 Then, we will talk about the last category that comes as the private cost and the social cost. Private and social cost are those cost which arise as a result of the function of a firm. But neither are normally reflected in the business decision nor are explicitly borne by the firm. Cost in this category are borne by the society. So, private and social cost are those cost generally it comes as a result of the function of firm, but neither are normally reflected in the business decision. So, typically if you look at this is a part of the byproduct or sometimes during the process of production whatever the cost incurred, this is not strictly decided by the firm that this is the cost has to be incurred or neither the firm explicitly takes care of this cost. Generally it passed to the society and cost this category generally borne by the society and generally this is related to the byproduct of the firm. So, total cost generated in the course of doing business may be divided into two categories one those paid out by the firm and those are those not paid or borne by the firm including the use of resources that freely available plus this utility created in the process of production. So, the total cost if you look at one is those paid out by firm. So, these are strictly the private cost they are incurring a expenses and the firms also paying for it and second not paid or the borne by the firm including the use of resources that is freely available plus this utility created in the process of production and the second category generally known as the external cost or the social cost. Now, if you look at the water pollution or the air pollution, water pollution from a oil refinery, air pollution cost by mills factory located near a city etcetera from the firm point of view such cost are classified as the external cost. This is not strictly part of a business decision and from the society point of view they are classified as the social cost. So, pollution if you look at they are the by product it is not that it is decided in the business it is a part of the business decision that the pollution has to be taken care of. So, water pollution from oil refinery here the main product is oil, but the by product is in that process since the waste or the since the discharges are into the local water body that creating a water pollution. Now, firm tries to say that these are external cost because this is discharge and somehow we have to make the discharge somewhere and they are targeting the local water bodies for that, but who is getting affected by that? The society the locality who is staying near the oil refinery they are getting affected by that and they are incurring a cost to it. So, for the firm's view point this is external cost, but from the society since even if they are not producing the product they are exposed to the by product of the firm, by product of the producer and that is the reason they are paying a cost to it. So, that is this is known as the social cost. Similarly, air pollution cost by the means and factory located near a city air gets polluted this is part of external cost for the firm because this is not a part strictly part of their business decision, but for the society those who are developing a respiratory diseases because of air pollution, because of their staying in the locality where the factory is located and the factory discharging creating air pollution because of that they are developing a respiratory disease this is the social cost to them. Since they are staying in a society since they are staying near to a factory they are incurring a cost to it, but for the firm it is always the external cost. So, social cost and the private cost is one private cost that is strictly paid by the firm, but when it comes to the external cost or the social cost it is not paid by the firm. Maybe it happens that sometimes the firm spends some amount of money in order to in order to reduce the pollution or in order to treat the pollutant, treat the effluent, but when it comes to major chunk of the cost it is always paid by the paid by the produce paid by the society because since they are staying at the part, since they are staying in a society and it is a part of their social cost. So, if you look at in the last few slides we discussed about the category of cost in two cases one where there is a accounting accounting perspective other when it is the case of the economic analysis. So, if you look at the theory of cost basically it deals with the cost and output relation, it is cause and effect since the output is there that is the reason there is a expenses of there is a cost. So, the basic economic principle state that total cost increases with the increase in the output, but here the focus is not the absolute increase in the total cost, but the direction of change in the average cost and the marginal cost and the direction of change in the average cost and marginal cost will depends upon the nature of the cost function. So, essentially if you look at this is a cost and output relationship whenever output increases that leads to increase in the cost whenever output decreases that leads to decreases the cost. Here the focus in case of cost output relationship the focus is not on the absolute increase in the cost due to increase in the output. Here the focus is that what is the average cost when output increases what is the average cost when output decreases, what is marginal cost when output decreases when the firm operates at different scale of the output different scale of the production. What happens to marginal cost when the firms operate in the different scale and the focus here is to know the direction of change in the average cost and marginal cost and which we can know from the nature of the cost function. So, a cost function if you look at it is a symbolic statement of the technological relationship between the cost and output per C is the cost, T c is the total cost it is always a function of the Q and the change in the Q is always greater than 0, then only it will lead to increase in the cost. The specific form of the cost function depends on the time framework for cost analysis that is the short run and long run. So, the specific form of the cost function depends on the time framework of the cost line whether it is cost short run function whether it is a long run cost function that depends upon the specific form. So, total variable cost if you look at short run cost we get total cost which is a combination of total variable cost and total fixed cost. Total variable cost is the total amount paid for variable inputs and it is increases as output increases. So, total variable cost