The Production Possibilities Curve (PPC) and Trade-offs

Trade-offs and Opportunity Cost

• PPC (Production Possibilities Curve) is a model that helps economists think about the trade-offs every economy faces.

• The PPC is used to improve understanding of trade-offs by considering a simplified economy that produces only two goods.

• You make a trade-off when you give up something in order to have something else.

• To analyze trade-offs, economists often use the PPC model.

• The key idea: a society’s choices depend on available resources and technology, so producing more of one good requires sacrificing some amount of the other good.

The Production Possibilities Curve (PPC): Key Concepts

• The PPC shows the maximum feasible combinations of two goods that an economy can produce with given resources and technology.

• Three important aspects illustrated by the PPC:

  • Trade-offs

  • Efficiency

  • Economic Growth

• Definitions:

  • Productive Efficiency: producing on the PPC (no attainable production point that could produce more of one good without reducing the other).

  • Allocative Efficiency: producing at a point on the PPC where resources are allocated to maximize consumer welfare.

  • Economic Growth: an outward shift of the PPC, indicating the economy can produce more of both goods over time.

• Points on the graph:

  • Inside the curve: feasible but not efficient (missed opportunities).

  • On the curve: feasible and efficient (productive efficiency).

  • Outside the curve: not feasible with current resources/technology.

Desert Island Example: Cocoa-nuts and Fish (two-good PPC)

• The PPC is often illustrated with two goods; in the desert island scenario the goods are coconuts and fish.

• Graph interpretation:

  • The horizontal axis shows the quantity of fish.

  • The vertical axis shows the quantity of coconuts.

  • Points on the curve are feasible and efficient.

  • Points inside the curve are feasible but not efficient.

  • Points outside the curve are not feasible.

• Alternative two-good examples (as in slides): the curve can be used to illustrate different pairings (e.g., Crab Puffs vs. Storage Sheds), but the core ideas remain the same: trade-offs, efficiency, and growth.

Efficiency on the PPC

• The PPC helps illustrate efficiency in two senses:

  • Productive Efficiency: economy is producing at a point on the PPC (no wasted resources).

  • Allocative Efficiency: given scarcity, resources are allocated to maximize consumer well-being; if achieved, this is Allocative Efficiency.

• If an economy allocates resources so consumers are as well off as possible, it attains Allocative Efficiency.

Opportunity Cost

• True cost of any good or service is not only the price but also what is given up to obtain it (Opportunity Cost).

• An economy is efficient if there are no missed opportunities; that is, you cannot make some people better off without making others worse off.

• When you produce the same amount of one good and give up the same amount of another, the opportunity cost is constant.

  • This is Constant Opportunity Cost.

• When the opportunity cost increases as you produce more of one good, the curve is bowed out (Increasing Opportunity Cost).

PPC and the Shape of the Curve

• Constant Opportunity Cost: PPC is a straight line between two goods.

• Increasing Opportunity Cost: PPC is bowed-out (convex to the origin).

• The shape of the PPC reveals the nature of the trade-offs between the two goods.

Practical Calculations from a Sample PPC (A–E data set)

• Given two goods: Coconuts (vertical axis) and Fish (horizontal axis).

• Points on a sample PPC data set:

  • A = (C = 30 coconuts, F = 0 fish)

  • B = (C = 27 coconuts, F = 10 fish)

  • C = (C = 25 coconuts, F = 20 fish)

  • D = (C = 20 coconuts, F = 30 fish)

  • E = (C = 0 coconuts, F = 40 fish)

• Unattainable region: any point outside the outer curve (e.g., F > 40 for the given C).

• Feasible but not efficient: a point like G that lies inside the curve but not on it.

• Unattainable: a point like F that lies outside the curve.

Ratio of Coconuts to Fish at Point C

• At Point C: C = 25 coconuts, F = 20 fish.

• Ratio of Coconuts to Fish at C:

  • 
    rac{C}{F} = rac{25}{20} = rac{5}{4} = 1.25.

  • This ratio is the trade-off rate at that point (how many coconuts you must give up per extra unit of fish).

Opportunity Cost Calculations (A to B and E to D)

• From A to B: A = (30, 0) → B = (27, 10)

  • Change in coconuts: riangle C = 27 - 30 = -3

  • Change in fish: riangle F = 10 - 0 = 10

  • OC of fish in terms of coconuts (cost of 1 more fish in coconuts):
    ext{OC}_{ ext{fish|C}} = rac{| riangle C|}{ riangle F} = rac{3}{10} = 0.3.

  • OC of coconuts in terms of fish (cost of 1 coconut in fish):
    ext{OC}_{ ext{C|fish}} = rac{ riangle F}{| riangle C|} = rac{10}{3} \, ext{≈}\, 3.333.

