 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 maybe in the other to put it in the other way, when all input changes then only the output changes or maybe 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 comes 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 then 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. When it is 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 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 three level of output because that leads to three 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 three 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, SSC 2 and SSC 3, it gives three 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 maybe the less amount of input 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 maybe 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 different amount of fixed cost and each plant size of a firm will give us a different sheet 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 a 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 of 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 all together 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 and 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 for 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 minimize 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 shape 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, if it is a case of U shape 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 is 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 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 reduce cost of production reduce 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 term cost output relation or in the long run cost output relation the long run cost output relation is similar to the short term 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 runs 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 is 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 firm 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 decreases 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.