Uni Reading List
Study guides /

Macroeconomic models: close the equations before using a multiplier

A multiplier is a conclusion of a model, not a number attached permanently to a policy. This route separates an accounting identity, a behavioral equation and the conditions that make their joint solution meaningful. Choose a spine by the question your course asks: evidence and institutions, a sequence of time-horizon models, or a policy-rule framework.

Course topic: Intermediate Macroeconomics

Study route and exercise: University Reading List editorial project. How we curate · Sources checked:

Download blank worksheet (Markdown) ↓
On this page

Scope and responsibility

For introductory-to-intermediate macroeconomics after algebra, graph reading and national-income concepts. The original classroom economy below has fixed prices, spare productive capacity, no trade, no interest, fixed investment and a specified consumption rule. Its tokens and parameters are invented; none estimates a real fiscal effect or recommends a policy.

Choose your starting point

I want a free model-and-evidence starting point

Use CORE 2.0, selecting aggregate demand before policy extensions. Write down each behavioral assumption rather than treating a graph as self-explanatory.

My course follows separate long- and short-run models

Use Mankiw’s 2025 twelfth edition and label the time horizon whenever an equation changes. Compare the goods-market exercise with, rather than equating it to, the full IS–LM framework.

I need institutions and policy rules in the same framework

Use Carlin and Soskice after introductory macro. Their three-equation approach adds policy and inflation interactions absent from the fixed-price packet here.

Compare the three books

The Economy 2.0: Macroeconomics

The CORE Econ Team · Edition: 2.0 · 2026

Free evidence-and-model spine

Choose it when
You need an accessible path from economic problems to a model and its limitations.
Use another route when
You need a graduate dynamic-optimization text or a universal numerical multiplier.
Selected reading
Version 2.0.0: unit 3 on aggregate demand and the multiplier; units 4–5 for inflation and policy.
Limits and trade-offs
The 2026 print identity is ISBN 9781647922481; the free online volume has noncommercial/no-derivatives terms. Free reading does not guarantee access to every instructor assessment.

Try before choosing

Separate Y=C+I+G from the consumption equation in the original packet. Label each as identity or stipulated behavior.

Check your work: The identity balances realized categories; it alone cannot predict how C or output responds to G.

Official free reading ↗

Book record and access options →

Macroeconomics

N. Gregory Mankiw · Edition: 12 (2025) · 2025

Time-horizon comparison spine

Choose it when
Your course compares income determination, growth, business cycles and debt using distinct models.
Use another route when
You want to apply one chapter’s closure unchanged to every horizon or edition.
Selected reading
2025 twelfth edition: chapters 3–4 for income, 12–14 for fluctuations and IS–LM, 19 for debt; verify against this edition’s contents.
Limits and trade-offs
The selected entry concerns the 2025 text. Later Digital Update packages and electronic-access identifiers need not identify that same object; instructor solutions are restricted.

Try before choosing

Make a table listing what is fixed and what adjusts in the short-run packet and a long-run model from your reading.

Check your work: Explain why assuming fixed output instead of spare capacity invalidates the same numerical demand prediction.

Book record and access options →

Macroeconomics: Institutions, Instability, and Inequality

Wendy Carlin; David Soskice · Edition: 2 · 2024

Institutions-and-policy framework

Choose it when
You are ready to connect output, inflation and monetary policy with financial institutions and distribution.
Use another route when
You still need introductory national-income vocabulary or expect a single fixed-price equation to represent its whole framework.
Selected reading
2024 second edition: select the three-equation model and financial-system/inequality discussions by title, following your syllabus.
Limits and trade-offs
The compact framework is richer than the packet below but needs more preparation. Digital simulators and activities depend on the format; no unverified chapter numbers are assigned.

Try before choosing

Draw arrows from an output change to inflation and a policy response, then mark those channels as excluded from the packet.

Check your work: A channel omitted for a classroom calculation is not evidence that it is absent in a real economy.

Book record and access options →

Check your preparation

Stock or flow?

Output, consumption, taxes and spending are measured over a period. Debt is measured at a date. A deficit changes debt under a stated financing rule; the two are not interchangeable levels.

How does the model close?

Specify consumption behavior and the treatment of taxes, investment, prices, trade and supply. An accounting identity without those choices leaves the response undetermined.

What stays constant in a comparison?

Each scenario below starts from opening debt 100 and spans one period. They are alternatives, not successive years; all token amounts share the same fixed-price unit.

A six-step study plan

These are your own study marks, not an assessment. They are not sent to this site.

  1. Label the equations

    Selected reading: CORE unit 3 or your spine’s income discussion.

    What to do: Make an identity/behavior/assumption table for C, T, I, G and Y.

