# Comparative Advantage Practice: Input and Output Tables

*2026-10-27*

Dana needs 4 hours to make a shelf. Rui needs 12. Dana also makes stools faster, yet Rui has the comparative advantage in stools. To find it, compare what each producer gives up to make one more stool.

An **input table** lists resources needed per unit. An **output table** lists quantities possible with a fixed resource budget. The opportunity costs stay the same when you convert between them, but the division changes. The fictional workshop below shows both formats, a feasible trade, and seven comparative advantage practice questions with explained answers.

![A potter offers one ceramic bowl while a woodcarver offers three wooden spoons in a shared courtyard](https://czaixyl0esghkd4s.public.blob.vercel-storage.com/marketing/dfc0ea8f1803f596ff54fb8e4e299b99b775d655414d96f8a164dd5ad0260e7d.webp)

## Start with the unit the table gives you

**Absolute advantage** compares productivity: who needs fewer resources per unit, or produces more with the same resources? **Comparative advantage** compares opportunity costs: who gives up less of the other good? [OpenStax introduces both concepts](https://openstax.org/books/principles-economics-3e/pages/33-1-absolute-and-comparative-advantage).

For this worksheet, labor is the only scarce production input. Each producer can move labor between two goods, and hours per unit stay constant. Goods of the same kind have the same quality. Ignore transport, trading, and setup costs; allow fractional quantities when interpreting rates. These are constant-opportunity-cost teaching problems, not measurements of real workshops.

Suppose you want the opportunity cost of **one shelf, measured in stools**:

| Table format | What the entries mean | Calculation |
| --- | --- | --- |
| Input | Hours needed per unit | `(hours/shelf) ÷ (hours/stool)` |
| Output | Maximum quantities of either good from the same labor budget | `maximum stools ÷ maximum shelves` |

Both calculations must produce **stools per shelf**. Find each producer's opportunity cost within that producer's row, then compare the answers. Dividing Dana's hours by Rui's hours compares producers; it doesn't tell you how many stools either gives up for a shelf.

## One workshop model in both formats

Here is the **comparative advantage input table**. Fewer hours per unit means greater productivity.

| Producer | Hours per stool | Hours per shelf |
| --- | --- | --- |
| Dana | 2 | 4 |
| Rui | 3 | 12 |

Dana has the absolute advantage in both goods: `2 < 3` hours per stool and `4 < 12` hours per shelf.

To make a shelf, Dana spends 4 hours that could instead produce `4 ÷ 2 = 2 stools`. Rui spends 12 hours that could instead produce `12 ÷ 3 = 4 stools`. Keep the units in the calculation:

```text
Dana: (4 hours/shelf) ÷ (2 hours/stool) = 2 stools/shelf
Rui: (12 hours/shelf) ÷ (3 hours/stool) = 4 stools/shelf
```

Dana gives up fewer stools per shelf, so Dana has comparative advantage in shelves. Reverse each producer's ratio to find the cost of a stool:

| Producer | Opportunity cost of 1 shelf | Opportunity cost of 1 stool |
| --- | --- | --- |
| Dana | 2 stools | 1/2 shelf |
| Rui | 4 stools | 1/4 shelf |

Rui gives up only `1/4 shelf` per stool, compared with Dana's `1/2 shelf`, so Rui has comparative advantage in stools. Being slower at both tasks doesn't prevent Rui from having the lower opportunity cost in one. [OpenStax explains this absolute-advantage-in-both-goods case](https://openstax.org/books/principles-economics-3e/pages/33-2-what-happens-when-a-country-has-an-absolute-advantage-in-all-goods).

### Convert the input table to an output table

Give each producer **24 labor-hours**. Divide the budget by hours per unit:

| Producer | Maximum stools in 24 labor-hours | OR maximum shelves in 24 labor-hours |
| --- | --- | --- |
| Dana | `24 ÷ 2 = 12` | `24 ÷ 4 = 6` |
| Rui | `24 ÷ 3 = 8` | `24 ÷ 12 = 2` |

These entries are **alternative maxima**. Dana can make 12 stools **or** 6 shelves. Making both listed quantities would take 48 hours. Any mixed production plan must share the 24-hour budget.

