Final answer:
A downward-sloping production possibilities curve represents scarcity of resources and opportunity costs in producing two goods, such as skis and snowboards. Each point signifies a trade-off, where producing more of one good results in less of the other due to the negative slope and concave shape of the curve.
Step-by-step explanation:
If the production possibilities curve is downward-sloping, this indicates that there are limits to what a production facility can produce due to the scarcity of resources such as capital and labor. As more of one product is made, such as snowboards, resources have to be shifted away from making another product, like skis, which results in producing fewer skis. This trade-off is represented by every point on the curve, illustrating that increasing the production of one good comes at the cost of producing less of the other good.
This fundamental economic principle is shown by a curve that typically has a negative slope and is bowed out or concave. The concave shape is due to the law of increasing opportunity cost, which states that as production of one good expands, the opportunity cost of producing additional units of this good increases. Therefore, each successive point on the production possibilities curve will cost more of the other good, indicating that resources are not perfectly adaptable for the production of both goods.
Economists use this curve to illustrate the production trade-offs and opportunity costs within an economy. The absolute value of the slope denotes the opportunity cost of producing an additional unit of the good on the horizontal axis.