 We will continue our discussion on theory of production cost. So, if you remember in the last class, we are discussing about the short run and long run cost analysis. We just introduced the short run cost analysis. In today's class, we will talk about the long run cost analysis, how long run cost curves are derived from the short run cost curve. Then we will talk about the break event analysis and learning curve. So, if you remember this is the topics what we discussed in the last class like we introduced the production cost, different type of cost in both accounting sense and economic analysis sense. Then we discussed about the cost and output relationship specifically in the context of short run cost analysis. In today's class, we will talk about the long run cost output relationship, break event analysis in case of linear cost and revenue function and break event analysis in case of non-linear cost and revenue function. So, as you know, I think we have already differentiated the difference between the short run and long run. One is the time specific and second in case of typically in case of production analysis, short run long run is on the basis of classification of the how the inputs behave, whether the inputs they are fixed or whether input they are the variable input. In case of short run, at least there is one input has to be fixed, but in case of long run all input has to be variable, which implies that when the output increases it and there is a requirement to change all the inputs or may be in the other to put it in the other way, when all input changes then only the output changes or may be we can take another implication of this that the change in the output is large. So, it cannot be changed only by changing few inputs all input has to be changed. So, long run is a period for which all input change are become variable and long run cost output relation implies the relationship between the changing scale of firms and firms total output. So, if it is come to a cost output relationship in case of long run, it is basically a relationship between the changing scale of firm and the firms total output. Whereas, if you look at in case of short run, generally the relationship is not the scale relationship rather it is the change in the output or change in the input with respect to a change in the output. So, it is one between the total output and in the specifically the variable cost. So, in case of long run it is a scale relationship and in case of short run this is a one to one relationship between the total output and the variable cost and the variable cost includes the raw material and the labor. And when it comes coming to the cost curve of the long run total cost or may be the long run cost all together this is composed of a series of short run cost curve. So, when you take a series or when you take a more than may be 2, 3 short run cost curve that gives us the long run cost curve. Assume that firm has only one plant with the corresponding short run cost curve given by suppose STC 1 that is short run cost curve in one period. And suppose the firm decide to add two more plants with associated two more short run cost curve given by STC 2 and STC 3. If you take both all this STC 1 that is cost curve in one short run, STC 2 that is cost curve in the second short run and STC 3 that is the cost curve in the third short run and all together STC 1, STC 2 and STC 3 they will they will come they will may be they will leads to the long run total cost curve. And similarly the long run average cost curve is also derived from the combining the short run average cost curve. So, this is the long run total cost and if you look at how this has been derived this long run total cost curve. This is as we say that this is the combination or may be this is the combination of a series of short run cost curve. And how this cost short run cost curve is derived? Suppose the output is 100 unit. So, by changing variable unit only the output can achieve up to 100 units. So, this is one short run cost curve. When the output which can be maximum change by 200 unit by changing the variable that is another short run cost curve or may be when the output can be changed by 500 unit of output by changing only the variable unit that is another short run cost curve. So, for a specific output level keeping the fixed input only the changing variable input how much maximum output can be increased that consist of one short run cost curve. So, taking a series of short run cost curve at different level of output that gives us the long run total cost curve. Now, we will see how the long run total cost can be derived from the short run cost curve at the different level of output. So, here we can say the output here we can say the total cost. So, may be we have one short run cost curve that is STC 1, may be we have another short run cost curve that is STC 2 or may be we have one more short run cost curve that is STC 3. So, when you join or sum together of all this short run cost curve that gives us the long run total cost curve. So, STC 1, STC 2 and STC 3. So, if you look at this is corresponding to may be this is Q 1 level of output, this is Q 2 level of output and this is Q 3 level of output. So, corresponding to Q 1 level of output the cost curve is STC 1, corresponding to Q 2 level of output the short run cost curve is STC 3. Short run cost curve is STC 2 and corresponding to Q 3 level of output the short run cost curve is STC 3. Taking all together all these three we get the long run total cost curve. So, long run total cost curve is the series of short run cost curve at the different level of output. Similarly, if you look at we can also derive the long run average cost curve taking the series of the short run average cost curve. This is x axis will take output, y axis will take the average cost since we are drawing the long run average cost curve. So, similarly we get a short run average cost curve here, then short run average cost curve 2 and similarly the short run average cost curve 3. So, corresponding to that we get 3 level of output because that leads to 3 