 So, in this session, we will continue our discussion on relationship between the total cost, total revenue, profit and loss, the break-even analysis, what we discussed in the last session also and we will see what is the profitable and non-profitable range of output, how the business activities plan on the basis of profit and loss. So, if you remember in the last class, we talked about the long-run cost and output relationship, generally how the long-run cost is derived from the short-run cost curves and how both of them they are related, in which case short-run cost curve is used and in which case the long-run cost curve is used. Then we introduced the break-even analysis, specifically in case of linear cost and revenue function, when linear cost and revenue follow a straight line. So, the break-even point is one where the total cost is equal to total revenue, beyond that it is a profitable range of output because total revenue is more than total cost and before this it is a non-profitable range because the total cost is greater than the total revenue and the break-even point is one where the total cost is equal to total revenue. So, to start with, we will continue again our discussion on the linear cost function, we will just look at the algebra behind the linear cost and revenue function specifically in case of break-even analysis. Then we will discuss about the non-linear cost and revenue function, then we will do the contribution analysis and then finally, we will discuss about the learning curve which is the again the background is on the shape of the long-run average cost curve. Generally the practice is that we follow that there is a economies of scale because of which the average cost is decreasing, but learning curve is the alternate method to understand or the expand that why long-run average cost is decreasing. So, to start with we will look at what is the algebra behind the break-even analysis. So, as we know that the at the break-even point the total revenue is equal to total cost. So, as we know total revenue is P multiplied by Q and total cost has two parts that is total fixed cost and total variable cost. Now, this total variable cost is alternatively we can say this is the average variable cost multiplied by the quantity and total cost is total fixed cost and in spite of TVC if you write average variable cost multiplied by Q, then this is this comes as total fixed cost and in in place of total variable cost we use average variable cost multiplied by Q. So, in this case we can write this as the if QB is the break-even level of output if it is a breaking level available output putting this total revenue is equal to total cost revenue is since it is PQ. So, QB by P and total cost is total fixed cost plus average variable cost and in case of this Q since QB is the break-even level of output we will use QB. So, QB by P multiplied by P is now simplify this again this is ABC QB equal to total fixed cost again simplifying this we will get if you take QB is out that is P minus ABC which is equal to total fixed cost or we can say QB is equal to total fixed cost divided by P minus ABC. So, if we know or it if the producer know what is the level of TFC, what is the level of TBC and what is the level of P then we can find out find out the quantity that is the break-even level of quantity through this that is QB is equal to TFC by P minus ABC. So, the algebra behind this is if you know the fixed cost if you know the average variable cost and if you know the price of it generally you can find out the find out the break-even level of output, but when it come to break-even analysis specifically in case of linear cost and revenue function it is applicable only if the cost and revenue are linear. So, in case of linear cost and revenue function the total cost and total revenue are straight line the intersect only at one point dividing the whole range of output as two parts that is profitable and non profitable like in the previous graph we saw that this is our total fixed cost, this is total variable cost this is total revenue cost and the total cost starts from here and this is the total revenue cost total cost. So, this is the break-even level of output because total revenue is equal to total cost and this divides the entire range of output into two level that is non profitable and profitable. This is possible only if it is a linear total revenue cost function or linear total cost function because they intersect each other only at one point and that is the reason clearly we can divide that this is the profitable range of output and this is the non profitable range of output, but if it is not a case of linear then the possibility is that they intersect more than twice or may be more than once and in this case we it is difficult to find out what is the profitable range of output and what is the non profitable range of output. So, what is the implication for this if it is a linear cost cost and revenue function we get two range of output profitable range of output and non profitable range of output, but the implication for this that the whole output beyond the break-even level is profitable right because the point beyond which total revenue is equal to total cost the total revenue is more than total cost beyond all the level which is which implies from a linear cost and revenue function, but when it comes to the real life this is not the fact as the conditions are different due to changing price and cost. So, it is not possible that the you get a when it say it is a case of linear cost and revenue function. So, if you look at the graph beyond this point we say any level of output is profitable right. So, implication of linear cost and revenue function is that beyond the break-even level any level of output is profitable, but in the real life the fact is condition are different due to the changing price and cost and that leads to the fact that the cost and revenue function may not be linear they may non-linear the cost function and the revenue function is non-linear. Because of the fact that the in case of real life