I’ve just begun a cost on economics and we’re now at opportunity cost. We’ve learnt the production possibility curve/frontier/boundary, and how the opportunity cost for producing one more X, in terms of Y, increases as more X is produced.
However, I’m confused as to why this is the case. Apparently, that’s because by the time that amount of X is produced, the better factors/inputs have been used up, and we’re left with less efficient inputs for the production of more Xs. However, I also know that in economies of scale, the more X is produced, the lower the costs.
Your question is worded sort of confusingly, but I’m going to take a shot at what you are confused about - economies of scale.
In an economy of scale for X, the cost for producing X will go down, at first. However, at some point, the cost curve will begin to curve upwards again as resources, etc. begin to run out and the cost for materials and production begins to climb. So, if you are looking at a cost curve you will see it drop as you go the right, but make a big enough curve, at some point it will begin to climb back up.
There is also an issue of supply vs demand. In general, as more of X is produced and is available, the cost of X drops. Sure, your manufacturing cost may be lower but since you are selling at a lower price (since that is all the market will bear) your margin on each unit of X will drop.
At some point, you can make more profit by manufacturing Ys instead of more Xs.
At any point on the curve, producing the next unit of X will give you a profit of X[sub]p[/sub]. Producing a unit of Y will give you profit Y[sub]p[/sub]. The difference between these two is the opportunity cost.
If X starts selling for cheaply enough and Y is still relatively expensive, you are actually losing money by continuing to manufacture more of X, no matter how cheaply you can make it.
The production possiblities frontier doesn’t have to be that shape. It could be a straight line (such as in Ricardian trade theory), or convex to the origin (increasing returns). The concave to the origin PPF reflects “generalised diminishing returns”. This is a bit of a fudge for teaching purposes in a simple 2 good 2 factor story. Underlying this fudge is the idea that some factors of production are better used in the production of some goods rather than others.
The reason the fudge is used is to avoid corner solutions. This is (a) realistic, and (b) allows you to focus on the first order conditions for solving optimisation problems.
[hijack]If IIRC the area under the PPF, including the boundry, is the production possibilities set, correct? For the “bowed out” PPF, this set is convex since any two points in it can be connected by a line that doesn’t leave the set, but the PPF function, i.e. the boundry of the set, is concave since f(aX + (1-a)Y) > af(X) + (1-a)f(Y), where X & Y are arguments in the domain (?) and X doesn’t equal Y. Is that correct?[/hijack]
That also has something to do with marginal costs.
Lets say you have an assembly line to produce Gadgets. Initially, it will be easy to add more workers to make more Gadgets. However, it will be more and more difficult to do so, as there is limited room, and more people will only get in each other’s way. However, since wages are fixed, you will get the “bowed out” curve.