Calculate the opportunity cost of a shelf from this **output table**:

```text
Dana: 12 stools ÷ 6 shelves = 2 stools/shelf
Rui: 8 stools ÷ 2 shelves = 4 stools/shelf
```

The answers match the input calculations. Within each row, the labor budget cancels in the output ratio. Changing that budget changes the maxima but leaves opportunity costs unchanged, provided productivity stays constant.

Read the column headings before dividing. With **hours per unit**, put the target good's input on top. With **alternative maximum outputs**, put the other good's output on top. Carry the units to check which question you answered.

## Check the terms of trade in each producer's hours

Suppose Dana gives Rui **1 shelf for 3 stools**. The terms of trade are `3 stools per shelf`.

| Producer | Produces and gives away | Receives | Hours needed to make the received goods directly | Labor-cost difference |
| --- | --- | --- | --- | --- |
| Dana | 1 shelf, costing 4 hours | 3 stools | `3 × 2 = 6 hours` | Saves 2 hours |
| Rui | 3 stools, costing 9 hours | 1 shelf | `1 × 12 = 12 hours` | Saves 3 hours |

Each can acquire the received goods through this exchange using fewer of their own labor-hours than direct production would require. The savings compare two ways of obtaining the same goods. They aren't measured reductions in anyone's working time or, by themselves, proof that either person prefers a particular consumption bundle.

Dana could make 2 stools in the time spent making the exported shelf, so Dana needs **more than 2 stools** for a strict resource-cost benefit. Rui would give up 4 stools to make a shelf directly, so Rui needs to pay **fewer than 4 stools** for a strict benefit:

```text
2 < stools paid per shelf < 4
```

That is the strict mutually advantageous range for this exchange direction under our assumptions. [Khan Academy's lesson summary](https://www.khanacademy.org/economics-finance-domain/macroeconomics/macro-basic-economics-concepts/a/lesson-summary-comparative-advantage-and-gains-from-trade) also explains the trade condition through the cost of importing a good compared with producing it domestically.

At **2 stools per shelf**, Dana is indifferent on resource cost and Rui benefits. At **4 stools per shelf**, Rui is indifferent and Dana benefits. Include an endpoint only if the question allows one producer to be indifferent rather than requiring both to gain strictly.

### A favorable rate still needs a feasible plan

An exchange rate doesn't establish how many goods are available or how many each person wants. Here is one plan that fits both 24-hour budgets:

| Producer | Original production, kept without trade | Revised production, before trade | Holdings after exchanging 1 shelf for 3 stools |
| --- | --- | --- | --- |
| Dana | 6 stools and 3 shelves | 4 stools and 4 shelves | 7 stools and 3 shelves |
| Rui | 4 stools and 1 shelf | 8 stools and 0 shelves | 5 stools and 1 shelf |

Dana's original plan uses `6 × 2 + 3 × 4 = 24 hours`; the revised plan uses `4 × 2 + 4 × 4 = 24`. Rui's original plan uses `4 × 3 + 1 × 12 = 24 hours`; the revised plan uses `8 × 3 = 24`.

The exchange then leaves each person with **one extra stool and the same number of shelves**. Across the workshop, stools rise from 10 to 12 and shelves stay at 4; trade distributes the revised output. The larger bundles are feasible. Whether each person prefers the new bundle depends on whether they want the extra stool.

Dana still produces both goods. Comparative advantage doesn't require prescribing full specialization for both producers: the production mix and trade quantity also depend on demand, capacity, and any costs the model excludes.

## Seven comparative advantage practice questions

Use the assumptions above and write units beside every opportunity cost. Try the questions before reading the explained answers below. All numbers are fictional.

