Final answer:
A nation's production possibilities curve is bowed out due to the law of increasing opportunity costs which arise because of the scarcity of resources and the principle of comparative advantage, causing resources to be reallocated less efficiently as production shifts between goods.
Step-by-step explanation:
A nation's production possibilities curve is typically drawn as a curve, rather than a straight line, to illustrate the concept of increasing opportunity costs that arise from the allocation of scarce resources. When Alpine Sports, in our example, transfers resources from the production of one good (skis) to another (snowboards), the cost of producing an additional unit increases. This phenomenon is due to the principle of comparative advantage, where each resource is not equally efficient in producing every good. As a result, as more of one good is produced, the resources must be reallocated from the production of another good, for which they are potentially more suited.
The negative slope of the production possibilities curve signifies scarcity of resources, meaning that to produce more snowboards, we must sacrifice the production of skis and vice versa. As more and more production units are combined, like in the case of an expanding firm, the curve becomes smoother while still retaining its negative slope and bowed-out shape. This smoothed, bowed-out curve reflects the real-world economy where numerous firms and workers produce a range of goods.