Notes: Interdependence and the Gains from Trade (Mankiw Ch.3)

Chapter Objectives

Panel (a): Shows Frank’s and Ruby’s production opportunities
Panel (b) and (c): Each’s PPF, assuming 8 hours of work per day
The trade-off (opportunity cost) is constant for both when modeling the simple economy

Point A (Frank’s choice): 4 hours on meat and 4 hours on potatoes
- Meat produced: 4 ext{ oz}
- Potatoes produced: 16 ext{ oz}
Point B (Ruby’s choice): 4 hours on meat and 4 hours on potatoes
- Meat produced: 12 ext{ oz}
- Potatoes produced: 24 ext{ oz}

Frank specializes in potatoes: 8 hours producing only potatoes
- Output: 0 ext{ oz meat}, \, 32 ext{ oz potatoes}
Ruby specializes in both goods: 6 hours for meat, 2 hours for potatoes
- Output: 18 ext{ oz meat}, \, 12 ext{ oz potatoes}
Trade: 5 oz of meat for 15 oz of potatoes
After trade outcomes:
- Frank: 5 ext{ oz meat}, \, 17 ext{ oz potatoes}
- Ruby: 13 ext{ oz meat}, \, 27 ext{ oz potatoes}

Specialization and trade enable Frank and Ruby to reach consumption points A* and B*, infeasible before trade
Trade allows each person to consume more meat and more potatoes overall

Gains from trade arise from specializing in the activity with a comparative advantage
Specialization and trade raise total production in the economy
The implicit prices paid between trading partners reflect the gains from trade

Absolute vs. Comparative Advantage:
- Absolute advantage: the ability to produce a good using fewer inputs than another producer
- Comparative advantage: the ability to produce a good at a lower opportunity cost than another producer
In a two-good, two-person world, a person can have an absolute advantage in both goods but cannot have a comparative advantage in both

Absolute advantage: produce more with the same resources; fewer inputs
- Example:
- A producer with higher output given the same inputs has an absolute advantage
Comparative advantage: lower opportunity cost for a good
- OppCost of one good is the inverse of the oppCost of the other good

Gains from specialization and trade are based on comparative advantage
Total economy output rises when each person specializes in their comparative advantage
Implicit prices (terms of trade) between trading partners reflect gains from trade
Trade can benefit everyone by allowing specialization according to comparative advantages

For both parties to gain, the trade price must lie between their opportunity costs
If the trade price falls between the two opportunity costs, both parties are better off
Formal idea: the acceptable price range is bounded by each party’s opportunity costs of the traded goods

Example dataset: daily production capacities for pizzas and wings
Gwen’s production: 60 pizzas in a day when solely producing pizzas
Absolute advantages:
- Absolute advantage in producing pizza: Gwen
- Absolute advantage in producing wings: Gwen
Comparative advantage is determined via opportunity costs (table-based approach)

Frank the farmer (simple economy) and Ruby the rancher setup from earlier slides
Opportunity costs (from the provided table):
- 1 oz of Meat costs 4 oz potatoes for Frank
- 1 oz of Potatoes costs \frac{1}{4} \text{ oz meat for Frank}
- 1 oz of Meat costs 2 oz potatoes for Ruby
- 1 oz of Potatoes costs \frac{1}{2} \text{ oz meat for Ruby}
Interpretation: lower opportunity cost for a good in a country indicates comparative advantage in that good for that country

If Frank proposes a deal: 5 oz of meat for 15 oz of potatoes, can trade occur?
Depending on the other party’s opportunity costs, the trade may or may not be favorable

Gwen vs. Blake: determine if trade is beneficial by comparing opportunity costs and proposed terms
Example 3: Gwen proposes 1 pizza for 2.5 wings; this can be a winning trade because 2.5 lies between Gwen’s and Blake’s opportunity costs for wings per pizza

Use the quantity table to identify who has absolute advantage in each good
Compare opportunity costs to identify who has comparative advantage in each good

Each country has 24 labor hours per week
Production requirements:
- Alpha: 1 coffee requires 2 hours; 1 donut requires 8 hours
- Beta: 1 coffee requires 3 hours; 1 donut requires 6 hours
Determine:
- Absolute advantage in each good
- Comparative advantage in each good
- The terms of trade

Maximum outputs in 24 hours:
- Alpha: 12 coffees (since 24/2 = 12) or 3 donuts (since 24/8 = 3)
- Beta: 8 coffees (24/3 = 8) or 4 donuts (24/6 = 4)

For Alpha:
- OC of 1 coffee in donuts: \frac{2}{8} = \tfrac{1}{4} donut per coffee
- OC of 1 donut in coffees: \frac{8}{2} = 4 coffees per donut
For Beta:
- OC of 1 coffee in donuts: \frac{3}{6} = \tfrac{1}{2} donut per coffee
- OC of 1 donut in coffees: \frac{6}{3} = 2 coffees per donut

Absolute advantage in coffee: Alpha
Absolute advantage in donut: Beta
Comparative advantage in coffee: Alpha
Comparative advantage in donut: Beta
Terms of trade: any price of donuts per coffee in the interval between the two countries’ OC for coffee in donuts, i.e. between frac{1}{3} and frac{1}{2} donuts per coffee
Equivalently, the reciprocal interval for price in coffees per donut lies between 2 and 3 coffees per donut

Trade creates gains from specialization when agents have different comparative advantages
The overall production possibility frontier of the economy expands with specialization and trade
Prices (terms of trade) arise from the relative opportunity costs and help allocate resources efficiently
The model abstracts from transport costs, tariffs, and other real-world frictions to illustrate the core gains from trade

Trade can improve welfare but may create winners and losers domestically; policy can influence distributional outcomes
Adoption of free trade vs. protectionism has ethical and practical considerations for employment, wages, and consumer prices
The analysis highlights the importance of recognizing opportunity costs in decision making and public policy