level of cost curve. So, this is SSC 1, SSC 2, SSC 3 and this is long run average cost curve. So, the edge we can derive the long run total cost curve from the series of total short run total cost curve. Similarly, we can also derive the short run average cost curve from the series of short run average cost curve. We can try the long run average cost curve and long run average cost curve is nothing but the series of the short run average cost curve at different level of output. Specifically in this case if you look at it is Q 1, Q 2, Q 3 which keeps 3 different level of output. So, now we will see what is the relationship between the short run and long run average cost curve. So, long run average cost curve shows the minimum average cost at each level of output when inputs are variable that is when a firm can have any plant size at one. So, there is a relationship between the long run average cost curve and the firm set of short run average cost curve. So, as we say that the long run average cost curve is the minimum average cost at each output level when inputs are variable. So, whether if you look at this SSC 1, SSD 2 and SSC 3 it gives 3 different level of variable cost and that is why this long run average cost curve takes out the minimum of average cost at each short run level of output and it gives the minimum average cost of each output level when the variable inputs or some inputs are at least variable. When it comes to the economic analysis of the short run and long run how they are related to each other, economics specifically use the term plant size to talk about having a particular amount of fixed input. So, choosing a different amount of plant equipment that is plant size, amount to choosing an amount of fixed cost. So, if the amount if you look at choosing a different amount of plant and equipment if it is a large plant obviously large amount of fixed input is required. If it is a small plant then it is a small may be the less amount of inputs are is required and that correspondingly has some amount has some in fact that correspondingly lead to the amount of the fixed cost. So, if it is a large plant there is a large fixed cost if it is a small plant that is a small fixed cost and since they use the term plant size. So, if the plant size is large fixed cost is more and it is in a different short run cost curve. If the plant size is less then it is a less fixed cost and the plant size is again different. So, generally that is the reason the plant size is a reference point for the short run average cost curve with regards to the fixed input and with regards to the fixed cost. So, economics want you to think of fixed cost as being associated with the plant and equipment bigger plant have large fixed cost and vice versa smaller plant has the less fixed cost. So, it always the may be when you are thinking about the cost of production the fixed cost and the variable cost of production always the plant size is in the back of the mind that what is the plant size because that has a direct impact on the fixed cost of the production at least the initial stages of production. So, each plant is associated with a different amount of fixed cost. If it is a large plant large fixed cost if it is a small plant this there is less fixed cost. So, each plant size is associated with a different amount of fixed cost then each plant size for a firm will give a different short run cost curve. So, if you look at in the previous graph also we are explaining the short run total cost curve 1, 2, 3 how they differ from each other they differ from one they differ from each other on the basis of output and second they differ from each other on the basis of the cost. So, obviously, if the output level is higher then the fixed unit is higher and also the variable input is higher and if it is a small then the fixed and variable cost is also differ. So, in this case STC 1, STC 2, STC 3 there shows three different level of output and also different level of cost. So, each plant size is associated with a different level of fixed cost and each plant size of a firm will give us a different shape of short run cost curve. Choosing a different plant size that is a long run decision then means moving from one short run cost curve to another or to simplify this when you are moving the output level or when you are trying to increase the output level from one level to another level basically it is a transition from one short run cost curve which is at the lower level of output to another short run cost curve which is a higher level of output. So, this is the typical example of the long run average cost curve and economics usually assume that the plant size is infinitely divisible that is variable and each small use curve is a short run average cost curve and this is the long run average cost curve. In the x axis we are taking the average cost for a firm and the y axis we are taking the maybe in the x axis sorry where x axis we are taking the average cost of the firm and the y axis we are taking the level of output. So, long run average cost curve is the summation of each small use shape short run average cost curve which is different from each other in two aspect in term of variable and in term of the different output and in term of the cost associated with that level of output. Then when it comes to formalizing the long run total cost curve. So, till the time we are assuming that the long run total cost curve or the cost curve altogether is a q is a function of labour and capital. When it comes to cost of production what is the expenses the firm they are incurring when they are producing a product. So, the major expenses come from the input to produce the product that is labour and capital. So, labour is the payment whatever we make to use labour as the input of products on that is wages and k whatever the payment we are spending on k that is comes as the interest rate. So, if you take W as the wages R is the interest rate then long run total cost is W L plus R k W is the payment for using labour L is the quantity of labour input R is the payment using capital k