The Production Function and Diminishing Returns - Video Tutorials & Practice Problems
On a tight schedule?
Get a 10 bullets summary of the topic
The more we want, the less we get. This isn't an inspirational quote from Instagram; we're talking diminishing returns!
1
concept
The Production Function and Diminishing Returns
Video duration:
7m
Play a video:
All right now we're going to discuss the production function and see what happens as we add more and more workers into a production. Let's check it out. So the production function, it's gonna relate the amount of inputs, right? The amount of inputs in this case we're gonna talk about workers to the amount of output, right? The quantity that we produce. Okay. So we're gonna talk about the marginal product of labor. Okay. This term sounds pretty technical but we've got marginal here. Right? What happens when we add one more? And I like to think product of labor, marginal product of labor. It's like the fruits of our labor. I like to think of it as the fruits of our labor, right? It's an easy way to think of um what this means, right? So it's what happens when we add one more worker? How much are we gonna get out of it? What are the fruits of our labor? What are the fruits from adding one more worker here? Right so increase in output from adding one more worker. That's the marginal product of labor. We're gonna use M. P. L. Actually let me let me write that in blue. So it stands out a little more marginal product of labor mp with a little L there for labor, right? Marginal product of labor. So let's go ahead and calculate marginal product of labor in this example. So we've got a local pizza shop leases two pizza ovens. So they've got two pizza ovens at a total daily cost of $100. And then the pizza company is deciding how many employees to hire At a wage of $80 per day. Right? So we're gonna just say that these are their their costs, right? They don't have any other costs. We're not gonna talk about ingredients here. So it's just gonna be the ovens and the workers. Right? So let's go ahead and see what happens on this table and put it here in the middle of the screen. So we've got um on the left hand side, we have what's given to us. This these numbers have to be given first. We've got the number of pizza ovens, right? They told us we have two ovens. So we're always gonna have two ovens, and we're gonna add more and more workers. Right? So they tell us when we have zero workers? 123, how many pizzas are going to be produced by this many workers? Right? So you'll see when there's zero workers, there's no pizzas, right? There's just two ovens there and nobody's making any pizzas. And then we add workers and we start seeing pizzas being produced, Right? So we're gonna calculate our marginal product of labor, right? We're gonna see how many extra pizzazz we get when we add one more worker, Right? So when we have zero pizzas, we can't calculate a marginal product, there's no workers there, there's no additional. So let's go on to when there's one worker, When we add one worker, right? We had zero pizzas, and then we add one worker and we're gonna get up to 30 pizzas, right? So 30 from zero, we've added 30 pizzas, Right? So by hiring a worker, we've increased our production by 30 pizzas. Now, what happens when we hire a second worker? So the second worker, we already made 30 pizzas with one, right? We've started with 30 pizzas in this case, and now we're adding one more worker and it gets us up to 80. Right? So, the 80 minus the 30 pizzas we already had. That tells us that we've got 50 Extra Pizzas, right? That second worker made an extra 50 pizzas. So you can imagine that maybe when there was one worker, he had to do everything right? He had to toss the dough, put the ingredients, put it in the oven, box it up, talk to the customers right, he's doing everything. And now, when we've got two workers, they can kind of split up the tasks and they get a little more productive. Right? That second worker brought in more pizzas than the first worker. Now, what about the third worker? So, we had another worker into the mix. We had 80 pizzas, and now we're up to 1 50. Right? So the 150 minus the 80. We already had. That's gonna be our marginal product of labor from that third worker, right, that third worker is gonna add this difference which is 70 pizzas, right? 1 50 minus 80 that's the 70 pizzas that the third worker added. So you can imagine that now we're getting even more pizzas from adding a worker. So they're able to specialize even more. Maybe now one guy is just tossing pizzas, right? One guys dealing with the customers, the other ones putting them in the oven. Right? So, now let's say we add 1/4 worker into the mix, right? So we had 100 and 50 pizzas, and now it's getting us up to 1 80. Right? So, what you're gonna see here, 1 80 minus 1 50 that's only an extra 30 pizzas, right? So, you're seeing that as we added workers were getting more and more pizzas per worker. And now we added this fourth worker and we're back down to 30 right? He was only able to add another 30 pizzas and look at this last worker, right? We went from 1 80 to 1 90. So, by adding one more pizza. One more worker here at the end, right? From 4-5, we only get 10 extra pizzas. Right? So, you can imagine once we start adding a lot of workers, right? Remember we've still only got two ovens. So maybe those workers are now kind of stepping over each other. Maybe now they've made the pizzas, but the oven is full and they can't get another pizza in there. So you see that their their marginal product ends up getting smaller and smaller here, right? And this leads us to this law of diminishing returns. We've talked about these ideas of diminishing returns as we do more and more, but this exactly, it comes into play again right here with output, right? So what we see is that as we add more and more variable inputs, right? We keep adding more and more workers to the same amount of fixed inputs, right? We only have those two ovens, eventually the marginal product will decrease, right? Eventually it's gonna decrease. So what's happened is that since there's only these two ovens and now we've got a bunch of workers, they're kind of stepping all over each other, right? They can't be as productive as if there