So, so far, we've only drawn a production possibility frontier. that's a straight
line. And I'd like us to, be a little bit more sophisticated and think about this
assumption of a straight line production possibility frontier. And so, I'm gonna
change our story a little bit. And in particular, I want us to think about what
happens if, As Robinson Crusoe catches fish, catching fish gets harder and
harder. So, you could think in your mind about various reasons why this might be
the case. maybe, as he catches fish, he's depleting. This natural resources of
fishing. so there are few fish in the pond. And so it takes more of a candy bar
to catch the. Still remaining fish. it might be, I don't know maybe he gets
tired. The more candy bar he uses for fishing. And he gets distracted. And the
fish come, and they grab a bit, piece of candy bar without him noticing. Whatever
the reason is, I'm changing our story a little bit. And I'm assuming that, as he
uses candy bars for fishing, it gets harder and harder to catch fish. And what
I'd like us to think about is, what does this imply about the opportunity cost of
fishing? And what does this imply about the shape of the production possibility
frontier? So I asked you to think about what the production possibility frontier
would look like if Robinson Crusoe. Found that the more he fished, the harder and
harder it was to catch fish. In other words, the first candy bar maybe he could
catch ten fish, but with the second candy bar he could catch fewer fish, maybe nine
fish, and I'm sure. Many of you realized that in this case the production
possibility frontier would look something like this. In other words, in this case,
the production possibility frontier is the familiar shape of a production possibility
curve. Let's see how this curve illustrates the fact that fishing gets
harder and harder. If we look at the slope of this line, we can see that, in the
beginning, each candy bar that Robinson Crusoe uses. He gives up five birds. But
the reward is a relatively high reward, of ma ybe ten fish. Later on, with each of
the candy bars that he gives up, in terms of birding, he gives up the same number of
birds, five birds but the gain in terms of fish is much smaller, maybe he only gains
two fish. So what does this slope of these two lines or again, what is the absolute
value of the slope? So for this first segment, the absolute value of the slope,
it is five over ten or one-half. And we can see that over here, the absolute value
of the slope. Is five over two or it's equal to two one-half, in other words we
can see that as we move down the production possibility frontier, the
opportunity cost of whatever is on the horizontal axis, in this case the
opportunity cost of catching a fish, in terms of whatever is on the vertical axis,
which in this case is birds. The opportunity cost is increasing. So as we
move along the production possibility frontier, the cost of fishing in terms of
birds is getting higher and higher. So let me leave you with another question. And
the question is as follows. Suppose I changed my story. And instead of telling
you that as we catch more fish. Fishing gets harder and harder. Suppose I told you
that as we catch more birds, birding gets harder and harder. So with each candy bar
we could still catch ten fish, but as we use the candy bars toward birding, birding
becomes harder and harder and we catch fewer, fewer birds. What would my
production possibility frontier look like in such a case? So draw the same graph,
again put fish on the horizontal axis and put birds on the vertical axis and draw
that production possibility frontier.