# Production functions indicate the relationship between domains

For that, it is more convenient to describe the firm's technology in terms of a A production function simply describes for each vector of inputs the amount of output ratio of marginal products,. MRTSij (x) . Continuous on its domain. For all w. Production function Image or range. • Set of all output elements. Domain. • Set of all input elements Utility function indicates the level of satisfaction obtained. that they would be applicable but rather to suggest the hopelessness of any formal justification of an aggregate production function in capital and labor mathematical relation that links the output with the inputs and which .. domain r in which the above relation holds (numerator) and the total domain.

Comparative advantage and the gains from trade Video transcript Let's say we've been hanging out in scenario E for a bunch of days. On average, we've been catching one rabbit, but gathering berries. We were in, I guess, a berry mood. So this is scenario E right over here.

## Production possibilities curve

But now all of a sudden, we're in the mood for more protein. So let me write down, we are in scenario E. And we're in the mood for more protein. And so we want to think about what are the trade-offs if we try to catch more rabbits? So what I want to do-- I want to say, if I want to catch 1 more rabbit, what am I going to have to give up? So if I catch one more rabbit-- so I go from 1 rabbit on average to 2 rabbits a day.

So I'm really going from scenario E to scenario D. What am I going to give up? So this is plus 1 over here. Well, I'm going to give up 40 berries. And you can see it visually right here.

If I try to get 1 more rabbit, I can't go into this impossible, this unattainable part right over here. I have to stay on the production possibilities frontier, sometimes abbreviated as PPF.

But if I want 1 more rabbit, the production possibilities frontier drops off, and I will have to give up 40 fruit. So 1 more rabbit means that I have a cost. So I have to give up, on average, 40 berries. And the technical term for what I've just described is the opportunity cost of going after 1 more rabbit is giving up 40 berries. So let me write this down. The opportunity cost of 1 more rabbit-- and this is particular to scenario E. As we'll see, it's going to change depending on what scenario we are in, at least for this example.

But if you get 3 rabbits then all of a sudden you will to get-- or if you're only getting 3 rabbits, you're now able to get berries. And let's do a couple more. I'm going to do two more scenarios. So let's say Scenario D, if you reduce the amount of time you spend getting rabbits so you get 2 rabbits, now all of a sudden you have enough time on average to get berries. And then, let's say you spend even less time hunting for rabbits, on average.

Then you have even more time for berries.

- Opportunity cost
- Production function

And so you're able to get to berries and I'll do one more scenario here. So let's say Scenario F-- and let's call these the scenarios. Scenarios A through F. So Scenario F is you spend all your time looking for berries. In which case, on average, you're going to be able to get berries a day. But since you have no time for rabbits you aren't going to get any rabbits. So what I want to do is plot these.

And on one axis I'll have the number of rabbits. And on the other axis I'll have the number of berries. So let me do it right over here. So this axis, I will call this my rabbit axis, rabbits. That will be 0. And then this will be 1, 2, 3, 4, and then that will be 5 rabbits.

And then in this axis I will do the berries. So this right over here, let's make this berries. This is berries. And then this is berries. And so this is my berries axis. Now let's plot these points, these different scenarios. So first we have Scenario A. Maybe I should've done all these colors in that Scenario A color.

Scenario A, 5 rabbits, 0 berries. We are right over there. That is Scenario A. Scenario B, 4 rabbits, berries. That's right over there. So that is Scenario B. Scenario C, 3 rabbits, berries. Let's see this would be So 3, if you have time for 3 rabbits you have time for about berries on average.

So this is Scenario C. And then Scenario D we have in white. If you have time for 2 rabbits, you have time for berries. So that is right around there. So this is Scenario D. Actually, a little bit lower. So this would beso is a little bit lower than that. So it'll be right over there. That is Scenario D.

### Production function - Wikipedia

Scenario E, if you have time for 1 rabbit, you have time for berries. So that gets us right about there. That is Scenario E.

And then finally Scenario F. You are spending all of your time looking for berries. You have no time for rabbits. So all of your time for berries, no time for rabbits. So this is Scenario F. So what all of these points represent, these are all points-- now this is going to be a fancy word, but it's a very simple idea.

These are all points on you, as a hunter gatherer, on your production possibilities frontier. Because if we draw a line-- I just arbitrarily picked these scenarios. So these are all points on the different combinations between the trade offs of rabbits and berries. So let me connect all of these. Let me connect them in a color that I haven't used it.

So let me connect them. And do you see-- this should just be one curve. So I'll do it as a dotted line. It's easier for me to draw a dotted curve than a straight curve. So this right over here, this curve right over here, represents all the possible possibilities of combinations of rabbits and berries. I've only picked certain of them, but you could have a scenario right over here. And then maybe it looks like you would get about 50 berries in that situation.

So all of these are possibilities. You don't have to just jump from 4 rabbits to 5 rabbits. Or maybe in this scenario you're spending 7 hours and in this scenario you spend 8 hours. But you could spend 7 hours and a minute, or 7 hours and a second. So anything in between is possible and all of those possibilities are on this curve.