the labor force for the standard measure.
Data tip, always define the population used in the denominator. AP questions usually assume the adult non institutional civilian population for LFPR and the labor force for $u$. Writing the exact formula with numbers prevents sign errors and earns credit on free response questions.

Types of Unemployment, Natural Rate, and Output Gaps

Frictional unemployment arises from normal job search and matching, seasonal unemployment is periodic, predictable, and follows the calendar, structural unemployment comes from skill or location mismatches, and cyclical unemployment reflects business cycle downturns. The natural rate of unemployment includes frictional plus structural components. When actual unemployment equals the natural rate, the economy is at potential output.
The output gap measures how far actual output deviates from potential, $ \%\text{gap} = \frac{Y - Y^{*}}{Y^{*}} \times 100\% $. A negative gap indicates a recessionary gap with cyclical unemployment above zero, and a positive gap indicates an inflationary gap. Use this sign logic to decide whether the economy needs stabilization that raises or cools demand.
Okun’s relationship links extra unemployment to output losses. A common rule for AP analysis is that a one percentage point rise in cyclical unemployment is associated with roughly a two percent negative output gap, which you can write as $ \%\text{gap} \approx -2\,(u - u^{*}) $. Use this to approximate missing values when only unemployment data are given.
Interpretation skill, distinguish changes in the natural rate from cyclical swings. When technology or education changes reduce structural mismatches, the natural rate falls, which raises potential output without immediate inflation pressure. When demand falls suddenly, cyclical unemployment rises, which creates a recessionary gap even if the natural rate is unchanged.
Graph tip, draw actual $Y$ around a rising potential $Y^{*}$ line to visualize gaps. Label the gaps with signs, then annotate likely movements in unemployment around those dates. This picture helps you explain the difference between short run fluctuations and long run growth.

Price Indices and Inflation

Building the CPI and Computing Inflation

The Consumer Price Index tracks the cost of a fixed market basket for a typical urban consumer. Compute the index as $ \text{CPI}_t = \frac{\text{cost of basket in year } t}{\text{cost of basket in base year}} \times 100 $. A base year always has an index of $100$, which makes percentage comparisons straightforward.
To find inflation between years $t-1$ and $t$, use $ \text{Inflation} = \frac{\text{CPI}_t - \text{CPI}_{t-1}}{\text{CPI}_{t-1}} \times 100\% $. Headline inflation uses the full basket, while core inflation removes food and energy to reduce short term volatility. State which measure you are using, since an answer can change if energy prices moved a lot.
Producer Price Indexes track prices for inputs that firms buy, which often move before consumer prices. A rise in PPI can foreshadow future CPI increases when costs pass through to retail prices. On AP questions, use PPI for early signals and CPI for consumer cost of living and indexing examples.
Example setup, if the base basket costs $ \$200 $ in the base year and $ \$230 $ this year, then $ \text{CPI} = 115 $. If last year’s CPI was $110$, then the inflation rate is $ \frac{115 - 110}{110} \times 100\% = 4.55\% $. Writing numbers into the formula reduces mistakes and makes your reasoning easy to grade.
Diagram tip, draw two stacked bars for the basket cost in the base and current year and label the percent change. This simple picture reinforces that the CPI is a ratio, not a sum. Add a small note that weights come from consumer expenditure surveys to connect the index to real spending patterns.

