# Macroeconomic models: close the equations before using a multiplier — Study worksheet

[Study guides](https://unireadinglist.com/guides/macroeconomic-models/)

[Course topic: Intermediate Macroeconomics](https://unireadinglist.com/subjects/economics/#course-intermediate-macroeconomics)

Sources checked: 2026-11-04

Study route and exercise: University Reading List editorial project.

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 · 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.

Your notes:

________________________________

ISBN: 9781647922481

[Official free reading](https://books.core-econ.org/the-economy/macroeconomics/)

[Book record and access options](https://unireadinglist.com/subjects/economics/the-economy-2-0-macroeconomics/)

### Macroeconomics

N. Gregory Mankiw · 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.

Your notes:

________________________________

[Book record and access options](https://unireadinglist.com/subjects/economics/macroeconomics-mankiw/)

### Macroeconomics: Institutions, Instability, and Inequality

Wendy Carlin; David Soskice · 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.

Your notes:

________________________________

ISBN: 9780198838661

[Book record and access options](https://unireadinglist.com/subjects/economics/macroeconomics-carlin-soskice/)

## Check your preparation

### Stock or flow?

Your notes:

________________________________

### How does the model close?

Your notes:

________________________________

### What stays constant in a comparison?

Your notes:

________________________________

## A six-step study plan

- [ ] 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.

Your notes:

________________________________

- [ ] 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.

Your notes:

________________________________

- [ ] 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.

Your notes:

________________________________

- [ ] 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.

Your notes:

________________________________

- [ ] 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.

Your notes:

________________________________

- [ ] 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.

Your notes:

________________________________

## 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.

Your notes:

________________________________

## 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.

Your notes:

________________________________

## 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.

## Answer and interpretation

### 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.

### Original economy: a spending flow and a debt stock

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.

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

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.

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.

## Sources and edition checks

- [CORE: free macroeconomics volume](https://books.core-econ.org/the-economy/macroeconomics/)
  The final 2.0 volume supplies the aggregate-demand route; earlier project plans are not the current contents.

- [CORE: version, year and permissions](https://books.core-econ.org/the-economy/macroeconomics/0-2-copyright.html)
  The 2026 version and online reading permissions are distinguished from the separate print identifier.

- [Hackett: final ten-unit contents and print identity](https://hackettpublishing.com/economics/the-economy-2-0-macroeconomics)
  The final ten-unit contents verify units 3–5 and the later financial-sector extension.

- [Macmillan: Mankiw twelfth edition, ©2025](https://www.macmillanlearning.com/college/us/product/Macroeconomics/p/1319473474)
  The 2025 twelfth-edition contents anchor the time-horizon comparison and debt reading.

- [UCL: Carlin and Soskice 2024 book and model scope](https://www.ucl.ac.uk/social-historical-sciences/news/2024/jan/professor-wendy-carlin-publishes-new-macroeconomics-book)
  The authors’ institutional announcement supports the three-equation, institutions and inequality comparison. The numerical economy is original.

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

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