Module 3: The Production Possibilities Curve Model

Trade-Offs and Scarcity

• Historical Illustration of a One-Man Economy:

  • In $1704$, crew member Alexander Selkirk feared his ship was not seaworthy and quarreled with the captain regarding needed repairs.
  • Selkirk abandoned the ship during a stop at a deserted island near Chile and lived alone for $4.5$ years using only the island's natural resources, items retrieved from the ship, and his own time and effort.
  • Selkirk's real-life ordeal inspired Daniel Defoe's $1719$ novel Robinson Crusoe.
  • Because Selkirk possessed limited resources, he operated as a simplified one-man economy facing scarcity.

• Scarcity and Trade-offs:

  • All economies, whether comprised of a single person or millions of individuals, face trade-offs due to resource scarcity.
  • Trade-off Definition: A trade-off occurs when something is given up in order to obtain something else.
  • Example: A castaway who devotes resources to catching fish benefits from having more fish, but cannot use those same resources to gather coconuts. The trade-off is receiving fewer coconuts.

The Production Possibilities Curve Model

• Model Purpose: Economists utilize the production possibilities curve (PPC) model to simplify real-world economic complexities by analyzing an economy that produces only two goods. This graphic model illustrates efficiency, opportunity cost, and economic growth.

• Production Possibilities Curve Definition: The production possibilities curve illustrates the trade-offs facing an economy that produces only two goods by displaying the maximum quantity of one good that can be produced for each possible quantity produced of the other good.

• Feasibility and Infeasibility:

  • Feasible Points: Any production point located inside or directly on the production possibilities curve (the shaded area) is attainable given available resources.
  • Point C: Represents producing $20$ fish and $9$ coconuts. This point is feasible because catching $20$ fish allows gathering up to a maximum of $15$ coconuts; thus $9$ coconuts is achievable.
  • Infeasible Points: Any production point lying strictly outside the curve is unattainable with existing resources.
  • Point D: Represents catching $40$ fish and gathering $30$ coconuts, which is not feasible.

• Axis Intercepts and Extreme Trade-offs:

  • Horizontal Intercept: At $40$ fish and $0$ coconuts, all resources are devoted entirely to catching fish per week, leaving no resources for coconuts.
  • Vertical Intercept: At $30$ coconuts and $0$ fish, all resources are devoted entirely to gathering coconuts per week, leaving no resources for fish.

• Intermediate Production Choices on Figure 3.1:

  • Point A: Catching $20$ fish allows gathering a maximum of $15$ coconuts.
  • Point B: Catching $28$ fish allows gathering a maximum of $9$ coconuts.

Economic Efficiency

• General Definition of Efficiency: An economy is efficient if there are no missed opportunities, meaning there is no way to make some people better off without making at least one person worse off.
  • Classroom Metaphor: A course meets in a room too small for its students (forcing some to stand or sit on the floor) while a larger classroom nearby sits empty during the same period. This represents an inefficient use of resources because switching to the larger room makes students better off without harming anyone. If all larger rooms were already occupied, the allocation would be efficient because making one class better off would require moving another class to a room that is too small.

• Productive Efficiency:

  • Definition: An economy achieves productive efficiency if it produces at a point directly on its production possibilities curve.
  • Points $A$ ($20$ fish, $15$ coconuts) and $B$ ($28$ fish, $9$ coconuts) achieve productive efficiency because maximum output of one good is achieved given the output of the other.
  • Productive Inefficiency: Occurs at any point inside the curve (such as Point $C$ with $20$ fish and $9$ coconuts), where resources are underutilized and the economy misses the opportunity to produce more of both goods.
  • Unemployment Impact:
  • Involuntary unemployment (people wanting work but unable to find jobs) leads to productive inefficiency.
  • Unemployment results in production at a point below the PPC.
  • Decreasing unemployment moves economy production closer to the PPC.
  • Increasing unemployment moves economy production further below the PPC.
  • The PPC itself represents full employment of all resources.

• Allocative Efficiency:

  • Definition: An economy achieves allocative efficiency if it produces at the point along its production possibilities curve that makes consumers as well off as possible.
  • Even if Points $A$ and $B$ are both productively efficient, they are not equally desirable. If Alex prefers consuming $28$ fish and $9$ coconuts (Point $B$) over $20$ fish and $15$ coconuts (Point $A$), then producing at Point $A$ is allocatively inefficient.

• Overall Economic Efficiency:

  • Requires both productive efficiency and allocative efficiency.
  • The economy must produce as much of each good as it can given the production of other goods (productive efficiency) AND produce the specific mix of goods that people most want to consume (allocative efficiency).

Opportunity Cost and PPC Shapes

• Definition of Opportunity Cost: The true cost of any good includes its price plus everything else that must be given up to obtain it.

  • Formula: $\text{Opportunity Cost} = \text{Opportunity Lost}$

• Constant Opportunity Cost and Straight-Line PPCs:

  • Occurs when the opportunity cost of an additional unit of a good remains unchanged regardless of the output mix.
  • Calculation Example (Figure 3.1):
  • Moving from Point $A$ ($20$ fish, $15$ coconuts) to Point $B$ ($28$ fish, $9$ coconuts) yields $8$ additional fish at the cost of $6$ coconuts. Opportunity cost per fish: $\frac{6}{8} = \frac{3}{4}$ coconut.
  • Moving from Point $B$ ($28$ fish, $9$ coconuts) to the horizontal axis ($40$ fish, $0$ coconuts) yields $12$ additional fish at the cost of $9$ coconuts. Opportunity cost per fish: $\frac{9}{12} = \frac{3}{4}$ coconut.
  • Slope of Straight-Line PPC: Equal to the opportunity cost of the good on the horizontal axis in terms of the good on the vertical axis. The curve in Figure 3.1 has a constant slope of $-\frac{3}{4}$.
  • Condition for Constant Opportunity Cost: Applies when there is no specialization of resources (all resources are equally suitable for producing either good). Examples include producing leather belts vs. leather hats, pizzas vs. calzones, or cappuccinos vs. lattes.