there is a changing price which leads to change in the cost changing price of inputs and changing price of problem materials which leads to the variation in the cost and which leads to the possibility that the cost and revenue function are non-linear. So, the non-linearity arises due because of average variable cost and the price vary with the variation in the output. Since the average variable cost changes due to change in the price which vary with the variation in the output and as a result total cost may increase at the increasing rate and total revenue may increase at the decreasing rate. Since the there is a non-linearity due because of average variable cost and price change with the variation in the output that leads to the possibility that total cost increase at the increasing rate and total revenue increase at the decreasing rate. So, at storm stages of output total cost exceeds the total revenue, but in case of linear cost how it was happening? It was like after the break even level the total revenue is always greater than the total cost, but in case of non-linear since total revenue will increase at the decreasing rate and total cost will increase at the increasing rate at least at some stage of output the possibility is that the total cost will increase the total revenue. So, in this case maybe we get two break even point that is the one break even point when total cost is equal to total revenue and the possibility is that another break even point where again the total cost is equal to total revenue which limits the profitable range of output and determine the lower and upper limit of output. So, it is not that the profitable range of output is unlimited rather it is the it is defined the lower and upper limit of the profitable range of output. So, there is a need to pretest there is a need to verify the validity of the linearity of cost and revenue function before assuming that the cost or the revenue is the linear. So, in this case there is a need of pretest there is a need of verification before taking the cost and revenue as the linear function. So, what happens in case of non-linear there is two break even point there is not only one break even point two break even point and that decides the limit upper limit and lower limit of the ranges of the output. So, let us find out the graph for the non-linear cost and revenue function in case of a break even analysis. This is total cost and revenue this is output suppose this is total fixed cost this is total revenue ok. So, this is total cost this is total revenue and this is total fixed cost ok. So, here the total fixed cost line it shows that the fixed cost at O F this is fixed cost and the vertical distance between total cost and total fixed cost it measures the total variable cost because this is the total fixed cost and total cost is always the summation of the total variable cost and total fixed cost. So, the vertical distance between the total cost and total fixed cost that gives us the total variable cost. The curve total revenue shows that the total sales or total revenue at different output level at the different price and the vertical distance between the total revenue and total cost measure the profit or loss for various level of output. So, the vertical distance between total revenue and total cost that will give you the various level of output. So, corresponding to that we get two break even level of output one is q 1 and second one is q 2. So, we can say this is p 1 and this is p 2. So, total revenue and cost intersect to each other at two different point one at the point p 1 second at the point p 2 where the total revenue is equal to total cost. Before p 1 before the level p 1 the total cost is greater than total revenue. So, this is the non profitable range of output beyond p 1 any level of output up to p 2 this is the profitable range of output. But like in case of linear cost and revenue function it is not unlimited the profitable range of output is non limited because we get another break even point at p 2 which leads to the fact that beyond this point total cost is greater than total revenue and again this range is non profitable range. So, in case of non linear cost function we get two break even level and which also identify the lower limit and upper limit of profitable range of output. So, q 1 is the beginning of the profitable range of output and q 2 is the end of the profitable range of output. This is the lower limit of profitable range of lower level of output where the profit can be achieved this is the higher level of output where the profit can be output. So, this represent lower and upper break even point p 1 is the lower break even point p 2 is the upper break even point. And for the whole range of output between OQ 1 and corresponding to the this and this Q 1 and Q 2 is the break even point corresponding to this output level the total revenue is greater than total cost. So, this is the profit, this is the lower break even point, this is the upper break even point. So, if the firm is producing more than OQ 1 then or less than OQ 2 they are making the profit. So, if the firm is producing more than OQ 1 it should be more than OQ 1 the Q should be more than OQ 1 and less than OQ 2 then only the firm is making the profit. So, the output level should be more than OQ 1 and less than OQ 2 then only the firm is making the profit and producing less or more than these limits will give rise to the losses. So, basically the essential difference between the linear and non-linear break even analysis is in case of linear break even analysis the profitable range of output is unlimited, but in case of non-linear analysis there is a limit of profitable range of output beyond that producing more before that producing less will lead to the loss. So, if you look at this is the loss because total cost is greater than total revenue this is also loss because the total cost is greater than total revenue. This is the profitable range of output where the total revenue is greater than total cost. Then we will come to the one more type of analysis may be