Ben and Sam are the only people in a small island. They both produce food and drink. Let F denote the quantity of food, and D denote the quantity of drink. The following equations summarize their individual production possibility curves (PPCs) per week.

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Ben: D = 21 − 3.8F

Sam: D = 144 − 10.9F

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In this closed economy, any admissible terms of trade between Ben and Sam have to be smaller than **[Answer]** units of drink per unit of food.

In a closed economy, admissible terms of trade between two individuals are limited by their opportunity costs, which are derived from their production possibility curves (PPCs). The opportunity cost of producing one good (say food) in terms of the other good (drink) indicates how much of the other good is forgone to produce one additional unit of the first good.

The PPCs for Ben and Sam are given as:

- **Ben:** \( D = 21 - 3.8F \)
- **Sam:** \( D = 144 - 10.9F \)

These equations can be rewritten in terms of opportunity costs.

### Opportunity Cost for Ben
The slope of Ben's PPC represents how many units of drink \( D \) Ben must give up for each additional unit of food \( F \). The slope is the negative of the coefficient of \( F \) in Ben's PPC equation:

\[
\text{Slope for Ben} = -3.8
\]

This means that Ben's opportunity cost of producing 1 unit of food is 3.8 units of drink.

### Opportunity Cost for Sam
Similarly, the slope of Sam's PPC represents how many units of drink \( D \) Sam must give up for each additional unit of food \( F \):

\[
\text{Slope for Sam} = -10.9
\]

This means that Sam's opportunity cost of producing 1 unit of food is 10.9 units of drink.

### Admissible Terms of Trade
For mutually beneficial trade, the terms of trade must lie between the opportunity costs of the two individuals. Ben's opportunity cost of food is lower than Sam's, so Ben has a comparative advantage in producing food, and Sam has a comparative advantage in producing drink.

The terms of trade must be between:
- **Ben's opportunity cost**: 3.8 units of drink per unit of food
- **Sam's opportunity cost**: 10.9 units of drink per unit of food

Thus, any admissible terms of trade must be less than **10.9 units of drink per unit of food** (Sam's opportunity cost).

### Final Answer
The admissible terms of trade must be smaller than **10.9** units of drink per unit of food.

Would you like a detailed explanation of opportunity costs or trade concepts?

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**Relative questions:**
1. What is a production possibility curve (PPC)?
2. How do opportunity costs determine terms of trade in a two-person economy?
3. Can you explain why Ben has a comparative advantage in food production?
4. How does the concept of comparative advantage affect trade decisions in this scenario?
5. How would the admissible terms of trade change if the PPCs were linear?

**Tip:** Always look for comparative advantage when determining terms of trade between two entities. It leads to mutually beneficial trade.

Ben and Sam are the only people in a small island. They both produce food and drink. Let F denote the quantity of food, and D denote the quantity of drink. The following equations summarize their individual production possibility curves (PPCs) per week.

---------------------------------

Ben: D = 21 − 3.8F

Sam: D = 144 − 10.9F

---------------------------------

In this closed economy, any admissible terms of trade between Ben and Sam have to be smaller than [Answer] units of drink per unit of food.

Explore how the admissible terms of trade between Ben and Sam in a closed economy are determined by their production possibility curves (PPCs). Learn about opportunity cost and comparative advantage, with a detailed explanation for students in Grades 10-12.

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