GDP Deflator versus CPI and Common Biases

The GDP deflator uses all domestically produced final goods and services, $ \text{Deflator}_t = \frac{\text{Nominal GDP}_t}{\text{Real GDP}_t} \times 100 $. The CPI uses a fixed consumer basket that can include imports. Therefore, the deflator captures price changes in investment goods and government purchases, while the CPI focuses on consumer outlays.
Because the CPI is based on a fixed basket, it can exhibit substitution bias when consumers switch toward relatively cheaper goods. New goods bias occurs when the index is slow to include new products that improve choices, and quality change bias occurs when improvements raise value that is not fully captured. These biases can cause CPI to overstate true cost of living growth.
Outlet bias occurs when consumers shift purchases to discount outlets or online stores that are sampled imperfectly. In exam answers, name at least two specific biases and explain the mechanism to earn full credit. Tie the explanation back to why measured inflation might differ from experienced inflation.
Interpretation skill, the GDP deflator is useful for converting nominal GDP to real GDP within the same year. The CPI is better for adjusting wages and benefits for cost of living, and for comparing prices across years for consumers. Choose the index that matches the question’s perspective rather than using them interchangeably.
Quick check, if nominal GDP rises but real GDP does not, the deflator must have increased. If the CPI rises faster than the deflator in a given year, imported consumer goods likely became more expensive relative to domestic investment goods. These comparisons let you infer which parts of the economy drove price changes.

Inflation, Disinflation, and Deflation

Inflation is a sustained increase in the overall price level. This reduces the purchasing power of money over time. Lenders and borrowers care about whether inflation is expected or unexpected.
Disinflation is a reduction in the rate of inflation. Prices still rise but at a slower pace than before. Disinflation often follows policy actions that reduce demand growth or ease supply pressures.
Deflation is a sustained decrease in the overall price level. Purchasing power of money rises, which can delay spending if people expect lower prices later. Persistent deflation can weaken demand and make recessions last longer.
Costs of inflation include shoe leather costs, menu costs, and unit of account costs. Unexpected inflation also redistributes wealth between borrowers and lenders. These costs guide why some contracts include indexing clauses.
Interpretation tip, always state which of the three concepts a problem is asking about. A fall in the inflation rate is disinflation and not deflation. A negative inflation rate is deflation and implies that the price level fell compared with last period.

Inflation Rate

The inflation rate measures how fast the price level changes over time. Using the CPI, compute $ \text{Inflation} = \frac{\text{CPI}_t - \text{CPI}_{t-1}}{\text{CPI}_{t-1}} \times 100\% $. Using the GDP deflator, the same formula applies with the deflator in place of the CPI.
When working with index numbers, the base year has a value of $ 100 $. Only relative changes matter for inflation calculations. You can compare any two years as long as the same index series is used for both.
Annualizing a multi period rate requires compounding. If a question gives a quarterly rate $ q $, an approximate annual rate is $ 4q $ and an exact annual rate is $ (1+q)^{4} - 1 $. State which method you used if precision matters for the answer.
When inflation is high, compare nominal and real changes to judge welfare. Real income is $ \text{Real} = \frac{\text{Nominal}}{\text{Price Index}} \times 100 $. A nominal increase below the inflation rate is a real loss.
Tip, show the fraction with both index values before computing. Label the period for $ t $ and $ t-1 $ so the grader can follow your logic. This habit prevents sign errors and earns method points.

Market Basket (for CPI)

The CPI uses a fixed market basket that represents typical urban consumer purchases. Each item has a weight based on its share of consumer spending. The cost of buying this basket each period defines the index.
The index formula is $ \text{CPI}_t = \frac{\text{Cost of Basket in } t}{\text{Cost of Basket in Base Year}} \times 100 $. The base year index is $ 100 $ by construction. A value of $ 125 $ means the basket costs $ 25\% $ more than in the base year.
Basket weights are updated periodically to reflect changing spending patterns. Between updates, substitution toward relatively cheaper goods can occur. This creates substitution bias that may overstate cost of living growth.
Quality improvements and new goods complicate measurement. If products improve in ways not fully captured, the index can overstate inflation. Delays in adding new products can also misstate the true cost of living.
Exam tip, when a prompt provides a basket with quantities and prices, compute the basket cost for each year first. Then plug those costs into the index ratio and compute the inflation rate from one year to the next. Always keep quantities fixed at the given basket when building a CPI.

