10. The Costs of Production
Isoquant Lines
10. The Costs of Production
Isoquant Lines - Video Tutorials & Practice Problems
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Isoquant Lines
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So let's discuss how we can make the same amount of production with different levels of inputs. These are called quant lines. So the idea is we're gonna try and produce some level of production. Say in this case 10,000 cookies, what we can hire a bunch of bakers or we can have a bunch of ovens or some combination of the two to make the same amount of production. Okay. So R. S. A. Quant curve. It's gonna show us all the combinations of two inputs that result in the same level of output. Okay, So in our example here we've got spooky cookies, bakes cookies. Using the information in the table below graph the ice A quant curves for spooky is production of cookies based on combinations of labor and capital. So generally when we deal with is a quant curves we're gonna be doing dealing with. Okay, if we hire more workers, we don't need as much capital or if we have a bunch of capital, we don't need as much workers. Right? If there's a lot of machinery that they can use, whereas, you know, robots that can be producing the cookies instead of labor or they hire a bunch of people instead of putting a lot of money into robots, something like that. Okay, so here we're gonna have our ovens, the amount of ovens that we have and the amount of bakers that we have making the cookies. So notice uh in our tables we're gonna have a certain level of production. Production of 500 cookies can be reached with any of these bundles of production, we're gonna call them bundles of production here. So in bundle a we have one oven and nine bakers which will make us 500 cookies. Right? We have a bunch of baker's preparing the cookies and then they all go in the oven or we can have more ovens so that more cookies can be baking at the same time and we need less uh bakers at that point. Right, So that's the idea here. So what we're gonna have is on one axis, we'll have the quantity of ovens over here, we'll have the quantity of ovens. And over here we'll have the quantity of labor. Okay, so the quantity of bakers that we have, so quantity of ovens and quantity of labor. So let's go ahead and graph our quant lines and that's just a matter of graphing these bundles. So let's start with bundles a through d. For a production level of 500 cookies. So if we have one oven we're gonna need nine. So that's nine out there. 56789, yep. Uh So that's a right there, that will be bundle a one oven and nine bakers. The next one we can have two ovens and we only need four bakers. Right? So let's go along here, let's grab all four of these points. So graph C bundle C would be ovens four and bakers too. So we'll put us right here, let's see. And finally bundle D. Is seven ovens, 567 and one baker. Right, so now there's tons of of ovens that they can all be cooking, baking the cookies at the same time and we only need one baker to be preparing them. Right. So that's kind of the idea here with the ice a quant lines, let's go ahead and graph the other ones here as well. So now notice we have a production level of 750 cookies. So you can imagine to produce more cookies we're gonna need either more labor or more ovens to to be able to handle this higher production level. So as you see in these bundles, let's go ahead and go through these bundles as well, bundle e notice we have to uh two ovens and 99 bakers. So by adding an extra whoops, that's not be that's e right there by adding an extra oven. These bakers can be more efficient and produced 7 50. And bundle F will be three ovens and five bakers. So that will come out to right here. It's bundle F. Excuse me, the next one, bundle G will have 55 ovens and three bakers put us right here and finally bundle H will have eight ovens and two bakers. So right here. So notice what these tell us, is that any of those E F. G or H. We're gonna be able to produce 750 cookies. So this becomes important because we want to be able to find the most cost efficient way to make our production right? We might do all this analysis and say hey we'll be able to sell 750 cookies. Let's find the best way we can produce those 750 cookies which is generally the most cost efficient way. Cool. So now let's go ahead and make our ice a quant lines. So notice it's ice a quant because isso means the same quantity quantity, right? The same amount of quantity. So any of these production levels makes the same quantity. Let's see if we can get a good ice a quant line here. So it's gonna be kind of curved like this and that's our quant line for 500 500 cookies will be that red line. And now notice our blue line is gonna be out here. And this should kind of be intuitive that the blue line the