### 1. Input table: bowls and mugs

| Producer | Hours per bowl | Hours per mug |
| --- | --- | --- |
| Mira | 3 | 6 |
| Noah | 4 | 5 |

Find each producer's opportunity cost of a mug and of a bowl. Identify absolute and comparative advantage for each good.

### 2. Output table: posters and signs

Each producer has the **same 12-hour budget**.

| Producer | Maximum posters | OR maximum signs |
| --- | --- | --- |
| Ana | 36 | 12 |
| Ben | 24 | 16 |

Find both opportunity costs for each producer. Identify absolute and comparative advantage for each good.

### 3. Change the labor budget

Convert Dana and Rui's original input table to maximum outputs for **36 labor-hours each**. Recalculate the opportunity cost of a shelf. Has either comparative advantage changed?

### 4. Test the endpoints

Dana exports shelves to Rui. Judge these payments for **one shelf**: 1, 2, 3, 4, and 5 stools. At each rate, does each producer gain, lose, or remain indifferent on resource cost?

### 5. Read a reciprocal rate

Someone offers Dana and Rui **2/5 shelf per stool**. Dana would export shelves and Rui stools. Is the rate strictly inside their mutually advantageous range? Check the whole-number transaction of **2 shelves for 5 stools** in each producer's hours.

### 6. Equal opportunity costs

| Producer | Hours per notebook | Hours per folder |
| --- | --- | --- |
| Elin | 2 | 6 |
| Sol | 4 | 12 |

Who has absolute advantage? Who has comparative advantage? Is there a rate of notebooks per folder that strictly benefits both through specialization and exchange in this model?

### 7. Output tables with unequal budgets

| Producer | Labor budget | Maximum tiles | OR maximum bowls |
| --- | --- | --- | --- |
| Tessa | 60 hours | 30 | 10 |
| Omar | 20 hours | 20 | 10 |

Could the raw output maxima, without the budgets, establish per-hour absolute advantage? Use the budgets to compare productivity, then find comparative advantage from each row's opportunity costs.

## Answers with the comparisons shown

### 1. Mira has comparative advantage in bowls; Noah in mugs

Mira's mug costs `6 ÷ 3 = 2 bowls`; her bowl costs `3 ÷ 6 = 1/2 mug`. Noah's mug costs `5 ÷ 4 = 5/4 bowls`; his bowl costs `4 ÷ 5 = 4/5 mug`.

Compare matching units: Noah's `5/4 bowls per mug` is below Mira's `2`; Mira's `1/2 mug per bowl` is below Noah's `4/5`. Mira also has absolute advantage in bowls, using 3 rather than 4 hours. Noah has absolute advantage in mugs, using 5 rather than 6 hours.

### 2. Ana has both advantages in posters; Ben has both in signs

Ana's sign costs `36 ÷ 12 = 3 posters`; her poster costs `12 ÷ 36 = 1/3 sign`. Ben's sign costs `24 ÷ 16 = 3/2 posters`; his poster costs `16 ÷ 24 = 2/3 sign`.

Ben gives up fewer posters per sign, while Ana gives up fewer signs per poster. Equal labor budgets also let you compare the output maxima directly for absolute advantage: Ana's 36 posters exceed Ben's 24, and Ben's 16 signs exceed Ana's 12.

### 3. The outputs change; the opportunity costs don't

Dana can make **18 stools or 9 shelves**. Rui can make **12 stools or 3 shelves**. Divide 36 by each hours-per-unit figure to get those maxima.

The opportunity cost of a shelf remains `18 ÷ 9 = 2 stools` for Dana and `12 ÷ 3 = 4 stools` for Rui. Dana keeps comparative advantage in shelves; Rui keeps it in stools. Only the labor budget changed.

