ARE 201 · Unit 3

Production Possibility Frontier & Comparative Advantage

TIME TWO TASKS POSSIBLE OUTPUTS
Volunteer lab · Round 1 of 2

How much of tomorrow would you spend at this job?

Session only: nothing is uploaded or retained after this page is refreshed.

You have up to five free hours tomorrow. The dining hall pays $15 per hour.

How many hours would you choose to work?
Enter a nickname and choose 0–5 hours.
Your task card for tomorrow
Choose a name and work time, then draw one fixed productivity profile.
Volunteer lab · Allocate the shift

How will you divide your work time?

Current volunteer

Complete the setup first

Work time
—
Total minutes
—
Dish rack
—
Chicken Wrap
—
All wrapsAll dishwashing
Dishwashing time—
Wrap time—
Dish racks—
Chicken Wraps—
All possible full-shift allocations · the line has not been named yet
Dish racks Chicken Wraps 0 — — Your choice
Complete the volunteer setup to activate this graph.
Observe before naming

Two volunteers created two production boundaries

— — — — — — — — Dish racks Chicken Wraps 0 — —
Session profiles
Volunteer 1 · waiting
Volunteer 2 · waiting
Complete two rounds—or simulate—to compare the boundaries.
Reveal the model

Economists give this production boundary a name

Production
Possibilities
Frontier
Volunteer 1
Complete or simulate the volunteer lab.
Volunteer 2
Complete or simulate the volunteer lab.
Production Possibilities Frontier: the maximum feasible combinations of two outputs that can be produced with current resources and technology.
Unpack the model

What each word in PPF contributes

Production
Possibilities
Frontier
Production

Combinations of outputs—not consumption preferences.

Possibilities

What current resources and technology make attainable.

Frontier

The boundary of maximum feasible production combinations.

PPF: the maximum feasible combinations of two outputs that can be produced with current resources and technology.
One volunteer, one linear frontier

Read the endpoints and the volunteer’s chosen point

Complete or simulate the volunteer lab to load one profile.
A

All Chicken Wraps

— dish racks
— Chicken Wraps

V

The volunteer’s choice

— dish racks
— Chicken Wraps

D

All dishwashing

— dish racks
— Chicken Wraps

Each point on this straight frontier uses the volunteer’s entire chosen shift. The PPF displays possibilities; it does not identify the preferred point.

Move right

Produce more dish racks.

Move down

Give up some Chicken Wraps.

Predict before revealing

What does each location mean for this volunteer?

Complete or simulate the volunteer lab to load one profile.
Dish racks Chicken Wraps 0—— I E U

Predict first. Then select a point to reveal its meaning.

Load a volunteer profile, then compare each point with the straight frontier.
Translate location into economics

Inside, on, and outside use the same volunteer benchmark

Complete or simulate the volunteer lab to load one profile.
I

Inside

Feasible but productively inefficient. Some of the chosen work time is unused, or some output is wasted.

E

On the PPF

Feasible and productively efficient. The full shift is allocated between dish racks and wraps.

U

Outside

Currently unattainable. The combination requires more time or faster task performance.

Important: “inside” does not mean impossible, and “on the PPF” does not mean personally preferred.
Move along one straight frontier

Every movement reallocates the same volunteer’s time

Complete or simulate the volunteer lab to load one profile.
ABCD Dish racks Chicken Wraps 0——
Selected movement

A → B

+

— dish racks

−

— Chicken Wraps

Load a volunteer profile to calculate this trade-off.
Turn the graph into economics

The slope measures this volunteer’s opportunity cost

Complete or simulate the volunteer lab to load one profile.
OC of 1 Dish Rack = | Δ Chicken Wraps ÷ Δ Dish Racks |

Move A → B

Load a profile to calculate the output changes.

— ÷ — = —
→

Use the task times

The same opportunity cost can be read directly from the two task speeds.

— min ÷ — min = —
With fixed task speeds, the straight-line slope—and therefore opportunity cost—stays constant.
Notice the linear pattern

Does the trade-off stay the same along this PPF?

Complete or simulate the volunteer lab to load one profile.
MovementDish racks gainedWraps given upWraps per dish rack
A → B———
B → C———
C → D———
Load a profile, then compare the final column before choosing.
Linear PPF: fixed task speeds create a constant trade-off between dish racks and Chicken Wraps.
Reverse the direction

Read the same trade-off in both directions

Complete or simulate the volunteer lab to load one profile.
Move toward more dish racks

OC of 1 Dish Rack

How many Chicken Wraps could be produced during the time needed for one dish rack?

Move toward more Chicken Wraps

OC of 1 Chicken Wrap

How many dish racks could be produced during the time needed for one Chicken Wrap?

Reveal each direction separately, then compare the two ratios.
Practice

Check the full chain from scarce time to a linear PPF

Question 1 of 4

Personal scarcity

Why can the volunteer not produce unlimited dish racks and Chicken Wraps?

Score: 0
Identify the economic constraint first.
Checkpoint · Before shifts

Checkpoint: one fixed constraint, one linear PPF

ScarcityThe volunteer has a finite amount of work time.
→
AllocationEach minute can go to dish racks or Chicken Wraps.
→
Linear PPFFixed task speeds map maximum feasible output combinations.
Turn and talk

In one sentence: why is a movement along the PPF costly?