is the quantity of capital input. So, W is the payment for labour L is the quantity of labour. So, this is price this is quantity again this is price this is quantity. So, this is a quantity of labour input this is price of labour input and long run total cost long run total cost is equal to the whatever the payment or whatever the cost of expenses what the firm is incurring on the two different level of output. So, long run total cost curve is W L plus R k where W and R as the price of labour and capital respectively and L at k is the input combination the expansion path that minimizes the total cost of producing output. Why we take the input combination on expansion path? Because that gives us the optimal production with the minimum cost of production and that is the reason we take the input combination the expansion path because that gives us the optimal output keeping the cost constant in the background. Then how to measure the long run average cost curve or algebraically how we can find out the long run average cost curve? It measures the cost per unit of output when production can be adjusted. So, that optimal output of each input is employed. So, long run average cost curve measure the cost per unit of output when production can be adjusted. So, that optimal amount of each input is employed. So, long run average cost curve is long run total cost curve divided by the Q. So, Q is the unit of output long run average cost curve is U safe increase decreasing long run average cost curve indicates economies of scale and increasing long run average cost curve indicates the disequenomics of scale. We will discuss more on this economies of scale and disequenomics scale at a later point of time specifically what are the economies of scale different type of economies of scale and what are the different type of disequenomics of scale. How economies of scale leads to decrease in the cost of production and how disequenomics of scale leads to increase in the cost of production. So, economies of scale is basically what is the meaning of economies of scale when output increases long run average cost curve decreases and that is the reason the long run average cost curve is decreasing at the initial scale and that is because of economies of scale. So, in if it is a case of U safe long run average cost curve then at the initial stages when it is decreasing if you take output here cost of production here then generally the long run average cost curve which follow a U shape where this because of economies of scale the decreasing part is economies of scale and the increasing part is disequenomics of scale. So, what is economies of scale as you mentioned that when the output increases. So, output is suppose q 1 output is q 2 output is q 3. So, q 1 q 2 q 3 at the different level of output the cost of production decreases and when it is a minimum point this is the minimum point this can be called as the optimal output because this is the level of output beyond which if you are increasing the level of output the cost of production increases. So, this is the up to this this is the evidence of economies of scale and beyond this if still the output is increasing the average cost per unit is increasing and that is the reason this is the evidence of the disequenomics of scale. So, the decreasing part of long run average cost curve is because of economies of scale that is reduced cost of production reduced average cost of production or may be the per unit cost of production and when it is increasing that is in term of increase in the cost of production or per unit cost of production beyond a certain level of output. The minimum point at the long run average cost curve is generally known as the point of optimal output that is the minimum cost that can be by incurring that that is the maximum level of output what the firm can produce. So, again this is the graphical example of disequenomics of scale and the meaning of disequenomics of scale is when output increases long run average cost increases and that is in the increasing phase of the long run average cost curve. So, if you look at whether it is a short run cost output relation or in the long run cost output relation the long run cost output relation is similar to the short run cost output relation with subsequent increase in output the long run average total cost curve initially first increases if it look at its first increases and then it decreasing rate and then at the increasing rate and as a result if you look at if it is a long run average cost takes this shape that is the reason initially the average total cost or as long run average cost curve is decreasing. So, with a subsequent increase in the output long run total cost curve is first increases at the decreasing rate then it is increasing at the increasing rate and since long run total cost is increasing at a decreasing rate initially the long run average cost curve also initially decreases and when long run total cost curve is increasing at the increasing rate then generally the long run average cost curve also increases because average cost is nothing, but derived directly from the total cost dividing by the number of unit of output. So, as a result when long run total cost curve is increasing at a decreasing rate long run average cost curve initially decreases until the optimum utilization of the second plant capacity and then it begins to decrease. So, this cost output relationship whether it is specifically in case of a long run it follows a law of return to scale. So, you remember your return to scale that when input increases in a fixed proportion if the output increases more than that this the case of increasing return to scale if the output increases less than that then this is a case of a decreasing return to scale and if the output is increasing in the same proportion as the input increases then this is the case of a cost and return to scale. So, the cost output relationship of long run it follows a law of return to scale when the scale of form expand the unit production cost initially decreases, but ultimately it increases. So, initially