Final answer:
The production possibilities curve (PPC) is concave to the origin due to the law of increasing opportunity costs, where producing more of good x means giving up more of good y. The absolute value of the slope indicates opportunity cost, and all choices on the PPC show productive efficiency, with different points indicating allocative efficiency.
Step-by-step explanation:
If producing each additional unit of good x requires giving up ever-increasing amounts of good y, the production possibilities curve (PPC) between x and y would be concave to the origin. This shape of the curve reflects the law of increasing opportunity cost, which states that as the production of one good increases, the opportunity cost of producing another good also increases due to the factors of production being not perfectly substitutable.
The absolute value of the slope of any PPC equals the opportunity cost of an additional unit of the good on the horizontal axis, which in this case is good x. As we move down the PPC to produce more of x, we give up increasingly larger amounts of y, thus the curve is bowed out. This effect is due to the law of diminishing returns, where additional resources put into production yield smaller increases in output.
Productive efficiency is indicated by any choice along the PPC, meaning no additional production of one good can occur without a reduction in the other good. However, the specific point on the PPC that society chooses based on its preferences is called allocative efficiency. Different countries may have PPCs with varying curvatures, indicating different comparative advantages, which can lead to gains in total production through specialization and trade.