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Current time:0:00Total duration:10:29

AP.MICRO:

PRD‑4 (EU)

, PRD‑4.C (LO)

, PRD‑4.C.1 (EK)

, PRD‑4.C.2 (EK)

, PRD‑4.C.3 (EK)

, PRD‑4.C.4 (EK)

we are now going to continue our discussion of factor markets and we're going to go beyond just thinking about labor as a factor in fact in this video we'll are going to start thinking about capital as well which we know is another one of the factors of production but just as a little bit of review we've already thought about it from a firm's perspective on what is the rational amount of Labor to hire based on the marginal revenue product of labor and based on the marginal factor cost of labour so in the horizontal axis we have the quantity of labour hired by the firm and in the vertical axis you have the wage rate wage rate which you could view as the price of labour and we've seen this multiple times you are likely to have a downward sloping marginal revenue product curve m RP and I'm going to be very specific that this one is the marginal revenue product of labor and then we have the marginal factor cost curve and if we're assuming that this firm is in a competitive perfectly competitive labor market well they're just going to have to pay whatever the wage is in the market and so that's why we have a horizontal line there so that's the marginal factor cost of labour and we've talked about multiple times that it's rational for the firm to keep hiring as long as the marginal revenue product of labor as long as the incremental revenue that the firm gets for each of those people or each of those units of labour that they hire is higher than the incremental cost of each of those units of labour and so it'll keep hiring until these two lines intersect and so it would be rational for it to hire that quantity of labour I'll do this as the labor for the firm and I'll put a little star over here so that quantity of labour and we can draw an analogous thing for capital so this is how a firm thinks about that input how thinks about labour but we could also do something similar for capital or we could do it for it land as well but hopefully so this is going to be the firm the firm as they think about capital and we'll see that they have analogous axis the horizontal axis right over here is going to be the quantity not of labor but the quantity of capital and then the vertical axis the price of capital you could view that as the rent rate rent or H if you're thinking about maybe you're renting some type of machinery and so you will have your marginal revenue product of capital we could still imagine that you have diminishing returns so that's why it's downward sloping so marginal revenue product and we typically use a K for capital just to we don't get the C confused with other things and then we have our marginal factor cost which is really just and we'll assume once again that this is a perfectly competitive capital market so you just have to pay whatever the market rate for renting that capital is and so that would be the marginal factor cost of the capital and so once again it makes sense to keep bringing on more and more and more capital as long as the incremental revenue that you get from each of those extra units of capital is higher than the cost of each of those extra units of capital and so here it would be rational for the firm if we were just looking at the dimension of capital to produce this much so this would be actually let me this would be the capital the quantity of capital for the firm to employ now an interesting question that might have already crossed your minds are is that firms have a certain amount of resources that they they are going to think about well how much do I put in labor versus how much do I put into capital so they don't just think about these these dimensions of how many how much inputs of these factors they want they have to think about them relative to each other and to help us think through this let's say that we are at a certain level of output so let's say that our output right now I don't know our current output our current output is I'm just going to make up something 1,000 units per day and at our current output we know what the marginal product of labor and the marginal product of capital is let's say that we know that our marginal product of labor at this output remember it changes as we have very different output and we bring on more labor or more capital so our marginal product of labor at that level is 90 units so another way to think about it for every incremental unit of labor we bring on we're going to be able to produce 90 more units of output so this is and then let's say that the price of labor which is the wage rate is equal to ten dollars ten dollars per unit of labour so let me call this output units output units and let's say that the marginal product of capital I'm just in a different color the marginal product of capital right now is 80 output units output units so every unit of this factor of capital we are able to produce an incremental 80 output units and let's say that the price of capital which would be the rent is equal to five dollars five dollars per input unit of the factor so at right at this moment if I have an incremental dollar would it be more rational for me to add more labour or would it be more rational for me to add more capital pause this video and see if you can figure that out well to think about which one is more rational you just ever think about which one do I get more of a bang for my buck so per dollar how many output units do I get when I put a dollar into labor versus per dollar how many output units do I get when I put that dollar into capital so let's do it first for labor so if you want your bang for the buck so to speak you would just take your marginal I'm just in a different color if you want your bang for a buck you would just take your marginal product of labor so your output and divide it by the price so this is going to tell you output per dollar and so in this situation it's ninety output units could we could say you widgets for a general term for output units output units over ten dollars over ten dollars and so this is going to be equal to nine output units per dollar so this is equal to nine output units per dollar so that's our measure of our bang per bang for our buck when we put an incremental buck into labor now what about for capital well our marginal product of capital divided by the price of capital right at this moment remember it changes depending on our output level and different combinations it's going to be equal to eighty output units divided by five dollars which is equal to 16 output units per dollar so which one would I get a better bang for my buck well right at this moment I'm getting a better bang for my buck from investing in capital every extra dollar I put I get 16 output units so it'd be rational for this firm that wants to maximize its profit and reduce its cost if it has an extra dollar to invest it would put it into capital and so maybe it puts it into capital and then it gets a little bit more output and then the marginal product of capital is likely to go down and so you could imagine at some point these things might be equal and then the firm might be indifferent between the two and then it may be at some point if they keep kept adding a capital then maybe the you get a better bang for your buck from the labor in general a firm would want to keep investing in one or the other until these two things are equal to each other so big picture you would look at the marginal product of the factor divided by the price of the factor and then you'd compare that to the marginal product of the other factors divided by the price of those other factors and whichever one has the best bang for the buck that's where it would be rational to invest in and then you have in some ways your one way is a very efficient combination is if you are you get to that point that you're indifferent when the marginal product divided by the prices of the various factors are equal to each other so for example if I were to tell you that we're at a different point of production let me let me cordon this off so for at a different level of production where our marginal product of labor is equal to I'll call it ten widgets it sees time and let's say that the price of labor is equal to five dollars and let's say that the price of capital is equal to ten dollars what would have to be the marginal product of capital for me to be indifferent between labor and capital pause this video and try to figure that out well in order for me to be indifferent right over here that means my marginal product of labor divided by price of labor needs to be equal to my marginal product of capital divided by my price of capital and so I would have 1000 over five would have to be equal to my marginal product of capital over 10 so 10 over five this is two widgets per dollar and so if I want to widgets per dollar over here this has got to be equal to 20 so at this point I'm indifferent between producing between bringing on more capital versus labor because in either case every dollar I bring on if the marginal product of capital is 20 then I'm able to forget two widgets per dollar of investing in either factor

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