in relation to this break even analysis that is called as the contribution analysis. So, till the time here we are considering the total revenue total cost to understand the break even analysis, but in case of contribution analysis we are not taking the total cost total revenue we are taking the incremental revenue and incremental cost of the business activity. So, contribution analysis is the analysis of incremental revenue and incremental cost of business activity and break even charts can also be used to measuring the contribution made by business activity towards covering the fixed cost. So, through contribution analysis we will use some break even charts and the what is the role of break even charts here the role of break even charts over here is to measure the contribution made by the business activity towards the covering the fixed cost. And in the graph always the variable cost is plotted below the fixed cost. So, fixed cost are constant addition to the variable cost total cost line will run parallel to the variable cost line because the change in the total cost is depend on the change in the total variable cost. And the contribution is the difference between the total revenue and variable cost arising out of the business decision. So, the difference between the total revenue and total cost gives us the profit and contribution is strictly defined as the difference between the total revenue and the total variable cost. So, this is how the contribution analysis if you look at the graph the total revenue curve which TR starts from the origin. Total cost is the summation of the variable cost and the fixed cost that is starting at a point in the y axis which includes the fixed cost. Variable cost is starting from the origin the total cost and the difference between the total cost and the variable cost gives us the fixed cost and which is alternately also known as the may be the difference between the total fixed cost and total variable cost and total cost. The difference between the total revenue and total cost is profit and the difference between the total revenue and the total cost is profit and the difference between the total revenue and the total variable variable cost is known as contribution ok. So, if you look at this contribution is nothing but also the fixed cost at the breakeven level. So, breakeven level is corresponding to if you look at the graph breakeven level is corresponding to the point Q where total revenue is equal to the total cost and the variable cost is VC and the difference between the total revenue and total variable and the variable cost gives us the contribution and the difference between the total revenue and total cost gives us the profit. So, if you look at this graph previously, ok is the breakeven level of output and the contribution equals to the fixed cost below the output ok to the total contribution is less than fixed cost that is amount of loss. Below this the contribution is less than fixed cost that is the reason this is the amount of the loss and beyond this point the contribution is more than the fixed cost and that is the reason if you look at this the case of the profit that is the contribution exceed fixed cost and the difference is the contribution towards the profit resulting from the business decision. So, beyond the break before the breakeven level of output total contribution is less than fixed cost. So, this is the amount to loss and beyond output OQ that is beyond the breakeven level of output contribution exceed the fixed cost and this is the difference in the contribution towards the profit resulting from the business decision. So, one is before breakeven level of output the contribution is less than fixed cost that is the reason this leads to loss and the other point is beyond the breakeven level of output which exceeds the fixed cost the contribution exceed the fixed cost and this is the difference in the contribution towards the profit resulting from the business decision. But if you look at the contribution over time over time period under review is plotted in order to indicate the commitment that the management has made to the fixed expenditure and to find the level of output from which it will be recover and profit will begin to emerge. So, over a time period contribution over a time period under the review is plotted in order to indicate the commitment that the management has made to fixed expenditure because there is a commitment even the output leads to profitable output or not still they have to incur a certain amount of the expenditure and to find the level of output from which it will be recover and profit will begin to emerge that will look from the contribution. So, if you look at the graph here, so we will just draw a graph that how the contribution emerge when there is a commitment when the management decides to or management has the commitment to made to the fixed expenditure and there we need to find the level of output from which level of output the fixed cost whatever the contributed before that can be recover and the new level of profit can be generated. So, we will take a total revenue curve here as a straight line this is the fixed cost to make it simplified by not adding the variable cost here. So, this is fixed cost and contribution on the on the y axis and output in the x axis. So, this is q and this is the contribution, but beyond the breakeven level since q is the breakeven level of output breakeven level of output o q is the breakeven level of output this is the loss because the contribution is less than the fixed cost and at the point o q the fixed cost is equal to the contribution and beyond this the fixed cost is less than the less than the contribution and that is why this is the net profit added to the firm beyond the breakeven level of output. So, at the output of level of o q contribution equal to fixed cost before this the contribution is less than the fixed cost that is why the firm is incurring loss and beyond this point the contribution is more than the fixed cost and that is the reason the firm is getting the profit.