higher production Is gonna have higher use of resources. Right? In all cases we're gonna need more resources to be able to produce a higher amount of cookies. So that's why it's further away from the axis there and that's gonna be 750 cookies. Is that a quant line? So now we've made our I want lines for 500 cookies 750 cookies. So it's discussed. One more thing here when it comes to ice a quant lines it's this marginal rate of technical substitution. So this is the idea of we could substitute one um One input for another. Right? As as you saw up here, we can substitute labor for ovens and still end up like we could substitute some of our ovens here for more labor and we could still end up making 500 500 cookies. So this marginal rate of technical substitution tells us how much we would have to give up how much of one input we'd give up to get the other input in that case. Okay, so the marginal rate of technical substitution, it's very easy to calculate its just the slope Of the ice a quant curve at a point. Okay, so remember when we calculate slope, well, that's just the change in Y over change in X. You might remember it as rise over run when you studied algebra, it's very easy to calculate this. Let's go ahead. And for uh the the production of 500 cookies. So here we're talking about 500 cookies. Um Let's go ahead and do our marginal rate of technical substitution. So, when we're using seven ovens, so when we're using seven ovens, what is our marginal rate of technical substitution? Let's go ahead and check this out over here. So we've got seven ovens. So this was 567. And notice what we're doing, we're gonna substitute ovens. We're gonna get rid of three ovens and we're gonna hire one more baker. Right? So by getting rid of three ovens, we hire one more baker and we'll be able to make the same amount of production. So we had our rise was three and it doesn't have to be positive or negative here, we're just looking for a number 3/1. So the M. R. T. S. Is going to equal 3/1, which is three here, right? Three, we give up three ovens and hire one more labor uh to make the same amount of production. This can be useful in making calculations right of figuring out what is going to be most cost efficient. Maybe these ovens are really expensive right to maintain these ovens. So by we in this situation we can get rid of three ovens and just hire one more worker. This is probably good for the company. Right? So now let's go on to the 2nd, 2nd 1 where we we have four ovens. Right? So now we're at point C where we have four ovens and now we're getting rid of two ovens uh and hiring two more workers, so notice in this case we're not able to get rid of 33 ovens anymore and just hire one more worker. Now we by getting rid of two ovens, we now have to hire two more workers. Right? So it's not the same rate of substitution because maybe those um ovens were more efficient. Right? This this goes with those diminishing returns as we have tons and tons of ovens. Well they're not as efficient as when we have the right amount of ovens. Right. A good amount of ovens the more we add they're not gonna add as much to our production. Right? So that's what's happening in this case we we take away two ovens even though before we were able to get rid of three ovens and just hire one more person. Well now even by getting rid of two ovens we have to hire two more people. Okay so our marginal rate of technical substitution here is we got rid of two ovens, had to hire two people. So it's one here, 1 to 1 right we got rid of for each one we got rid of. We needed one more uh person hired. So last but not least we've got M. R. T. S. When we have two ovens. So that's here. We're already at b. We have two ovens and to keep the same level of production if we get rid of one oven notice, look how many more workers we're gonna have to hire to make up for that. We're gonna have to hire five more workers to make up for that oven loss. So you can see that those ovens become more and more useful when we have less of them. Right? So that's exactly what's going on here. That last oven that we got rid of. We needed a lot more workers to make up for that. So we got 1/5. Well that's that's gonna be an M. R. T. S. Right here is just gonna be the 1/5. So for each oven we got rid of. We needed five more workers in that case that's what's going on behind me. M. R. T. S. For each one oven we got rid of. We need to hire five more workers. Okay. So as you see here we had you tails there. You'll notice that this is very similar to when we study indifference curves. So if you have to study indifference curves as well, you'll see that what you learned with indifference curves. It makes a lot of sense and you can carry it over here with a quant lines as well. Alright, so that's about it for this discussion. Let's go ahead and move on to the next video.