[Music] welcome back to the fourth week in this week the first video is going to be about cost curve and this is going to be the final video on cost curve the previous videos are titled cost curve one and from cost curve to supply function so this video we will conclude our discussion on cost curve so in the last video last video of the last week we learned how to move from cost curve to supply function and we will do that quickly here this is what we had figured out we have taken two axis on this x axis we have quantity sometime we also indicate it using Y let me make it bigger so that it's clearer to you and then we were able to draw first average variable cost curve we also understood that average variable cost decreases when marginal cost is below average variable cost and average variable cost increases when marginal cost is above average variable cost and we also figured out that at very very low level say that at zero level the marginal cost is equal to average variable cost at that level so it helps us draw the marginal cost curve so it should look like and this is the marginal cost curve so that's what we had figured out and then we talked about Supply function so we said that for Supply function what we need to give Q as a function of p and this p is the market price of the item of the item on per unit basis so of course we already know higher the price higher is the willingness to Supply but using this graph we were able to quantify it clearly so first we figured out because you know if at this level of price we see the marginal cost curve can give us two different levels so which label to take and we had figured out that this particular label we should be taking and not the this one so from here we figured out that marginal upward sloping part of the marginal cost curve is really important so where is the upward sloping part this is the upward sloping part and so this can give us the supply function okay then we said that we have to be careful about one more item and that is that is firm should check the firm manager should check whether it is good idea to produce any output then setting down the operat having the zero output and that can be good idea when your marginal cost happens to be lower than average variable cost curve here it's not good idea to produce anything why it's not a good idea because you are not even able to recover your variable cost when you produce you incur variable cost and the price is so low that you are not even able to recover your variable cost from the market so you should not produce anything when your price is lower than average variable cost this is called setting down the operation why would you not care about fixed cost because fixed cost is already sunk in the short run you should not worry about it so then what is the conclusion the conclusion is very simple you should pay attention to the upward sloping part of the marginal cost curve that lies above average variable cost curve so simply speaking that P is equal to McQ because when we are drawing we have p on y AIS and Q on x axis so even when we say the supply function is Q as a function of P but when we are drawing we are drawing p as a function of Q and this curve is the basis marginal cost curve gives us that Supply fun function with two caveat that we just discussed that we have to pay attention to the upward sloping part and the part lies above average variable cost curve and that's how we get the supply function that is what we did uh during the last video of the last week now let us move further now we are going to talk about short run versus long run cost and we alluded to this in the last video also so little bit is revision but then we will also learn new things about it so we have this axis where let us say on x axis you have l and y axis you have K and then you can draw the iso cost curve remember the isoc cost curve are going to be parallel to one another this is the way isocost line will look like you know because how do we get the isocost line we take rk+ WL where R is price of one unit of renting the capital and W is the price of uh one unit of Labor in hourly basis or whichever unit that we are using so this is if we put it equal to a number let us say that number is C or C KN we get an isoquant by changing this c not we can get different isoquant so isoquant is basically the combination of capital and labor that cost us same in hiring so let us again take constant return to scale cob dougas function let us say for example K to the power half and L to the power half this gives us the output Q or Y whichever way you want to so we can say let us say we can say it like this let us let me draw and this is going to be let us say and some you know some we are drawing not all so this corresponds to q1 this corresponds to Q2 this corresponds to Q3 and we can say this is the optimal label of Labor Capital this is optimal label of Labor here this is optimal label of capital and this is the optimal level of labor and this is optimal level of capital okay let's make it bigger so that you are able to understand it well of course we are talking about long run why we are we talking about long run because we are able to vary both capital and labor in short run we we have discussed that we won't be able to vary Capital then what would be the situation let us say the situation is that capital is at K2 lbel this is you know let us say this is the way now what will happen here that if this is the case how much would be the cost to produce q1 unit of output if we pay attention to ISO cost it would cost this much to produce q1 label of output in the short run clearly we see the cost here in the short run is higher how about when we want to produce Q2 label of output in this case it so happens that K2 is optimal level of capital required and you will select L2 to produce Q2 label so short run total cost and long run total cost both would be equal what would be the case here if we draw the isocost line it will be something like this for Q3 of course it's high than this is the isocost line you know this combination K3 and L3 are on this isocost line but if you have fixed capital of K2 and you need to produce Q3 you need to come here and isocost line that you will be using is going to be higher so what did we figure out that in case of in case of q1 short run total cost is going to be more than wrong long run total cost in case of Q2 short run total cost is going to be equal to long run total cost and in case of Q3 short run total cost is again going to be higher than long run total cost it doesn't matter we started with K2 level of capital and therefore here both short run and long run are giving the same cost we could have started with key1 level of capital and in that case srtc1 that is short run total cost at q1 is going to be long run total cost at q1 and similarly if we had started with K3 the short run total cost at three is going to be equal to long run total cost at three and at all other level short run cost cost is going to be going to be higher then then the corresponding corresponding long run cost we can spend one minute to understand that why it is happening that why at K1 they are equal so long run total cost how are we getting this is not just any cost this is the optimal level of cost and this is basically the cost to hire L1 unit of Labor let us say here L1 unit of Labor and K1 unit of capital that's what you have done in the long run but in the short run you already have K1 level of capital and you are allowed to hire the optimal amount of Labor so you will hire L1 and therefore both would be equal but when you have given1 amount of capital and you want to produce Q2 amount of output q1 is not optimal you could have used more of more of capital that would have given you lower price lower cost but you are forced because in the short run you cannot change the capital immediately so you are forced to use K1 and therefore your total C cost in the short run case you know when you are using K1 you know here your short run cost in case of two is going to be your long run total cost in case of two so this logic is valid everywhere okay and that's why