Hi, I'm trying to learn opportunity cost and this is an image I took from Khanacadmeny. They said that due to the bowed out shape, it means that there is an increasing opportunity costs of production. Does it mean increasing opportunity cost of producing basketballs when the curves moves along the x axis? Such that at point(6,6), there is a greater opportunity cost of producing basketballs compared to (3,7.5), which is the efficient point located on the left? Would this also work in reverse? Such as the opportunity cost of making fidget spinners is higher at point (3,7.5) compared to (6,6) since you are giving up more basketballs? Thanks!
Yes your intuition is correct. The opportunity costs are represented by the slope of the curve, which increases (in absolute terms) as you go along the x-axis. Because if you "buy" some amount of "x" (move to the right along x-axis), you will have to give up some amount of "y", and you can see this rate dy/dx is getting steeper as you move more to the right implying higher opportunity costs.
Lets compare the point (3, 7.5) and (6,6) like you did in your question. At the point (6,6) you can give up 6 Spinners for 3 Basketballs, dy/dx=2. Whereas at point (3, 7.5) you need only to give up 1.5 Spinners to end up in (6,6) and thus gain 3 Basketballs, dy/dx=0.5. Implying that the higher x is the higher dy/dx is. Note that moving to the left along the x-axis gives the same conclusion, dy/dx = -dy/-dx. In a math class you should not work with dy/dx as I do in this answer, but it illustrates the point for this example rather nicely I think.
You are absolutely correct!
The PPC(Productions Possibilities Curve) can either be bowed out or constant. In the case you uploaded, it is a bowed out curve because the materials used to produce basketballs cannot directly translate to the production of spinners. In simple terms, this means that if all production were to stop for basketballs, would you be able to efficiently produce spinners? The answer is no, because the materials needed for basketballs cannot directly translate to spinners. Hence, the law of increasing opportunity cost.
To directly answer your question about there being a greater opportunity cost of producing basketballs at (6,6) as opposed to production at (3, 7.5), you are correct. Once again, this is made possible because of trade-offs. Production of basketballs is only possible by producing less of spinners and the same works in reverse.