### 4. Both gain strictly only at 3 among the listed rates

Dana compares the payment with 2 stools; Rui compares it with 4 stools. These are resource-cost comparisons for Dana exporting shelves:

| Stools Rui pays for 1 shelf | Dana | Rui |
| --- | --- | --- |
| 1 | Loses | Gains |
| 2 | Indifferent | Gains |
| 3 | Gains | Gains |
| 4 | Gains | Indifferent |
| 5 | Gains | Loses |

### 5. The reciprocal rate is inside the range

Convert before comparing: `1 ÷ (2/5) = 5/2 = 2.5 stools per shelf`. This satisfies `2 < 2.5 < 4`.

You can instead use the reciprocal range, `1/4 < shelves per stool < 1/2`, because `1/4 < 2/5 < 1/2`. Taking reciprocals of positive quantities reverses the inequalities.

For **2 shelves exchanged for 5 stools**:

- Dana spends `2 × 4 = 8 hours` making shelves and receives stools that would take `5 × 2 = 10 hours` to make: a **2-hour saving**.
- Rui spends `5 × 3 = 15 hours` making stools and receives shelves that would take `2 × 12 = 24 hours` to make: a **9-hour saving**.

Each saving uses that producer's own technology. Adding the two figures isn't needed to decide whether both benefit on resource cost.

### 6. Elin has absolute advantage in both; neither has a strict comparative advantage

A folder costs Elin `6 ÷ 2 = 3 notebooks` and Sol `12 ÷ 4 = 3 notebooks`. A notebook costs each `1/3 folder`. Their opportunity costs are equal despite Elin's greater productivity.

A folder exporter would need more than 3 notebooks for a strict gain; the importer would need to pay fewer than 3. No rate meets both conditions. At exactly 3 notebooks per folder, both are indifferent on resource cost.

### 7. Omar has absolute advantage in both; Tessa has comparative advantage in tiles

Without the budgets, you couldn't infer per-hour productivity from the raw maxima. With them:

| Producer | Tiles per labor-hour | Bowls per labor-hour |
| --- | --- | --- |
| Tessa | `30/60 = 1/2` | `10/60 = 1/6` |
| Omar | `20/20 = 1` | `10/20 = 1/2` |

Omar produces more of either good per hour, so Omar has absolute advantage in both. Tessa's larger tile maximum reflects a larger labor budget.

Within each producer's row, however, the same budget produces either maximum, so the opportunity-cost ratio still works. A bowl costs Tessa `30/10 = 3 tiles` and Omar `20/10 = 2 tiles`; Omar has comparative advantage in bowls. A tile costs Tessa `1/3 bowl`, below Omar's `1/2 bowl`; Tessa has comparative advantage in tiles.

## Keep the unit on your review card

After checking your answers, pick one decision you missed and try recalling it later with the solution hidden. A short card can help you revisit the rule; a fresh full problem checks whether you can apply it.

| Front | Back |
| --- | --- |
| An input table gives 4 hours/shelf and 2 hours/stool. What is the opportunity cost of a shelf? | `(4 hours/shelf) ÷ (2 hours/stool) = 2 stools/shelf`. |
| An output table gives 12 stools OR 6 shelves from one labor budget. What is the opportunity cost of a shelf? | `12 stools ÷ 6 shelves = 2 stools/shelf`. The maxima are alternatives. |
| A shelf costs the exporter 2 stools and the importer 4 stools. What payment strictly benefits both on resource cost? | More than 2 and fewer than 4 stools per shelf. At an endpoint, one producer is indifferent. |

For help scheduling those later attempts, see [how often to review flashcards](/blog/how-often-should-you-review-flashcards/). On your next economics problem, hide the formula and write the answer unit first: **other good per unit of the good being produced**. Build the ratio that produces it.

*Production note: AI tools substantially assisted with research, writing, and exercise construction. All producers and production data are fictional. The worked model and exercise arithmetic were checked with exact rational arithmetic in Python. No workshop measurements, classroom trials, or learner-outcome tests were performed. The illustration is AI-generated.*

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