when the scale of output increases when the level of output increases then the unit production cost is initially decreases, but ultimately beyond a level beyond the minimum cost of production after that generally the unit production cost is increasing. So, the decrease in the increasing cost decrease is the unit cost that is the average cost is attributed to the internal and external economies of scale as we discussed just before couple of minutes because economies of scale is the reduced cost of production. And so, the decrease in the unit cost is attributed due to the economies of scale which is of two type one is internal economies and another is the external economies. And eventually when there is a increase in the cost that is because of the diseconomies and diseconomies is again two types that is internal and external diseconomies. Then we will come to the long run marginal cost and as you know marginal cost is nothing, but the addition to the total cost when there is a production of one more unit of output. So, long run marginal cost curve measures the rate of change in the long run total cost as output changes along the expansion path. So, it is the rate of change in the long run total cost as output changes along the expansion path. So, long run marginal cost curve which the change in the long run total cost curve that is delta LTC divided by change in the quantity that is del Q. So, LMC is the change in the LTC with respect to change in the Q or we can say this is the first order derivative of the total cost with respect to the Q. When you grab the long run marginal cost curve and long run average cost curve both the costs are you say initially it decreases with the increase in the output, but it increases when there is a increase in the output is more than that. The long run marginal cost curve is always intersect long run average cost curve at the minimum point. So, at the minimum point of average cost curve the long run marginal cost is equal to the long run average cost curve. So, if you look at the relationship between the long run marginal cost curve and long run average cost curve the first evidence comes here is that when long run average cost curve is minimum at this point the long run average cost curve is equal to the long run marginal cost curve. So, long run marginal cost curve is you say the long run marginal cost curve is below the long run average cost curve. LMC is less than LSE when LSE is decreasing and long run marginal cost curve is greater than long run average cost curve when long run average cost curve is increasing that is in this segment. And corresponding to this the long run average cost curve is equal to the long run marginal cost curve. So, long run marginal cost curve is below long run average cost curve when it is decreasing and long run marginal cost curve is above long run average cost curve when it is increasing. At this point the long run average cost curve is equal to the long run marginal cost. Apart from this two more facts that both the curve that is LMC and LSE both of the both the curves they are u shape and always the LMC intersect LSE at the minimum point of the long run average cost curve. Then we will discuss about may be few more types of long run average cost curve which generally not follow a regular shape of the long run average cost curve that is u shape. And then we will find out what is the reason behind not following a specific shape or regular shape of the long run average cost curve. So, if you look at the graph initially in the first graph you are taking the average cost in the left axis and output in the right axis that is x axis. And if you look at it is a case of early day signal means because the long run average cost curve is increasing much before reaching the minimum cost and much before reaching the mid point of the curve. So, this is the evidence of early day signal means and what is the implication of early day signal means the input increases or input increases at the higher cost of production or when the firm expanding its production when the firm is increasing the scale of production generally the input or generally the cost of production is increasing. So, if it is a case of the general trend then in this case generally it initially decreases, but first decreases, but in case of early day signal mean what it has happened that the cost of production has reduced much before the optimal point or much before the minimum point. Then if you look at the second graph that is extended economies in this case the minimum point or the decreasing portion is the decreasing portion of cost of production is more than the normal level or the regular level. And this is the evidence of the extended economy and extended economies means the reduced cost of production is enjoyed to a larger extent by the firm. So, economies of scale is reduced cost of production when the scale of output increases, but in this case of specifically in the case of the second graph the economies of scale has been enjoyed by the firm to a larger extent and that is the reason this is the case of the extended economies of scale. If you look at the third graph it is the case of the extended cost and LSE and what is this extended cost and LSE? This is interesting to look that the minimum cost of is not a point rather it is in a segment. So, this output level, this output level, this output level suppose this is Q 1, this is Q 2, this is Q 3, this is long run average cost curve and if you look at the economies of scale has been achieved from this point because the cost of production is decreasing, but this should be the minimum point and ideally after this point again it should follow a increasing trend. If it is a case of the long run average cost curve the normal shape of the long run average cost curve, but if you look at the minimum point is extended over a range of production which implies that at the minimum cost, at the same level of cost the firm has moved from Q 1 unit of output and Q 3 unit of output. Generally when you look for the evidence of this type of average cost in the real world