• From E to D: E = (0, 40) → D = (20, 30)

  • Change in coconuts: riangle C = 20 - 0 = 20

  • Change in fish: riangle F = 30 - 40 = -10

  • OC of coconuts in terms of fish (cost of 1 more coconut in fish):
    ext{OC}_{ ext{C|F}} = rac{| riangle F|}{ riangle C} = rac{10}{20} = 0.5.

  • OC of fish in terms of coconuts (cost of 1 fish in coconuts):
    ext{OC}_{ ext{F|C}} = rac{ riangle C}{| riangle F|} = rac{20}{10} = 2.

Constant vs Increasing Opportunity Cost (interpretation from slides)

• If the economy shows a constant OC (a straight-line PPC), then to produce more of one good you give up a constant amount of the other:

  • Constant OC: straight PPC implies the trade-off rate is constant along the curve.

• If the OC increases as you produce more of one good (bowed-out PPC), then the opportunity cost is higher for additional units:

  • Increasing OC: bowed PPC implies you must sacrifice progressively more of one good to gain additional units of the other.

Economic Growth and Shifts of the PPC

• Economic Growth means an outward shift of the PPC, allowing more production of both goods.

• Causes of outward PPC shift:

  • Increase in the resources available for production (e.g., more land, labor, capital).

  • Advancements in technology that improve production efficiency.

• Visual interpretation: the original PPC lies inside a New PPC; the new PPC lies further to the outer-right and/or up, indicating higher production possibilities.

• Illustrative data (from slides): a comparison between Original PPC and New PPC shows higher quantities of coconuts and/or fish along corresponding points, demonstrating growth.

Check For Understanding (Practice Setup from Page 8)

• Task: Build a PPC with coconuts on the y-axis and fish on the x-axis, using the given coordinates:

  • A = (30 coconuts, 0 fish)

  • B = (27 coconuts, 10 fish)

  • C = (25 coconuts, 20 fish)

  • D = (20 coconuts, 30 fish)

  • E = (0 coconuts, 40 fish)

  • F = unattainable point beyond the curve

  • G = feasible but not efficient (inside the curve)

• Questions to answer:

  • What is the ratio of Coconuts to Fish at Point “C”? (Answer: rac{25}{20} = rac{5}{4} = 1.25.)

  • What is the Opportunity Cost from Point A to Point B? (Answer given above: OC of fish in coconuts = rac{3}{10} = 0.3.; OC of coconuts in fish = rac{10}{3} \,\approx\, 3.333.)

  • What is the Opportunity Cost from Point E to Point D? (Answer: OC of coconuts in terms of fish = rac{10}{20} = 0.5.; OC of fish in terms of coconuts = rac{20}{10} = 2.)

  • Is this Constant OC or Increasing OC? (Based on the shape: constant OC indicates a straight-line PPC; Increasing OC indicates a bowed-out PPC.)

• The exercises reinforce the core concepts: feasibility, efficiency, OC, and how to read PPC graphs.

Connections to Foundational Principles and Real-World Relevance

• PPC links to fundamental trade-offs faced by economies: choosing between present consumption and investment, or between different goods in scarce-resource settings.

• Efficiency concepts connect to real-world policy: productive efficiency ensures scarce resources are not wasted; allocative efficiency relates to welfare and how well a society meets consumer needs.

• Opportunity cost underlines the idea that choices have costs, shaping decisions in business, government budgets, and daily life.

• Economic growth explains long-term improvements in standard of living as societies accumulate resources and improve technology, shifting PPC outward over time.

Summary of the PPC Model and Its Implications

• PPC provides a simplified framework to analyze how economies face trade-offs between two goods.

• Points on the curve = feasible and efficient; inside = feasible but inefficient; outside = infeasible with current resources/technology.

• Efficiency has two dimensions: productive (on the curve) and allocative (optimal distribution for welfare).

• Opportunity Cost captures the cost of foregone alternatives when making choices; it can be constant (straight line) or increasing (bowed-out curve).

• Growth shifts the curve outward, reflecting greater production capabilities due to more resources or better technology.

• Practice problems (like the coconut–fish example) illustrate concrete calculations of OC, ratios, and the interpretation of point locations on a PPC.

The U.S has the absolute advantage in planes

France and the U.S has the absolute advantage in cruise ships

France has the comparative advantage in cruise ships

France has the lower opportunity cost on cruise ships (6 planes)  meaning France will produce cruise ships

This means France can trade 1 cruise ship to the U.S between 6 and 10 planes

The U.S will produce planes and trade 1 plane for between ⅙ and 1/10 a plane

Korea has the absolute advantage in Motorcycles

Germany has the absolute advantage in cars

Korea has the comparative advantage in motorcycles

Germany has the comparative advantage in cars

Korea has the lower opportunity cost for motorcycles

Germany has the lower opportunity cost for cars

Germany will trade 1 car to Korea for between 2 and 3 motorcycles

Korea will trade 1 motorcycle for between ⅓ and ½ of a car

Mexico has the absolute advantage for both

Mexico has the comparative ad