The PPFs in Figure 1.1 define the amounts of the goods that each individual can produce while using all of their productive capacity—time in this instance. The national, or economy-wide, PPF for this two-person economy reflects these individual possibilities combined. Such a frontier can be constructed using the individual frontiers as the component blocks.
First let us define this economy-wide frontier precisely. The economy-wide PPF is the set of goods combinations that can be produced in the economy when all available productive resources are in use. Figure 1.3 contains both of the individual frontiers plus the aggregate of these, represented by the kinked line ace. The point on the V axis, a=27, represents the total amount of V that could be produced if both individuals devoted all of their time to it. The point e=30 on the horizontal axis is the corresponding total for fish.
Economy-wide PPF: the set of goods combinations that can be produced in the economy when all available productive resources are in use.
To understand the point c, imagine initially that all resources are devoted to V. From such a point, a, we consider a reduction in V and an increase in F. The most efficient way of increasing F production at the point a is to use the individual whose opportunity cost of F is least – Zoe. She can produce one unit of F by sacrificing just 1/2 unit of V. Amanda on the other hand must sacrifice 1.5 units of V to produce 1 unit of F. Hence, at this stage Amanda should stick to V and Zoe should devote some time to fish. In fact as long as we want to produce more fish Zoe should be the one to do it, until she has exhausted her time, which occurs after she has produced 18F and has ceased producing V. At this point the economy will be producing 18V and 18F – the point c.
Figure 1.3: Economy-Wide PPF
From a, to produce Fish it is more efficient to use Zoe because her opportu-
nity cost is less (segment ac). When Zoe is completely specialized, Amanda
produces (ce). With complete specialization this economy can produce 27V
From this combination, if the economy wishes to produce more fish Amanda must become involved. Since her opportunity cost is 1.5 units of V for each unit of F, the next segment of the economy-wide PPF must see a reduction of 1.5 units of V for each additional unit of F. This is reflected in the segment ce. When both producers allocate all of their time to F the economy can produce 30 units. Hence the economy’s PPF is the two-segment line ace. Since this has an outward kink, we call it concave (rather than convex).
As a final step consider what this PPF would resemble if the economy were composed of many persons with differing degrees of comparative advantage. A little imagination suggests (correctly) that it will have a segment for each individual and continue to have its outward concave form. Hence, a four-person economy in which each person had a different opportunity cost could be represented by the segmented line abcde, in Figure 1.4. Furthermore, we could represent the PPF of an economy with a very large number of such individuals by a somewhat smooth PPF that accompanies the 4-person PPF. The logic for its shape continues to be the same: as we produce less V and more F we progressively bring into play resources, or individuals, whose opportunity cost, in terms of reduced V is higher.
Figure 1.4: A Multi-Person PPF
The PPF for the whole economy, abcde, is obtained by allocatinig produc-
tive resources most efficiently. With many individuals we can think of the
PPF as the concave envelope of the individual capabilities.
The outputs V and F in our economic model require just one input – time. But the argument for a concave PPF where the economy uses machines, labour, land etc. to produce different products is the same. Furthermore, we generally interpret the PPF to define the output possibilities when it is running at its normal capacity. In this example, we consider a work week of 36 hours to be the ‘norm’. Yet it is still possible that the economy’s producers might work some additional time in exceptional circumstances, and this would increase total production possibilities. This event would be represented by an outward movement of the PPF.