On the frontier, current productive capacity is fully used, so producing more of one output requires redirecting resources and giving up some of the other output.
So far: fixed work time and fixed task speeds create one straight-line PPF with constant opportunity cost.
A new question

Did the choice change—or the constraint?

Complete or simulate the volunteer lab to load one profile.
AB Current PPF New PPF Dish racks Chicken Wraps 0——
Diagnostic rule

Ask what stayed fixed

Same time + same task speeds
A different output mix is a movement along the same PPF.

Resources or productivity change
The maximum feasible combinations change, so the PPF shifts.

Load a volunteer profile, then compare the two cases.
Resources change · Relative productivity does not

More or less work time shifts the entire PPF

Complete or simulate the volunteer lab to load one profile.
— — — — — — Fewer resources Current More resources Dish racks Chicken Wraps 0
Selected case

Current productive capacity

Work time—
Slope—
Max dish racks—
Max wraps—
W = — − —D

Load a profile to compare productive capacity.

Resources fixed · Relative productivity changes

Task-specific productivity rotates the PPF

Complete or simulate the volunteer lab to load one profile.
— — — Dish racks Chicken Wraps 0
Same total work time

Chicken Wrap productivity rises

Total time—
Task time—
Fixed intercept—
OC of 1 rack—
W = — − —D

Load a profile to compare relative productivity.

Classify the change

What happens to the volunteer’s PPF?

Scenario 1 of 5

Reallocate time

The volunteer moves 30 minutes from making wraps to washing dishes. Total work time and task speeds stay fixed.

Score: 0
First ask: did resources or productivity change?
Keep the concepts separate: preferences and wages may change the chosen point, but only resources or productivity change production possibilities.

Calculate the Opportunity Costs

WorkerT-shirts per hourLoaves of bread per hour
Worker 1——
Worker 2——
New example · two consumer goods

Absolute advantage: who can produce more per hour?

WorkerT-shirts per hourLoaves of bread per hour
Worker 1——
Worker 2——
T-shirts

Who produces more?

Compare T-shirts per hour, holding work time fixed.

Loaves of bread

Who produces more?

Compare loaves per hour, holding work time fixed.

Absolute advantage: producing more output with the same amount of resources—in this example, one hour of work.
Two consumer goods · compare opportunity cost

Comparative advantage: who gives up less?

WorkerOC of 1 T-shirtOC of 1 loaf of bread
Worker 1——
Worker 2——
T-shirts

Who has the lower OC?

The worker who gives up fewer loaves has comparative advantage.

Loaves of bread

Who has the lower OC?

The worker who gives up fewer T-shirts has comparative advantage.

Allocation rule: assign production by comparative advantage—the lower opportunity cost—not by absolute advantage alone.
Pause · predict before the example

Are absolute advantage and comparative advantage always aligned?

Consider this claim
If one producer can make more of both goods per hour, must that producer also have comparative advantage in both goods?
YESThey always point to the same producer.
NOThey do not necessarily point to the same producer.
Think for 20 seconds → vote → explain your reasoning
Why comparative advantage matters

Comparative advantage is about relative cost

Comparative advantage: the ability to produce a good at a lower opportunity cost than another producer.
Output in one hour

Worker A is faster at both

WorkerT-shirtsLoaves
A1020
B44
What each output costs

But compare opportunity costs

WorkerOC of 1 T-shirtOC of 1 loaf
A2 loaves0.5 T-shirt
B1 loaf1 T-shirt
Different questions: absolute advantage compares productivity; comparative advantage compares opportunity cost.
From comparative advantage to gains from exchange

Specialization and exchange can benefit both

Core idea: specialization can create additional output, and exchange can distribute those gains so both people consume bundles they could not produce alone.
Step 1

Specialize

Assign each good to the producer with the lower opportunity cost.

Step 2

Produce more

Using time where it is relatively most productive can expand total output.

Step 3

Exchange

Trade at terms between the two opportunity costs, then divide the larger output.

Comparative advantage→ Specialization→ Larger total output→ Mutually beneficial exchange
Case study · agricultural production

North Carolina and Idaho: who should produce what?

Stylized production possibilities: maximum output from the same 100 acres over one growing season. These are classroom values, not observed state totals.
StateSweet potatoesPotatoes
North Carolina60 units30 units
Idaho20 units40 units
Step 1

Calculate opportunity cost

For each state, calculate the opportunity cost of one unit of each crop.

Step 2

Recommend specialization

Based on comparative advantage, how should the two states divide production?

North Carolina–Idaho case · compare land allocations

Which state should produce which crop?