• Increasing Opportunity Cost and Concave (Bowed-Out) PPCs:

  • Occurs when catching/producing more of a good requires giving up progressively larger quantities of the other good.

• Calculation Example (Figure 3.2):
  • Producing the first $20$ fish (from $0$ to $20$ fish) requires giving up $5$ coconuts (going from $35$ to $30$ coconuts at Point $A$).
  • Producing an additional $20$ fish (from $20$ to $40$ fish) requires giving up $25$ more coconuts (going from $30$ to $5$ coconuts).
• Condition for Increasing Opportunity Cost: Results from the specialization of resources.
  • Agricultural Example: Soil and climate suited perfectly for corn but poorly for wheat allow growing a small amount of corn at low opportunity cost in sacrificed wheat. Expanding corn production requires utilizing land well suited for wheat, escalating the opportunity cost of corn.

Economic Growth

• Definition: Economic growth represents an expansion of an economy's production possibilities, allowing the economy to produce more of everything.

• Graphical Representation: An outward shift of the production possibilities curve. Moving from initial Point $A$ ($20$ fish, $25$ coconuts) on the original PPC to Point $E$ ($25$ fish, $30$ coconuts) on the new PPC shows attainable growth that was previously impossible.

• Two Primary Sources of Economic Growth:

  1. Increase in Resource Availability (Factors of Production):
  • Factors of production include labor, land, capital, and entrepreneurship.
  • Example: If fish become more abundant around the island, catching fish becomes more productive, enabling higher output of fish without reducing coconuts (or higher coconut output without reducing fish), shifting the PPC outward.
  1. Progress in Technology:
  • Technology Definition: The technical means for producing goods and services.
  • Example: Inventions like a fishing net or a wagon to transport coconuts shift the PPC outward.
  • Specific Technology: Technological advances specific to only one good (e.g., a fishing net) expand possibilities along that good's axis while leaving the opposite axis intercept unchanged if all resources were devoted to the non-benefiting good.

• Production Choices vs. Potential Growth:

  • Economic growth increases what an economy can produce, not necessarily what it chooses to produce.
  • An economy might choose to consume only one good or produce less of one good after growing (e.g., motor vehicles replacing horse-drawn carriages), but growth has still occurred because higher production of everything was possible.
  • Economic Contraction: An inward shift of the PPC caused by a loss of resources or technology (e.g., due to war or natural disaster).

Review Questions and Solutions

• Check Your Understanding Solutions:

  • 1a: False. An increase in resources available shifts the PPC outward.
  • 1b: True. A technological improvement increasing fish-catching ability relative to coconuts shifts the PPC outward.
  • 1c: False. Points inside the PPC are feasible but productively inefficient; points outside are non-feasible (unattainable).

• Multiple-Choice Questions:

• Q1: Which point(s) on the graph represent productive efficiency?

  • Answer: c ($A, B, C, \text{and } D$)

• Q2: An increase in capital goods produced without decreasing consumer goods is represented by:

  • Answer: d (movement from point $E$ to point $B$)

• Q3: An increase in unemployment could be represented by a movement from point:

  • Answer: d (point $B$ to point $E$)

• Q4: Moving from point $B$ to point $F$ might be allowed by:

  • Answer: e (all of the above: more workers, discovery of new resources, building new factories, technological advances)

• Q5: Since capital goods are a resource, producing at which point today results in the largest future outward shift of the PPC?

  • Answer: a (Point $A$)

• Q6: The PPC will certainly be straight if:

  • Answer: c (no resources are specialized for the production of either good)

• Q7: Allocative efficiency is achieved:

  • Answer: e (at the point along a production possibilities curve that makes consumers as well off as possible)

  • Free-Response Questions and Rubrics:

• FRQ 1 (6 points total):

  • a. Does this country's PPC exhibit increasing opportunity costs? Explain.
    • Rubric (2 pts): Yes ($1$ pt). The PPC is concave (bowed outward), so with each additional unit of butter produced, the opportunity cost in terms of gun production (indicated by line slope) increases. Likewise, producing more guns increases the opportunity cost in terms of butter ($1$ pt).
  • b. If point C is initially allocatively efficient, but the country goes to war, which point is most likely allocatively efficient during war? Explain.
    • Rubric (2 pts): Point $B$ ($1$ pt). The country would choose an efficient point with more (but not all) military goods to fight the war. Point $A$ is unlikely because it produces zero social goods needed for minimal living standards ($1$ pt).
  • c. If the economy entered a recession, the country would move from point C to which point? Explain.
    • Rubric (2 pts): Point $E$ ($1$ pt). A recession causes unemployment, which is represented by a point below the PPC ($1$ pt).

• FRQ 2 (5 points total):

  • Assume an economy chooses between food and shelter at constant opportunity cost. Draw a labeled PPC and label: efficient point E, unemployment point U, non-feasible point I.
    • Rubric: Requires a straight-line downward sloping PPC with food on one axis and shelter on the other. Point $E$ placed on the curve, Point $U$ inside the curve, and Point $I$ outside the curve.