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“So why don t you get here their number. I got so when you actually actually solve the same equation. But this time for q. Equals.
225. Instead of 50 are the new numbers of labor. You get laid when capital is 20 labour s 31. When capital is 50 labor.
13. When capitals 100 labor is six when capital is 125 labor is 5. And you take these new numbers and plot them in the same diagram while you get is a curve like this red curve. Right here.
Which has the same shape as the original aiesec. 1. When q was equal to 50. But it s closer to the origin and if you have done this for q.
Equals. 75. You would have gotten the same curve. But this time to the right of the origin.
So basically this is like the utility curve right when they are output is larger. The aiesec. One is going to shift to the right when high when output is smaller. The iso coin would shift to the left and along the isoquant it s the same output.
But with different combinations of the inputs all right now let s connect let s go a little more detail about this i soaked. One stuff. So let s go back and put the same numbers in here. So career gets created this here.
So i more space to work and get rid. I wanna get that one let s get rid of one there and the real numbers. We have for output was when output was equal to 50 and this was 125 this was 50 this was 25 and this was 20. Now let s focus a little bit on there and the slope of the isoquant.
Which going to have a really important implication for production. So you know that along the isoquant along the isoquant. What i just told you is that that the change in output is going to be the same so that means that when you let s say you re moving from you know from from a to b right. So let s say you re moving from this point to this point.
So. What you what you re going to gain. Some capital and you re going to lose some labor right so so you re gaining in capital is going to be well. It s going to be versus.
It s going to be the increase in capital times. The the amount of output that you get every time you increase your capital by one and that we know we call them marginal productivity in this case of capital and that s going to be negative since we are actually losing capital if we re moving from a to b. But we are actually gaining labor. So we had to add that to our output.
We re getting we gain an output from the additional labor we lose in output because we are losing some capital. But we re going to replace that output with additional labor and that the increasing in output from labor is going to be equal to well whatever more labor. We re going to add times how much output. We get for every additional units of labor.
Which is the marginal productivity of labour. So in essence. What you ve what you have is that the change in output is going to be equal to the marginal productivity of capital times. The change in capital and the marginal productivity of labour times.
The changing labor. But you already know that the change in output alone. I so quite is zero. So essentially what you have here is that along the i so kwan these two terms are essentially the same right because if out is the change in output is zero.
And i bring one of this term to the other side. What i have is this change in capital times marginal productivity of capital equals change in labor times marginal productivity of labor. If the change in capital is zero and since all i want to do here is to focus on the slope of this curve. Which is changing capital.
We re changing labor. Let s solve for that so first of all we re going to divide this by the marginal productivity of capital. So we re going to end up with change in capital equals changing labor times. The marginal productivity of labour divided by the marginal productivity of capital and now since what we want is the slope let s divide again this whole thing by the change in labor.
We re going to end up with the changing capital over the change in labor equals. The marginal productivity of labour. The marginal productivity of capital. This is a really interesting and useful result so in here.
What are we having here. We have the slope of the isoquant changing k. Over. Changing l.
Change on the y axis. Change over over change in the horizontal axis and that is telling me that the slope of the isoquant is going to be the same as the ratio of the marginal productivity of labour to capital does that make sense well think about it. But we you said before is that when this when this slope is actually very high a large in absolute terms. When you have very little labor.
Every additional unit of labour replaces. A lot of capital so that means that when you have very little labor. This number. The module productivity of labour will be high and the marginal productivity of capital is going to be low so this slope.
Which is a ratio the marginal productivity is going to be small so that makes a lot of sense now when the this ratio. The change in capital. A change in slaver is actually very small in absolute terms. We look up here that s when you be let s say somewhere around studios in red that will be when you re let s say around here and at that point how much how productive is labour.
Well according to this this this value has to be small so the marginal productivity of labour had to be actually pretty low and the more productivity of capital have to be high. If not this ratio here is not going to be this equal to this slope. And that makes a lot of sense. That s exactly how it is because we know that when you have a lot of labour.
When you are a and you want to move to b you re going to need a lot more labour to actually replace a capital than when you actually have very little labor. So that s because in my your particular labor is actually very low. When you actually have a lot of labour. So you need a lot more units of labour to replace for capital.
When you re moving from a to b. Let s say from b to b to a you re going to need 75 units of labor to replace 30 units of capital. Which is a lot more than you will need if you re moving from d to c. Which is when you have very little labor from d to c.
Five units of labor. Replaces 25. Units of capital. So these results makes complete sense right the slope of the isoquant is going to be equal to the ratio.
The marginal productivity of labour and when you have very little labor. The manual productivity of labour is going to be high which means the slope of the isoquant will be high in absolute terms. But when you have a lot of a lot of labour. Very little capital the marginal productivity of labour will be low the marginal productivity of capital will be high and your slope will be low in absolute terms.
We call this since since this slope it really tells you how much labour. You need to replace capital or vice versa. We call it the marginal rate of technical substitution. Very similar to the name that economies have for the utility function right.
Which is a marginal rate of substitution well in here since we are actually dealing with inputs. We solve some sort of measure of technology. We are calling it the marginal rate of technical substitution. Which is the slope of the isoquant and in any point.
It will tell you how much unit of one input. You need to replace the other input while keeping the output. The same marginal rate of technical substitution okay in the next video. I m going to show you how to do ” .
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