为什么两种商品是由相同的生产函数生产的，生产可能性边界就是一条直线

Give an example of conditions when the production possibilities frontier might not be
concave.

The production possibilities frontier is concave if at least one of the production functions exhibits decreasing returns to scale.

If both production functions exhibit constant returns to scale, then the production possibilities frontier is a straight line. If both production functions exhibit increasing returns to scale, then the production function is convex.

The following numerical examples can be used to illustrate this concept. Assume that L = 5 is the fixed labor input, and X and Y are the two goods. The first example is the decreasing returns to scale case, the second example is the constant returns to scale case, and the third example is the increasing returns to scale case. Note further that it is not necessary that both products have identical production functions.

楼上回答的比我好。。这个倒没有什么可纠结的

现在回头看看觉得画图说话比较客观，但还是说不清道理，例证向来不是最终方案。

还是应该用宽泛的生产函数和规模报酬的基本表达来证明。慢慢研究。