Production possibilities curve

Definition

Consider two goods $A$ and $B$, and a graph whose axes represent quantities of $A$ and $B$ respectively. Each point corresponds to a quantity of $A$ produced (its $A$-quantity coordinate) and a quantity of $B$ produced (its $B$-quantity coordinate). We say that one point dominates another if, in both coordinates, its value is at least as much as that of the latter.

The production possibilities curve or production possibilities frontier is the set of points in this graph such that it is possible to produce the quantities of $A$ and $B$ given by that point, but no point that dominates it can be achieved. In other words, it is the frontier, or boundary, of the possible quantity combinations that can be produced.

The multiple points on the production possibilities curve represent different ways of allocating the factors of production and different choices of technology and methods used to produce $A$ and $B$.

Shape of the curve

Intercepts

The $A$-quantity intercept (i.e., the point where the curve intersects the $A$-quantity coordinate axis) represents the quantity of $A$ that can be produced if all resources are devoted to the production of $A$, without attempting to produce anything of $B$. Analogously, the $B$-quantity intercept represents the quantity of $B$ that can be produced if all resources are devoted to the production of $B$.

Downward slope

The production possibilities curve is a downward-sloping curve. Given any two points on the production possibilities curve, neither dominates the other. Thus, if one point has a higher $A$-coordinate, the other has a higher $B$-coordinate.

Convexity

The production possibilities curve is convex. This means that if any two points on the production possibilities curve are joined, the line segment lies on the inside of the curve.

The intuition behind this is that certain resources are better suited for the production of $A$ and other resources are better suited for the production of $B$. Thus, when almost all resources are devoted to producing $A$, the marginal effect of diverting (the most suitable) resources to $B$ on the production of $B$ is high, with only a small drop in the production of $A$. However, as more and more resources get devoted to $B$, increasing production of $B$ by a small amount requires diverting resources better suited to $A$. Thus, a small increase in $B$ requires a larger drop in $A$.

Production possibilities curve and other points

Points on the inside

A point that is dominated by a point on the production possibilities curve is a poin tthat can be achieved, but achieving that point would be inefficient, since it is possible to increase the quantities produced for both goods. Thus, the points on the inside represent the feasible but inefficient.

Points on the outside

A point on the outside of the production possibilities curve is infeasible: the current technology and the amount of resources available does not allow for this point. The fact that points lie outside the production possibilities frontier is evidence of the reality of scarcity.

Comparison of points on the production possibilities curve

A priori, there is nothing making one point on the production possibilities curve preferable to another. Rather, the decision of what point on the production possibilities curve to pick depends on how consumers, or those ultimately buying the goods, value the two goods.

For instance, if consumers have no use for good $A$, then it makes sense to produce only good $B$.

More generally, it makes sense to construct the indifference curves of the consumer, i.e., the level sets of the consumer's utility function. The point on the production possibilities curve that intersects the most outward of the indifference curves should be chosen. This will be either one of the intercept points, or a point where the production possibilities curve is tangent to the indifference curve, with the indifference curve on the outside.

Shifts in the production possibilities curve

The production possibilities curve can move in any of these ways:

• Outward along both axes: This happens if some change favors greater production for both goods. If the production possibilities curve moves outwards for both axes, both its intercepts increase. Also, it is expected that all points move outward.
• Inward along both axes.
• Outward along one axis, inward along another axis.

Shifts due to technology

Technological changes, in general, are expected to move the production possibilities curve outward, because knowledge of production techniques is expected to improve with time. However, the effect of technological change on knowledge for producing the two goods need not be equal. For instance, technological change may improve knowledge on producing $A$, without affecting knowledge on producing $B$. In this case, the $A$-quantity increases and the $B$-quantity intercept remains constant.

Shifts due to changes in resources

Natural resources can get depleted or deteriorate in quality. For instance, for agricultural goods, the quality of land, water, and climate can deteriorate with time. More importantly, some changes such as climate changes (such as an increase in temperature, or a change in the annual precipitation rates) can have favorable effects on the production of some goods and unfavorable effects on the production of other goods. For instance, a shift towards hotter and wetter climates may reduce the quantity of wheat that can be grown and increase the quantity of rice that can be grown.

Thus, the production possibilities curve may move inward, move outward, or even move inward along one axis and outward along the other.

Related notions

• Indifference curve