North Carolina · lower OC of sweet potatoes0.5 potato unit per sweet-potato unit
Idaho · lower OC of potatoes0.5 sweet-potato unit per potato unit
North Carolina100 acres

Split land between crops

50 acres per crop · (30 sweet potatoes, 15 potatoes)

Idaho100 acres

Split land between crops

50 acres per crop · (10 sweet potatoes, 20 potatoes)

Total output

50–50 land split
Sweet-potato units40
Potato units35
Sweet potatoes
40
Potatoes
35
The 50–50 land split produces (40, 35). Compare it with specialization.
North Carolina–Idaho case · separate production from consumption

Exchange expands consumption possibilities

Terms of trade: North Carolina gives sweet potatoes; Idaho gives potatoes. A one-for-one rate lies between their opportunity costs. 1 sweet-potato unit ↔ 1 potato unit

North Carolina

orange: PPF · green: with exchange
B (30, 15) P (60, 0) C (42, 18) 42 18 06030 Sweet-potato units Potato units

Idaho

orange: PPF · green: with exchange
B (10, 20) P (0, 40) C (18, 22) 18 22 02040 Sweet-potato units Potato units

B = 50–50 no-trade bundle · P = specialized production · C = consumption after exchange

North Carolina consumes(42, 18)
Idaho consumes(18, 22)
Total remains(60, 40)
At q = 18, both states consume more of both crops than under their 50–50 no-trade allocations.
Trade does not shift either state’s production PPF. It separates consumption from production, allowing each state to consume beyond its own frontier.
Terms of trade · calculate before revealing

What trading rate would both states accept?

Let p be the number of potato units exchanged for 1 sweet-potato unit.
North Carolina · exporter of sweet potatoes

What must North Carolina receive?

Producing one sweet-potato unit costs North Carolina the potatoes it could have produced instead.

OC = 0.5 potato unit
Idaho · importer of sweet potatoes

What is Idaho willing to pay?

Producing one sweet-potato unit itself would cost Idaho the potatoes it must give up.

OC = 2 potato units
Strictly mutually beneficial interval
< p <

Use each state’s opportunity cost to fill in the two bounds.

Think one step further: What happens exactly at either boundary?
Terms of trade · test proposed rates

Why do some trading rates work—and others fail?

p = 1
p ≤ 0.5
NC will not gain
0.5 < p < 2
both states gain
p ≥ 2
Idaho will not gain

North Carolina

Accepts

It receives 1 potato unit and gives up production worth 0.5 potato unit.

Exporter gain: +0.5 potato unit

Idaho

Accepts

It pays 1 potato unit instead of giving up 2 potato units to produce the crop itself.

Importer gain: +1 potato unit
North Carolina–Idaho case · combine production

Now combine two states into one production problem

North Carolina–Idaho case · apply comparative advantage

Which state should reallocate land first?

North Carolina–Idaho case · combined production

Build the two-state production frontier

Sweet-potato units Potato units 0
Three land allocations

Trace the efficient boundary

Start at A, where both states produce potatoes.
North Carolina–Idaho case · generalize the pattern

From two states to a smooth concave PPF

lower OC higher OC Sweet-potato units Potato units 0
Selected view

Two states: one visible kink

Each state contributes one constant-cost segment.

First sweet potatoesOC = —
Later sweet potatoesOC = —
Diminishing marginal returns · definition and intuition

Each additional input eventually adds less output

Definition

Diminishing marginal returns occur when, with technology and other inputs held constant, successive units of one input eventually generate smaller additions to total output.

Marginal product = the extra output produced by one more unit of input

Why might the next unit contribute less?

1

Expand onto less-suitable land

A farm plants its best-watered, most fertile parcels first. Later 20-acre blocks may have poorer soil or sit farther from irrigation.

ResultThe next 20 acres add fewer crop units than the previous 20 acres.
2

Add workers to limited equipment

The first workers keep one harvester and loading area busy. Additional workers begin waiting, crowding, or duplicating tasks.

ResultEach additional worker adds less harvested output.
3

Apply more fertilizer

The first application corrects the largest nutrient shortage. Later applications address smaller shortages, and excessive fertilizer can damage plants.

ResultEach additional application creates a smaller yield increase.
North Carolina · sweet-potato production

Later land blocks add less output

Fixed inputs: irrigation, equipment, and management
Variable input: 20-acre blocks planted
FIXED SUPPORTING
INPUTS
1
2
3
4
5
Total sweet-potato units20
Marginal product20
20-acre blocksTotal sweet-potato unitsMarginal product of block n
12020
23616
34812
4568
5604
The first 20-acre block adds 20 units. Add land blocks while irrigation, equipment, and management remain fixed.
North Carolina–Idaho case · return to the combined PPF

Link land reallocation to rising opportunity cost

The same 200 acres—100 in each state—are divided into ten stylized 20-acre blocks and reallocated in order of increasing opportunity cost.

Concave PPF

The highlighted segment moves one land block toward sweet-potato production.

P0 P1 Sweet-potato units Potato units 08070

Marginal OC of sweet potatoes

Each point measures potato units lost per additional sweet-potato unit.

OC = 0.25 Sweet-potato units OC · potato units 0800714

Drag once: the highlighted segment and the OC point move together.

Blocks · SP / P1 / 9
Gain sweet-potato units+16
Give up potato units−2
OC per sweet-potato unit0.125
The first reallocated block adds many sweet-potato units and gives up few potato units, so marginal opportunity cost is low.
← → / Space to navigate · P to print