Real versus Nominal Measures

Deflators, Real GDP, and Growth Rates

Deflating converts nominal values into real values by removing the effect of price level changes. The general formula is $ \text{Real} = \frac{\text{Nominal}}{\text{Price Index}} \times 100 $, where the index is in base year equals $100$ form. This is required when a question asks about changes in actual output rather than changes in prices.
Real GDP growth focuses on quantity changes, which is what business cycle analysis uses. Compute growth as $ \%\Delta \text{Real GDP} = \frac{\text{Real GDP}_t - \text{Real GDP}_{t-1}}{\text{Real GDP}_{t-1}} \times 100\% $. When you compare nominal and real growth, a large gap indicates that inflation contributed a lot to nominal increases.
Chain weighting updates weights frequently so the measure reflects current spending patterns better. In AP contexts you rarely compute chain indexes by hand, but you should know that real GDP based on chain weighting reduces substitution bias. Use the idea to explain why real GDP series can be revised when new weights are adopted.
Base year changes rescale index numbers but do not change real relationships. If the base year switches, the level of real GDP changes, but growth rates across years remain the same. Always compare percent changes rather than index levels when the base year is different.
Interpretation tip, when real GDP grows and unemployment falls, you are likely in an expansion. When real GDP falls for several quarters and unemployment rises, you are likely in a contraction. These facts connect measurement to business cycle diagnosis on multiple choice items.

Converting Wages and Prices Across Years

To compare wages across time, convert to real terms using CPI. The real wage is $ \text{Real Wage} = \frac{\text{Nominal Wage}}{\text{CPI}} \times 100 $ with the CPI in base equals $100$ form. This tells you purchasing power rather than pay in dollars.
To convert a price from Year A to Year B dollars, use $ \text{Amount in B} = \text{Amount in A} \times \frac{\text{CPI}_B}{\text{CPI}_A} $. This method is essential when a question asks whether something is cheaper today after adjusting for inflation. Always show the fraction and label both CPIs so graders see your method.
Example, if a movie ticket cost $ \$8 $ when $ \text{CPI}=120 $ and today $ \text{CPI}=300 $, the equivalent today is $ 8 \times \frac{300}{120} = \$20 $. If the actual ticket is $ \$16 $, then it is cheaper in real terms today. This conclusion depends on indexing correctly, so write each step.
Real incomes can rise even when nominal incomes are flat if prices fall. Conversely, nominal incomes can rise while real incomes fall if inflation is faster than wage growth. This is why exam questions often ask you to compute both nominal changes and real changes.
Tip, if a problem mixes CPI and the GDP deflator, choose the index that matches the item you are adjusting. Use CPI for wages and consumer goods, and use the deflator for economy wide output comparisons. Using the wrong index leads to incorrect interpretation about purchasing power.

Business Cycles

Phases, Indicators, and NBER Dating

The business cycle has expansion, peak, contraction, and trough phases. Expansions feature rising real GDP, falling unemployment, and often rising inflation later in the phase, while contractions feature falling real GDP and rising unemployment. The long run trend grows with productivity and population, while the cycle moves around that trend.
The National Bureau of Economic Research dates recessions by looking at broad and persistent declines in economic activity. The common classroom shortcut is two consecutive quarters of falling real GDP, but the official dating uses monthly series and many indicators. On AP items, if asked about the official arbiter, name the NBER and explain its broader method.
Leading indicators move before the economy, coincident indicators move with it, and lagging indicators move after it. Examples include new orders and yield spreads for leading, employment and real personal income for coincident, and unemployment duration for lagging. Use these categories to reason about where the economy is heading rather than only where it has been.
Diagram tip, draw real GDP against time with a smooth upward trend and a wavy actual path. Mark peaks and troughs and place vertical lines to label the dates. Add arrows to show how unemployment and inflation typically move in each segment to practice narrative explanations.
Interpretation skill, short expansions can still be strong if productivity is accelerating, and long expansions can still have mid cycle slowdowns. Always combine output, unemployment, and inflation evidence rather than using a single statistic. This habit prevents overreliance on one noisy indicator.

