Notes on the Production Possibilities Curve (PPC/PPF)

The PPC (also called the Production Possibilities Frontier, PPF) is the same concept with different naming; it summarizes the limits of production that a society faces.
It shows the maximum amount of one good that can be produced for every possible level of production of another good, given available resources and current technology.
The curve represents the trade-offs a society faces when choosing how to allocate scarce resources between two goods.

Two goods in a 2D space: the y-axis represents Apples (A) and the x-axis represents Bananas (B).
The blue curve (the PPC) marks the boundary of what is feasible, given resources and technology.
Any point on the PPC is feasible/attainable; any point inside the curve is attainable but inefficient; any point outside the curve is unattainable with current resources/technology.

On the curve (feasible and efficient):
- If Bananas = $65{,}000$ , then Apples = $9{,}250$ (A_max given B = 65,000).
- If Bananas = $0$ , then Apples = $13{,}000$ (A_max when B = 0).
- If Bananas = $100{,}000$ , then Apples = $0$ (A_max when B = 100,000).
- If Bananas = $35{,}000$ , then Apples = $12{,}000$ (trade-off point on the curve).
- If Apples = $6{,}000$ , then Bananas = $85{,}000$ (trade-off point on the curve).
Points beyond the curve (unattainable):
- Point D = (Bananas = $85{,}000$ , Apples = $12{,}000$ ) is described as unattainable given the stated combination on the curve.
Points inside the curve (attainable but inefficient):
- Point E is attainable but inefficient (you can produce more of at least one good without reducing the other).
- In the example: if you have a combination like E where you produce fewer than the maximum feasible amounts given the bananas or apples, there exists a point on/inside the curve that yields a clear improvement (more of one good at the same level of the other).

Attainable/Feasible: A point that could be produced with current resources and technology. This includes points on the curve and inside it.
Efficient: A point where you cannot increase the production of one good without decreasing the production of the other. This occurs for points on the PPC (the blue curve) – trade-offs exist at every point.
Inefficient: A point that is attainable but could be improved by reallocating resources to produce more of one good without reducing the other (points inside or below the curve).
Unattainable/Infeasible: Points to the right/above the curve that cannot be produced with current resources/technology.

Negative slope: To increase production of one good, you must give up some production of the other due to scarce resources (trade-off).
Scarcity of resources (land, labor, capital) creates the trade-off; you cannot simultaneously increase both goods without sacrifice.
Bowed-out shape (concave to the origin) reflects increasing opportunity cost: the more of one good you try to produce, the more of the other you have to give up, and the amount you must give up rises as you move along the curve.

At one end of the curve (e.g., near 13,000 apples and 0 bananas): increasing bananas a little costs only a small amount of apples because some resources are relatively less suited to banana production.
- Example: starting from A = 13,000, increasing B slightly costs a small amount of A.
At the other end (e.g., near 0 apples and 100,000 bananas): increasing bananas further costs much more apples because the most productive resources for bananas have already been used for bananas; the remaining resources are more suited to apples.
This rising per-unit opportunity cost makes the slope steeper as you move down the curve; hence the curve is shaped with increasing magnitude of the slope as you move from left (high apples) to right (high bananas).
The phrase for this is increasing opportunity cost: the opportunity cost of producing an extra unit of one good increases as you produce more of that good.

Moving along the PPC from one feasible point to another requires sacrificing some quantity of one good to gain more of the other (trade-off).
Efficiency means you are on the frontier; any effort to produce more of one good without reducing the other is impossible if you are on the curve.
If you are inside the curve, you can reallocate resources to improve both goods’ production (inefficient use of resources).
The PPC captures the core idea of opportunity cost and scarcity: to gain more of one good, you must give up some of the other.

The PPC shows the feasible set of production combinations given current resources and technology.
Points on the curve are efficient; points inside are feasible but inefficient; points outside are unattainable.
The curve is negatively sloped due to the trade-off between the two goods.
The curve is bowed-out because of increasing opportunity costs as production shifts from one good to the other.
Numerical examples from the transcript illustrate specific coordinates on the curve and the corresponding trade-offs:
- $B = 0 ightarrow A = 13{,}000$
- $B = 65{,}000 ightarrow A = 9{,}250$
- $B = 100{,}000 ightarrow A = 0$
- $B = 35{,}000 ightarrow A = 12{,}000$
- $A = 6{,}000 ightarrow B = 85{,}000$

Let A denote Apples, B denote Bananas.
PPC is the set of feasible pairs S = ig{(A,B) ig| A easible, B easible\big} on or below the frontier.
On-frontier (efficient) condition implies: for a tiny move along the frontier, the trade-off satisfies a negative slope: ext{opportunity cost} = rac{ ext{change in A}}{ ext{change in B}} < 0.
Typical example of an opportunity-cost calculation moving from point c: if we increase apples by $riangle A = 3{,}250$ (from 6{,}000 to 9{,}250) and bananas fall by $riangle B = -20{,}000$ (from 85{,}000 to 65{,}000), then the cost per extra apple is
$rac{ riangle B}{ riangle A} = rac{-20{,}000}{3{,}250} \approx -6.15 ext{ bananas per apple}.$
If instead we increase bananas by $riangle B = 15{,}000$ and give up $riangle A = -6{,}000$ apples, the cost per banana is
$rac{| riangle A|}{| riangle B|} = rac{6{,}000}{15{,}000} = 0.4 ext{ apples per banana}.$