were less workers there. So you can imagine as we add more and more and more workers, there's just gonna be a point where there there's just so many workers in the in the bakery, right? They're all just kind of crammed in there and they can't do anything right? Their marginal products gonna get way down. So, that's kind of the law of diminishing returns there. Before we finish filling out this table. Let's talk about this production function a little more down here. So, what you'll see is we've got a graph and this this graph um it doesn't have the marginal product of labor on the axis. What we have down here is the quantity of workers, right? And up here is the total pizzas. So this graph, the production function, it's taking this column, right? The number of workers and the number of pizzas. So the marginal product of labor is actually the different the what's happening in these slopes, right? These slopes are what the marginal product of labor are. Um at the different different points here. So you'll see what the production function is showing us. Is this diminishing return, right? You can see as we added a few workers at the beginning, we had this slope up, right, It was sloping up and up very steep. But then we got to the diminishing returns right? Where we're getting less uh product per worker. And that's what happened here for four and 5. You see it's getting less steep again, right? And you can imagine it's gonna as we add more workers be less and less steep. Alright, so that's the diminishing returns. And what we're gonna see is as we add a few workers, we're gonna have positive returns, but then eventually it's gonna be worse and worse and worse. All right. Um So, that's gonna be it for the production function. Why don't we pause right here, and then start up in the next video, we'll go ahead and finish completing this table. Alright, let's do that. Now
2
concept
Calculating Fixed Cost, Variable Cost, and Average Total Cost
Video duration:
5m
Play a video:
Alright, cool. So we're back here on the table, let's go ahead and finish filling it in. So the next column here was fixed costs. And that's the cost of our ovens. Right? And this this problem, we just had the cost of the ovens and the cost of the workers. Right? So the fixed cost is gonna be the ovens, no matter how many pizzas we make those ovens are gonna cost us the same amount every day, Right? So it doesn't matter how many workers we have, how many pizzas we have, the ovens are always gonna cost us $100. Right? That was what it told us in the problem of daily cost of 100. So all of these, all the way down is gonna be 100. Right Now, what about our variable costs? So our variable costs go up as we make more and more output. Right? So as we um as we want to make more pizzas, we're gonna need to hire more workers. So when we were hiring zero workers, right, our variable costs were zero because we didn't hire any workers, but then we hired our first worker and it tells us that the wage is $80 per day per worker. So the one worker is gonna get $80 here Two workers right now we're paying two workers, $80, and that's gonna get us 160, right, 80 times two. And the next one, we have three workers, so we're just gonna do 80 times three workers, right? So that's 2 40 then four workers, it's gonna be 80 times four workers. Right? So you see what's happening here, we're just multiplying the number of workers, Right? It's gonna be the number of workers times the wage. That's gonna be our fixed cost. So this last one here, we've got five workers. Uh So we've got five workers times the wage of 80. That's gonna get us up to lips, That gets us up to 480 times five is 400. So there we go to get our total costs. We just have to add our fixed costs plus our variable costs. Right? So that's gonna be our total cost. So we just have to add across here 100 plus zero is 100 100 plus 80 is 1 80 100 plus 1 62 60 100 plus to 40 is 3 40. Right? So this is pretty easy here for 20 And last but not least 100 plus 400 is 500. Cool. Alright, so the last column here is the average cost per pizza. Right? How do we find average cost? Well, that's when we divide by quantity, right, and this is average total cost, right? Average total cost. I'm gonna put this tea here for average total cost. So, we're just gonna take our total cost, column and divided by quantity. Alright. And that's how we're gonna get these numbers here. So the first one we had 100 total cost but we didn't make any pizzas. So if we didn't make any pizzas, we're not gonna have an average cost. We're just gonna leave that one empty. How about the next one? We had $180 for 30 pizzas. So we would do 100 and 80 divided by 30. And we're gonna get $6 as our average cost per pizza there. Right? So if we did the $6 times 2 30 pizzas that we made it would get us to that total cost of 100 and 80. Right? So the next one, we had 260 in total cost, divided by 80. Right? We had 80 pizzas when we had two workers. So to 60 divided by 80 gets us $3.25 per pizza. Right, Let's go on to the next one. We've got 340 in total cost, divided by the 150 pizzas in this case. Right, We made 100 and 50 pizzas. So each pizza costs us $2 and I'll round it here 27 cents. Right? $2.27. So, let's keep this up for 20. Right? The next 14 workers, we have 4 20 in total cost divided by 1 80. The amount of pizzas. And we're gonna get a total cost here of 2:33. The last but not least. We've got 500 in total cost divided by 190. And that gets us a total cost or average cost. Excuse me. $2.63. So, look what's been happening here as the marginal product was rising, right? We saw this marginal product going up well here, the average cost is going down as that marginal product is rising, and then that marginal product starts falling again, right? And as that marginal product falls, that price go right. And the reason here is that we're getting less from each worker, right? Once that marginal product starts falling, we're getting less value from adding a worker. So that's causing the price to increase, Right? So, as we're getting more and more value from adding workers, the price goes down and then we start getting less value from the diminishing returns and the price starts going back up. Cool, Alright, so let's go ahead and move on to the next video.