maybe it is difficult to find, but possibly it is the sometime if it is a batch production and the same level of cost of production is used for a specific batch of production. So, initially when the cost of production has decreased or the cost of production has incurred for a specific level of output generally at the same level of output specific case a batch of production the possibility is there that you get a constant long run average cost curve. Otherwise finding evidence for this type of constant output relationship is difficult when you take this example to the real world scenario. So, when it comes to the relationship between the short run and long run cost curve again the long run marginal cost curve intersect LSE when later is at the minimum point at each output where particular to ATC is tangent to LSE the relevant SMC is equal to LMC and will examine this relationship again with the help of the long run average cost curve. How it becomes a series of long run average cost curve and then how they both of them they are related to each other. This is ATC 2 where K is equal to capital is fixed at 3 because this is the case of short run and this is average total cost curve 3 where K is equal to 60. So, if you look at what is the difference between ATC 1, ATC 2 and ATC 3 it is three different short run cost curve in case of average total cost this is short run capital is fixed at 10 in case of average total cost curve in case of 2 that is capital is fixed at 30 and in case of average total cost curve 3 the capital is fixed at 60. So, this is 2000 suppose this is 2000 then this is 5000 may be this is called can be called as the optimal level of output this is 3000 this is 7500 this is 10,000 and this is 12,000. So, if you look at if it is the output level 2000 there is no much choice left for the firm to only they have to operate at the short run cost curve by capital H 10. When the output level is 3000 either it can be produced through average total cost curve 2 by using capital H 30 or through average total cost curve 1 that is using capital at 10, but if the firm is still interested to expand for them it is always better to operate at the decreasing portion of the cost curve and that is the reason the 3000 is the when 3000 unit of level of output is produced it is desirable for the firm to operate at a higher capital input mix because with that the firm can still expand up to the point 7500, but if it is a case of means the firm is no more interested to expand the output for them it is always preferable to operate at the short run cost curve 80 C 1 where k star is equal to 10 because the capital requirement is less. Similarly, if you look at the output level 5000 this is the optimal level of output because this is produced with the minimum cost of production. Similarly, if you look at the output level 7500 this can be produced either by using short run cost curve 3 that is 80 C 3 or may be the short run cost curve 2 that is 80 C 2. If it is produced with the help of 80 C 2 it is lying at the increasing cost portion of the average total cost curve and if it is produced through 80 C 3 then it can be produced through the decreasing portion of the short run cost curve. So, if the firm still interested to expand they can always pick up the short run cost curve 3, but if they want to just stop here they are no more interested to invest more in this capital and they will choose a combination that is average total cost curve 2. So, it is always the individual firm decision that whether for that level of output whether they will take a short run cost curve where the capital requirement is more or then take a short run cost curve where capital requirement is less. If it is if they are still if it is this is the point beyond which they are not going to expand the output they will always prefer a short run cost curve where the capital combination is or the capital input combination is less, but if there is still scope to increase the output or still they prefer to increase the scale of production they will always pick up a short run cost curve which is at a higher capital requirement or higher capital input requirement because that still if the scope when they further increase the scale of production where or whether further increase the output because with the same level of capital just changing the variable cost still they can increase the output level. So, this is how the short run and long run average cost curve they are related, but this long run average cost curve is also known as the planning curve or the envelope curve because it serve as a guide to the entrepreneur in plan to expand the production and this is called as the envelope curve because in the long run average cost curve is basically envelopes the different short run cost curve. Like if you look at the graph also this long run average cost curve generally it envelopes the short run average cost curve 1 short run average cost curve 2 or short run average cost curve 3. So, in this case it generally known as an envelope curve because it takes the different scenario of short run cost curve and put them as a longer planning horizon. So, if this is the capital this is the input this should be the level of output or up to this level of output this short run cost curve can be used or this or in a more reference case we can say this is the capital input combination can be used to used to produce this level of output. And this is known as the planning curve because since it gives a scenario of different capital input combination this different short run cost curves and that helps the entrepreneur that helps the firm to identify the capital input combination at the different level of output what is the cost associated with that or may be sometimes it helps in the planning the efficient cost analysis when at the different level of the output. And that is the reason it is known as the envelope curve and it is also known as the planning curve this long run average cost curve. Then we will come to the discussion of optimum plant size how it can be achieved in case of a long run cost