 And 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 quantities 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 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 maybe 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 de-signalment 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 de-signalment and what is the implication of early de-signalment is 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 de-signalment 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 is decreased or the cost of production is incurred for a specific level of output generally at the same level of output in case of 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 10000 and this is 120000 ok. 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 as 10. When the output level is 3000 either it can be produced through average total cost curve 2 by using capital as 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 makes 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 ATC 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 ATC 3 or may be the short run cost curve 2 that is ATC 2. If it is produced with the help of ATC 2 it is lying at the increasing cost portion of the average total cost curve and if it is produced through ATC 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 use 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 and 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 an 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 firm 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 firm 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 firm 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 firm. 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 firm in economic analysis, they 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 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 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 difficulty comes even though you know at which level the output is leads to maximum amount of profit, it 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 if 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 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 will see through the break even analysis or it is also called as the profit contribution analysis this is an important analytical technique using 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 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 ok. 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 the variable cost varies at a constant drop 10 because this is the C will change with respect to Q ok. 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 level 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 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 ok. Now, to understand this relationship or the break even analysis with the help of the graphical representation with 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 queue 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 10 100 is the fixed cost the output level will be 20 break even a 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 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.