Edited- Explanation for the convex shape of the PPC

The PPC is a grraphical way to represent the trade off between two goods - producing more of one while give up less of another - in an efficient way. The curve is in a downward slope, and curving outwards. The downward slope can be explained by the scarcity of resources. And also, when the resources are specialized, it is likely to be more productive than trying to produce certain quantity of both and therefore create the convex shape of the PPC. When the resouces to make guns are transferred to make butter, the output of butter does not equal to the amount of resource that guns given up (as shown in the diagram below). This is due to the law of increasing opportunity costs.  Each time that we transfer resources from the production of guns to butter, each additional unit of butter will cost more than the previous one.