curve. The short run cost curve are helpful in the determination optimum utilization of a given plant. If the given plant size is 500 unit the short run cost curve will help you in identifying what is the optimum utilization of a given plant. What is the right input makes when there is a fixed input and the output can be changed only by the variable input generally the short run is helpful in the determination of the optimum utilization. If it is a case of a given plant or in the other word we can say that the they helps in though they helps the firm the helps the business for determining the least cost output level means what is the optimal output which can be produced with the lowest cost of production. However, when it comes to long run cost analysis long run cost curve on the other hand can be used to show how a firm can decide on the optimum size of the firm. So, in the first case we talk about the optimum utilization of the given plant, but in case of short run, but in case of long run we generally use this long run cost curve to decide what is the optimum plant size means how best it can be achieved with the same level of the plant size or what should be the optimum capacity used on the basis of the input requirement on the basis of the output level. So, the optimum which one is the optimum size of the firm or how to decide the optimum size of the firm? The optimum size of the firm is one which ensure the most efficient utilization of the resources. So, the optimum size of the firm is one in which long run average cost curve is minimized. So, how to define a optimum size of a firm? The optimum size of the firm is one which ensure the most efficient utilization of the resources and the optimum size of the firm is also one in term of the long run average cost curve, when the long run average cost curve is minimized. So, that will analyze this optimum plant size with the help of a break even analysis, maybe that is through revenue analysis, that is through profit analysis, that is through cost analysis, but in general when it comes to the optimum output, the optimum size of a farm in the long run, this is always the point at which the long run average cost curve is minimized. So, then we will introduce the break even analysis specifically in case of linear cost and revenue function, and then we will analyze in case of non-linear cost and revenue function. So, the basic objective of any business farm is to maximize the profit. So, if you look at any economic agent, if their optimization problem, it is related to either for the maximization of profit or for minimization of cost. So, the basic objective of any business farm is to maximize the profit, but it is not that the maximum profit always coincide with the minimum cost. If it is maximum profit coincide with the minimum cost, that is the that is the optimal level of output or that is the optimum operational level for the farm. So, even if the optimization problem is to maximize the profit, it is not that always the maximum profit coincide with the minimum amount of the cost. And if you look at go back to any traditional theory of farm in economic analysis, this says that maximum profit can be achieved with a minimum cost. But when you take this example to a real world scenario, it is not that every time the maximum profit coincide with the minimum cost. And that is the different point, difference point over here is that maximum profit can be achieved also, not at the minimum point of the cost of the production. Profit is maximum at a specific level of output which is difficult to know beforehand. So, which level of output where profit is maximum, it is difficult to know at least in the beforehand, because it is not that before production start or before production level, it is it is easy to know at which level of output profit is maximum. And in case if it is known, it cannot be achieved when the production operation is on. So, first difficulty comes here is it is difficult to know which one is the specific level of output where profit is maximum. Second, the second difficulty comes even though you know at which level the output is leads to maximum amount of profit, it cannot be cannot be achieved at the outset of the production. So, in real life firms begin their activity even at loss in the anticipation of profit in the future. So, when someone starts business, it is not that the day one they get the profit. So, initially there is a threshold time where the firm begin the activity, they continue the activity even if it is a loss and why they continue the activity even if they are incurring a loss, because there is a anticipation that they will get profit in the future. So, the production level is not known generally, if it is known also it is known also difficult to achieve the production level where profit is maximum. And there is one more dynamics here also in the firms behavior is that the business activities continues even if there is a loss, because there is a anticipation of profit. Nevertheless, the firm plan their production activity is much better way if the level of production for which total cost and total revenue break even is known. So, even if all these uncertainties are there still firm plan their production activity much better if the level of production for which total cost and total revenue break even is known. This implies if the firm known knows the profitable and non profitable range of production. So, the relationship between the total cost and total revenue at different stages of output that gives us which one is the profitable level of profitable range to operate for the firm and which one is the non profitable range to operate for the firm. So, that we will see through the break even analysis or it is also called as the profit contribution analysis. This is an important analytical technique used in studying the relationship between the total cost, total revenue and total profit or losses over the whole range of stipulated output. So, break even analysis or as known as the profit contribution analysis is a technique through which we study the relationship