How Inflation and Unemployment Move Over the Cycle

In expansions, unemployment falls toward the natural rate and can dip below it late in the cycle. When the economy runs above potential, upward pressure on inflation often builds as demand strains capacity. This pattern helps you explain why policy makers sometimes tighten conditions during late cycle booms.
In contractions, unemployment rises above the natural rate and inflation pressure usually eases. If the contraction is sudden and deep, inflation can drop quickly, and in rare cases prices can fall. Distinguish disinflation, which is a fall in the inflation rate, from deflation, which is a fall in the price level.
Short run Phillips curve logic connects unemployment deviations from the natural rate to inflation changes. When unemployment is below the natural rate, inflation tends to accelerate, and when it is above, inflation tends to decelerate. For AP analysis, state clearly that this is a short run relationship subject to shocks.
Supply shocks can move inflation and unemployment in the same direction. A negative supply shock can raise inflation and raise unemployment, which is called stagflation. This exception explains why demand based rules are not sufficient when the problem is on the supply side.
Tip, when you are asked to narrate a cycle, start with output relative to potential, then infer unemployment relative to the natural rate, and then discuss inflation dynamics. This order keeps your reasoning consistent with the model structure. It also aligns with how many rubrics allocate points.

Data Skills and Worked Examples

Worked Example, GDP by Expenditure

Suppose consumption is $ \$600 $, investment is $ \$150 $, government purchases are $ \$250 $, exports are $ \$100 $, and imports are $ \$120 $. First compute net exports, $ X_n = X - M = 100 - 120 = -20 $. Then compute GDP, $ \text{GDP} = C + I + G + X_n = 600 + 150 + 250 - 20 = \$980 $.
Interpretation, a negative $X_n$ means the country is a net importer, which subtracts from aggregate demand in the expenditure identity. The level of $I$ still matters for future capacity because it adds to the capital stock. On a multiple choice question, watch for tricks where imports are listed as a positive number without a negative sign.
If inventories rose by $ \$10 $ within the $I$ figure, that means some production was not sold this period. This is still counted as current output because firms produced it. In contrast, selling down inventories reduces measured investment because sales exceed current production.
Check units and time periods to avoid mixing annual and quarterly values. If one component is reported at an annual rate and others are not, convert to the same frequency first. Consistent units prevent arithmetic errors that lose easy points.
Quick extension, if nominal GDP is $ \$980 $ and the deflator is $ 105 $, then real GDP is $ \frac{980}{105} \times 100 = \$933.33 $ in base year dollars. This extra step shows how to move from spending to real output. Always round sensibly and show the fraction before computing the final number.

Worked Example, CPI, Inflation, and a Real Wage

Assume the basket has two goods, four loaves of bread and two bus passes. In the base year bread is $ \$2 $ and a pass is $ \$10 $, so the basket costs $ 4 \times 2 + 2 \times 10 = \$28 $. In the current year bread is $ \$3 $ and a pass is $ \$12 $, so the basket costs $ 4 \times 3 + 2 \times 12 = \$36 $.
Compute the index, $ \text{CPI} = \frac{36}{28} \times 100 = 128.57 $. If last year’s CPI was $120$, the inflation rate is $ \frac{128.57 - 120}{120} \times 100\% = 7.14\% $. State both the index level and the rate so the reader sees the level and the change.
Suppose a worker earned $ \$20 $ per hour last year and $ \$21 $ now. The real wage last year in base dollars was $ \frac{20}{120} \times 100 = 16.67 $, and the real wage now is $ \frac{21}{128.57} \times 100 = 16.33 $. Real purchasing power fell slightly because prices rose faster than nominal pay.
Interpretation, nominal raises do not guarantee real gains, which is why contracts sometimes include cost of living adjustments. If a contract indexed pay to the CPI at last year’s level, the raise would need to at least match $7.14\%$ to keep purchasing power constant. This example shows how indexing protects real incomes.
Tip, when a problem asks whether someone is better off, convert to real terms and compare. If you only compare nominal numbers, you can reach the wrong conclusion when inflation is high. Always write the real wage formula to guide your steps, $ \text{Real Wage} = \frac{\text{Nominal Wage}}{\text{CPI}} \times 100 $.