    Check your work: Do not call an assumed propensity an observed causal estimate.

  2. Solve the baseline

    Selected reading: The same model discussion.

    What to do: Substitute the tax and consumption rules into goods-market balance and solve Y.

    Check your work: Check the solution by independently recomputing C+I+G.

  3. Reconcile saving

    Selected reading: Income accounting in the selected spine.

    What to do: Compute private saving Y−T−C and public saving T−G.

    Check your work: Their sum equals investment under the stipulated closed-economy accounting.

  4. Connect flow to stock

    Selected reading: Mankiw debt discussion or CORE financial-sector unit.

    What to do: Use ending debt = opening debt + G−T under the zero-interest financing rule.

    Check your work: A negative public balance is a positive addition to debt, not the debt level itself.

  5. Change a behavioral margin

    Selected reading: The follow-up and selected tax/multiplier discussion.

    What to do: Replace lump-sum tax with the stated proportional rule and resolve both spending scenarios.

    Check your work: The consumption slope with respect to Y changes; copying the old multiplier is invalid.

  6. Write a bounded interpretation

    Selected reading: CORE model applications or Carlin/Soskice policy framework.

    What to do: Report the comparison and three excluded adjustment channels.

    Check your work: Fixed prices, spare capacity and fixed investment are assumptions, not empirical findings.

Worked exercise

Original economy: a spending flow and a debt stock

A fictional closed economy has C=20+0.75(Y−T), T=20, I=25 and G=30. Solve output, consumption, private/public saving and ending government debt. Then compare G=38, holding the other rules fixed. Each alternative begins with debt 100.

Assumptions

All flows cover one period in fixed-price tokens. Output adjusts to planned expenditure with spare capacity. No trade, interest, inflation, transfers, valuation changes or other debt financing exists. Debt follows B_end=100+G−T. This is a complete invented teaching closure.

  1. Substitution gives Y=20+0.75(Y−20)+25+30=60+0.75 Y, so Y=240. Consumption is 185, and 185+25+30=240.
  2. Private saving is 240−20−185=35; public saving is 20−30=−10. National saving 25 equals I. Ending debt is 100+30−20=110.
  3. At G=38, Y=68+0.75 Y gives 272; C=209, private saving=43 and public saving=−18. They still sum to 25. Ending debt is 118.
  4. The spending change 8 produces output change 32, multiplier 4=1/(1−0.75), under these assumptions. Output is a period flow; 118 is a date stock, so their levels cannot be substituted for one another.

Answer and interpretation

Baseline: Y = 240, C = 185, private saving 35, public saving−10, ending debt 110. Higher G: Y = 272, C = 209, private saving 43, public saving−18, debt 118.

Test the result

Recompute both goods-market sums and both saving identities. If output were supply-constrained or investment responded, the packet would require a different closure.

Change an assumption

Changed tax rule: the marginal leakage changes the multiplier

Replace only the tax rule by T=20+0.20 Y. Keep C=20+0.75(Y−T), I=25, all other assumptions and the two alternative G values 30 and 38. Each alternative again begins with debt 100. Recalculate the same quantities.

  1. Now C=20+0.75(0.80 Y−20)=5+0.60 Y. At G=30, Y=60+0.60 Y yields 150; T=50 and C=95. Private saving=5, public saving=20, total 25; ending debt=80.
  2. At G=38, Y=68+0.60 Y yields 170; T=54, C=107, private saving=9, public saving=16, total 25; ending debt=84.
  3. The output response is 20 for spending 8, multiplier 2.5=1/(1−0.60). Taxes rise by 4 between these alternatives, so debt rises by only 4, from 80 to 84. These are separate one-period scenarios, not a path beginning from the previous ending debt.

Answer and interpretation

The proportional-tax scenarios give Y = 150/170 and ending debt 80/84. Their multiplier 2.5 differs from 4 because an extra unit of Y adds only 0.60 to consumption.

Test the result

Check 95+25+30=150 and 107+25+38=170. Public surpluses reduce debt under the stated rule; no conclusion about an actual government’s financing follows.

Common mistakes

Identity treated as a behavioral law

Y=C+I+G does not specify how spending or output responds.

Stock confused with flow

A one-period deficit and a date’s outstanding debt are different quantities.

Model result presented as a policy estimate

The multiplier changes with taxes, imports, supply, prices and financial responses excluded here.

Before moving on

  • I can distinguish identity, behavioral equation and closure.
  • I can reconcile all spending, saving and debt calculations.
  • I can explain why the tax change alters the multiplier and what the model leaves unresolved.

Sources and edition checks

Sources checked:

These are proposed study activities, not official course assignments or a claim that every book has been read cover to cover.

How we curate →