The Community Production-Possibilities Curve

Prof. Michael Sproul, Econ 130, 12/99

The production-possibilities curves (PPC’s) of two individuals, A and B, are shown in figures 1.1 and 1.2. A has a comparative advantage at producing y, and B is best at x. As shown, A is producing 3x and 10y, while B is producing 12x and 4y. Note that the PPC’s extend beyond the axes, meaning that negative production is possible. At point R, for example, A is producing –4 units of x and 17 units of y. The interpretation of this is that A uses x as an input in producing y. In the case shown, A would have to be buying 4 units of x from someone, and using them to produce y. If he had been unable to buy x from anyone, the most y he could have produced would have been 15. The four purchased units of x enable him to produce 17y—two more than he could have produced without being able to buy x.

Figure 1.3 shows the construction of the community PPC, or CPPC. B’s curve is rotated 180 degrees and placed tangent to A’s curve, with a tangency at point P. If you placed a pencil at B’s origin, and slid B’s PPC along A’s PPC, the pencil would trace out the community production-possibilities curve CPPC. The condition that the two PPC’s are kept tangent to each other assures that production is efficient. The slope of any PPC equals the marginal cost of producing x, so if the slopes of the two PPC’s are equal, then A’s marginal cost of producing x is equal to B’s marginal cost, and production is efficient. As shown, A is producing 3x and 10y, while B produces 12x and 4y. The community produces 15x and 14y. If you have trouble visualizing the construction of the CPPC, try cutting out two pieces of paper shaped like the PPC’s of A and B. Then turn B’s PPC upside-down and slide it along A’s PPC. The corner (i.e., origin) of B’s PPC will trace out the CPPC.

Figure 1.4 shows the CPPC when one person is producing negative amounts of some good. As shown, A

produces –3x and 13y. This means he is buying 3x from B and using it to produce y. If he had not been able to buy x from B, the most y he could have produced would have been 9 units. B is producing 14x and 2y. The community as a whole is producing 11x and 15y. Note that even though B produces 14x, the community produces only 11x, because A uses up 3x in producing y. In both figures 1.3 and 1.4, you should note that when people specialize in x or y, their PPC is either relatively flat or steep. When you combine a specialist in x (flat PPC) with a specialist in y (steep PPC), the resulting CPPC is not as flat or steep as either individual PPC, but the CPPC is quite a bit larger than either PPC. This illustrates the gains from specialization, which is often called the Law of Comparative Advantage.

Figure 1.5 shows an individual whose PPC passes through the origin—meaning that he has no initial endowment of either x or y. (He does, however, have the ability to transform x into y or vice versa, and this is an ‘endowment’ of sorts.) This might represent the situation of a penniless immigrant. Even though he has nothing, he can still buy 8x from someone (on credit) and transform it into 15y. Assuming that x and y both sell for $1 each, he can earn an income of $7 and achieve the budget line shown. The location of point P, his productive optimum, is income-maximizing—that is, he has reached the highest budget line that he can reach with his PPC.

Figure 1.6 shows what happens when the penniless immigrant of figure 1.5 (call him B) moves into a community. B’s PPC is turned upside-down and placed tangent to the original CPPC at point P. Note that B’s origin does not coincide with the tangency point P. Thus, your imaginary pencil placed at B’s origin will trace out a new CPPC that is higher than the original one. The one exception is the point Q. At this point, as you slide B’s PPC along the original CPPC, B’s origin would coincide with the tangency point P, and the new CPPC would be no higher than the original CPPC. This means that a penniless immigrant whose PPC has exactly the same slope as the existing CPPC will not be able to make a living, nor will he add any goods to the community. However, this only occurs at point Q. At every other point, the immigrant earns a living, and raises community income. In a sense, there is no overpopulation problem in this world, since every new individual added to the community shifts the CPPC outward.