you are getting different cost structure so what we have figured out that short run total cost at label let us say label n is either equal or greater than corresponding long run total cost that's what we have learned now if we want to draw it in a graph that we have on x axis the amount of output and on the y axis we have total cost in short run as well as in long run so if we want to do it for the long run we have already learned that as we are taking the constant return to scale it's going to be linear as we have already learned that average cost long run average cost is constant in the case of constant return to scale and long run total cost is linear because if it's constant then it's going to be linear so it's going to look like this this is the long run total cost how about short run cost we figured out that if we use let us say the optimal value then the short run total cost either is going to be equal to long run total cost at corresponding level or it's going to be higher so we can get some like let us say this and this is the short run total cost but of course short run total cost here we have used let us say this is the Q not so for short run total cost Q not what we are using the optimal capital and that's why the short run and long run total cost are equal if I want to draw another short run total cost curve let us say at label of q1 what it means that at q1 let me use a different color so black so it's going to be something like this and let me write here s run total cost q1 here it's equal but at other place but how to figure out the way we have drawn and we are assuming that q1 is greater than Q what we are assuming that let us if we extend the curve this is going to be fixed cost and this is going to be you know fixed cost in the second case and what we have two things that we have figured out that short run total cost in q1 here the fixed cost is higher than let us say fixed cost at Q the other thing that we have figured out that the marginal cost at q1 is also greater than marginal cost at Q2 why because we see that average here the short run total cost at q1 is climbing at a smaller rate than short run total cost curve at q1 so we try to understand these two things in the next slide so first let us look at the fixed cost when we talk about short run total cost at q1 how are we getting the fixed cost the fixed cost is coming from coming from Capital so r K1 is the fixed cost this and manager is not allowed to vary okay so if you look at srtc Q not then RK KN and as we are assuming that K1 is greater than K KN of course R K1 is going to be RK so higher fixed cost mystery is solved total cost cost in the long run is simply r k KN plus WL KN if if the output is Q okay let us look at it so that part is clear now we have to look at the higher climb rate in one versus the other so let us look at from where are we getting the margin marginal cost in the short run what is the marginal cost the cost to produce one more unit one more unit so capital is already fixed capital in the short run is fixed so the variable so the variable part is coming from labor okay how much of Labor you need to produce one extra unit let us say marginal productivity of Labor is MPL what does it mean that one labor gives you MPL unit of extra output but we want just one extra unit of output so how many labor would be required the labor required would be 1 by MPL and so how much will it cost the cost marginal cost because a labor cost W so marginal cost is going to be W by MPL this is the marginal cost this is what we are getting as marginal cost that is the relation in the salt run now if let us say the way in the previous to previous graph we have used K3 is greater than K2 is greater than K1 or in the last graph we have used K1 is greater than K if we have higher amount of capital if Capital complements labor it means in presence of Labor in presence of capital labor has higher productivity we can say in if capital is fixed at K1 m is going to be higher than m0 it means Capital complement labor in that case of course higher the capital higher would be the denominator and lower would be the slope because slope is coming from the marginal cost so this is exactly what we do we say labor and capital the complement one another and MC is equal to W by MPL as in this case we have lower capital and therefore lower MPL and therefore higher marginal cost and that's how we get the slope so now the graph should be very very clear to you so now we have clarity about total cost in short run as well as in the long run let us look at the average cost as well as marginal cost in short run as well as in long run this we have already done marginal productivity and marginal cost we have already figured out so let us look at average cost so if we have the constant return to scale then long run average cost Curve will look like simply a straight line that we have figured out and now the short run average cost would depend on the amount of capital that a firm is using of course this is short run average cost for the first case when capital is lowest short run average cost for the capital is middle level short run average cost for Capital at higher level that's the way it would go and we will see long run average cost is going to be enveloping these short run average cost from below that's what we have figured out let us look at the graph once again at this point for Q not short run average cost and long run average cost both would be equal at all other places if capital is optimal for Q not then at all other places short run average cost let us say like for example this label the average short run average cost is going to be higher because this angle this is the total cost so this angle will give us average cost for long run and this angle will give us the average cost for short run so everywhere it's going to be higher the other case we can consider when long run average cost itself is first falling and then it's increasing so what we mean that here in this Zone we have economies of a scale scale and in this Zone we have dis economies of scale we have discussed about them here there is q that is increasing and then it's possible that we will have short run average cost curve like this and then this is the way we will have uh short run average cost curve this is in the case one this is case two and this is case three again these three are representative the way I'm drawing that only three levels of capitals are possible it's in reality it's possible that five levels of capital are possible and also it's possible in reality that Capital can also continuously vary so from here of course we already had logic that how would that marginal cost curve look like let us say we are talking about the case one only in that case the marginal cost Curve will pass through the bottom of short run average cost curve that we have drawn that's the way we had obtained the supply function and at this point let us say at this point the short run at this point the short run marginal cost curve marginal cost is going to be equal to let say here and this is the optimal let us say q1 but q1 Dash the marginal cost for both entity would be equal and this is the way it looks like so if we do it for the long run the marginal cost curve would be something like you know something like this let us say that marginal cost in this particular case is going like this so that's the way marginal cost curve would look like so one can say that how would long run look like if there are only three labels for example only three labels of capital possible let us say short run average cost curve is so this black is not possible because it it assumes that in long run we can vary Capital continuously so it's very very clear that it will look like this this is the way it would look like okay so I hope this concept about short run and long run are clear to you if there are doubts we can discuss it during live session this is very very important for you understand I'm willing to clarify these things once again if required but I would say it's very very important that you understand all these things best this is it for the cost curve thank you