between the total revenue, total cost, profit and loss over a stipulated level of output, because there is a certain level of output and then certain level of output we can study the relationship between revenue, cost, profit and the loss. And the technique through which we study the relationship between all these four variables that is generally known as the break even analysis or profit contribution analysis. So, the break even analysis it is a technique of previewing the profit prospect and the tool for profit planning. It integrates the cost and revenue estimate to ascertain the profit and loss associated with the different level of output. So, it is a technique that is preview the profit prospect and tool of profit planning, because when you know the relationship between profit, total revenue, cost, loss over a period of time that helps the producer to plan for the profit planning at what level they have to operate and it generally integrates the cost and revenue function in order to study the profit and loss. So, to understand this break even analysis more we will just take an example of a numerical function to understand how this cost and profit they are related. We will take a linear cost and linear revenue and let us assume that the cost function is c which is equal to 100 plus 10 q and revenue function is which is equal to 150 q. Now, if you look at what is the if typically in the case of total fixed cost, here what this is the total cost function 100 plus 10 q. What is the fixed factor over here in case of the cost function? The fixed cost is equal to 100 and what is the total variable cost? What is the total variable cost? The variable cost varies at a constant of 10, because this is the the c will change with respect to q. This happens in case of variable cost, because fixed cost is constant at 100 whenever there is a change in the output that will lead to change in the variable cost and the variable cost will change by which change by 10 times because this is the rate at which the variable cost is changing. So, the total fixed cost is 100, variable cost is increasing at a constant rate of 10 per unit in response to increase in the output and the revenue function implies that the market price for product is 150 and this is the when it comes to the per unit sale, this is equivalent to this is equivalent to 150 q. So, this implies that the market price for firm product is 150 per unit of sale. So, when you identify the break even point. So, looking at this how we should identify the break even point? We have known as the total cost that is 100 plus 10 q and we know the total revenue that is 150 q. So, total revenue should be equal to total cost. So, this is actually 15 sorry this is if you take this as 15 q then at the break even total revenue has to be equal to the total cost. So, in this example if you look at this total revenue is 15 q which is equal to 100 plus 10 q and if you simplify this this is 5 q is equal to 100, q is equal to 20. So, this q is equal to 20 what is the implication for this? It follows that the break even analysis or the break even level of output is equal to 20 units. So, this 20 units is what? 20 units can be achieved at total revenue equal to total cost. So, break even achieved at a point when total revenue is equal to total cost and break even output level is 20 unit because this is achieved through the equalization of the break even condition that is total revenue is equal to total cost. Now, when you look at the graphical analysis of this, look at the total cost, total cost total revenue, total cost, total variable cost, total fixed cost. So, output is in the x axis cost and revenue are in the y axis. So, this is the total revenue, this is the total fixed cost, this is the total cost and this is the total variable cost. This is 100 and this is 20. Now, to understand this relationship or the break even analysis with the help of the graphical representation, the help of the graphical representation what is the break even condition? The break even condition is total revenue is equal to total cost. So, this is the total revenue which starts from origin because any level beyond 0 level of output the firm is incurring the total revenue. Total fixed cost is fixed at 100, total variable cost starts from origin whenever there is a whenever there is a Q, the corresponding variable cost is there. Total cost is summation of total fixed cost plus total variable cost that is the reason it starts from 100 because up to this this is total fixed cost plus the total variable cost. Now, what is the break even point? Break even point corresponding to this the total revenue is equal to the total cost. So, corresponding to this we get the level of output as 20. Now, assuming 100 is the fixed cost, the output level will be 20, break even level of break even output level will be 20 because at this point the total revenue is equal to the total cost. So, break even analysis generally tells us the relationship between the total revenue and total cost. Now, what happens if it is the output level is below 20 or output level is more than 20. If it is below 20 the cost is more than the revenue it is not profitable for the firm. If it is the produce beyond 20 then the total revenue is greater than total cost. So, this is the profitable level of output. The firm is going to get profit if it is a higher level of output and that is the reason if you look at this is known as the profitable range of output and this is known as the non-profit range of output because if the firm is operating at output beyond 20 the total revenue is more than total cost and if the firm is operating before 20 the total cost is more than total revenue. So, this is known as the non-profitable range of output and this is known as the profitable range of output. So, we will talk about the algebra behind this algebra behind this break even analysis and how the break even analysis works before in case of non-linear cost function in the next session. So, these are the session references that is being followed exclusively for preparing this session.