MODULE 01Scarcity & trade-offs

Production Possibilities Frontier

Baseline · 1,000 cars / 3,000 computersAll modules

Module 01 · Theory

The Production Possibilities Frontier

Mankiw · Ch. 2 · pp. 58–61

The PPF shows the combinations of output an economy can produce given its factors of production and technology. With only cars and computers, every point on the frontier is a full-employment, productively efficient outcome.

Efficiency vs. inefficiency

A point on the curve is efficient: producing more of one good requires giving up some of the other. A point inside the curve (D) is inefficient — unemployment or misallocation means the economy could produce more of both. A point beyond the curve (C) is unattainable with current resources.

Opportunity cost is the slope

The magnitude of the frontier’s slope is the marginal rate of transformation: how many computers must be sacrificed for one more car. Moving from A to B raises car output by 100 and lowers computer output by 200, so the average opportunity cost is2 computers per car.

Why it bows out

Resources are not equally suited to both industries. As the economy shifts more workers and capital into cars, it increasingly uses inputs that are relatively better at making computers — so each additional car costs more computers. That is thelaw of increasing opportunity cost.

Growth vs. shocks

A neutral technology improvement expands the whole frontier. A biased improvement — say, better computer technology — lifts the computer intercept and rotates the frontier outward along that axis, making previously infeasible combinations attainable.

Formula

MRT = |ΔQ_comp / ΔQ_cars|

At the baseline, the A→B segment has MRT = 2. The slope steepens as car production rises.

Try this

01Place P at (700, 2,500). It is infeasible — then raise computer technology to 4,000 and watch it become attainable.
02Set P to (300, 1,000). It is inefficient: the economy could move to the frontier without sacrificing either good.
03Switch to the linear frontier. Constant opportunity cost means A and B are no longer attainable combinations.

Live frontier600 cars → 2,200 computers

Increasing cost

Efficient frontierInefficient (D)Infeasible (C)Inspection P

Click the plane to place P, drag it to inspect, or focus it and use the arrow keys (Shift for larger steps). A and B sit on the frontier at baseline.

Live readout

What the frontier says

bowed

Current output

2,200

computers

600 cars · on the frontier

MRT at current output

2.00

computers / car

Marginal opportunity cost of one more car

Inspection point P

(800, 2,600)

Infeasible

Beyond the frontier: unattainable with current resources.

A → B opportunity cost

100 more cars cost 200 computers

2.00comp/car

MRT range

Increasing cost as production shifts toward cars

0.67→11.33

Slider

Production choice

Cars produced600 carsMaximum 1,000 cars. The slider walks the frontier.

Computers produced2,200

Technology

Frontier intercepts

Computer technology (Aᶜ)3,000Biased growth: lifts the vertical intercept.Automotive technology (Aˣ)1,000Biased growth: pushes the horizontal intercept.

Shape

Frontier curvature

Increasing opportunity cost: each extra car costs more computers as the economy specializes.

Mankiw presets

Guided states

Inspector

Point P (x, y)

CarsComputers

P is infeasible. Drag it on the graph or edit the coordinates.

URL state · on