is the cost incurred from the variable inputs total amount paid for the variable input and it increases whenever there is a increase in the output. Total fixed cost is the total amount paid for the fixed input of production. It does not vary with the output generally this is a part of the short run because this total fixed cost is always a part there will essentially related with the fixed input and fixed input is the feature of a short run cost analysis and total cost is the combination of the total fixed cost and total variable cost. So, this if you look at this is the short run total cost schedule per column 1 talks about the output, column 2 talk about the total fixed cost, column 3 is total variable cost and total cost is total fixed cost plus total variable cost. So, this is just a hypothetical example. So, if you look at from 0 unit to 600 unit the total fixed cost is 600. So, there is no change in the fixed input from 0 unit to 600 unit, but from 100 unit to 600 unit the variable cost is changing and that leads to all these changes in case of the total cost. So, this is the graphical representation of the total cost, total variable cost and total fixed cost. Since total fixed cost is fixed up to 600 units of output this is just a horizontal straight line parallel to x axis, where x axis represents the unit of output and y axis represent the cost and total variable cost is total variable cost is starting from origin and its goes on increasing when there is a increase in the output. Total cost is the summation of the total variable cost and total fixed cost that is the reason total cost starts from the 6000 unit of output which is at the total fixed cost. Then we look at the average cost, average variable cost is total variable cost divided by the unit of output that is represented by Q, average fixed cost is the total fixed cost divided by Q which is unit of output and average total cost is Tc that is total cost which is a summation of total variable cost and total fixed cost divided by Q and that leads to the average total cost is equal to the average variable cost plus average fixed cost. Marginal cost measures the rate of change in the total cost as output increases or decreases. So, short term marginal cost is change in the total cost with respect to change in Q. So, change in the if you look at in the short term marginal cost curve when you talk about the change there is no change in the fixed input there is only change in the variable factor. So, that is the reason when we say that change in the total cost directly there is a change in the total variable cost and with respect to change in the output because there is no change in the fixed input. So, this is the example of average and marginal cost schedule. So, the first one is output second one is the average fixed cost, third one is the average variable cost, fourth one is average total cost and last one is the marginal cost curve and since fixed cost is constant the average fixed cost goes on goes on decreasing when the there is a increase in the output. This is the graphical representation of average fixed cost average variable cost marginal cost curve and average total cost curve. So, if you look at whether it is average variable cost, average total cost or certain on marginal cost curve all it follows a U shape and here one thing is missing we need to find out what is the shape of a average fixed cost which is not U shape as compared to the other. So, as we know average total cost, average variable cost and marginal cost all these three cost curve are U shape. However, when it comes to the average fixed cost average fixed cost is nothing but the total fixed cost divided by Q and which goes on decreasing and that is the reason we get a rectangular hyperbola shape for the average fixed cost even if it is close to both the axis y axis and x axis, but it is not it never touches any of this axis. So, it can be never 0 and that is the reason it cannot touch to either y axis or x axis. So, if you look at all this cost curve average total cost average variable cost short on marginal cost curve it can be U shape, but average fixed cost that is AFC is rectangular hyperbola it never touches even if it is close to x axis and y axis it never touches the axis and it goes on decreasing when the output increases till the specific level because there is no fixed input which leads to no fixed increase in the fixed cost of production. Then we will come to the relationship between the production and the short run production and short run cost. So, if you remember the law variable proportion where we essentially discuss about the relationship between the total product average product and marginal product. So, if you remember how the average product and marginal product they are related. So, this is our marginal product this is our average product average product is equal to the marginal product where average product is maximum. Corresponding to this we will see how this is related to the marginal cost and average cost of production. So, if you remember when marginal product is highest this is the point when the law of diminishing return takes place because beyond this there is no increase in the output whenever there is a increase in the input no increasing return to scale. So, in this case if you look at corresponding to this we will see that our marginal cost is minimum corresponding to the marginal product maximum of the marginal product. Similarly corresponding to the equality between the marginal product and the average product our average cost will be equal to the marginal cost. So, from this if you look at the figure over here also we are showing the average product and marginal product at the upper part of this graph and marginal cost and the average variable cost at the lower part of this graph. So, what is the relationship between this short run cost and production when marginal product is increasing marginal cost is decreasing that is from the first part of the curve. So, if you look at if marginal product is increasing marginal cost is decreasing when average product is increasing average cost is decreasing when marginal product is decreasing marginal cost is increasing when average product is decreasing average cost is increasing. So, marginal product average product marginal cost average cost there inversely related. So, when marginal product is increasing marginal cost is decreasing, when marginal product is maximum, marginal cost is minimum, when marginal product is decreasing, marginal cost is increasing. Similarly, when average product is increasing, average cost is decreasing, when average product is decreasing, average cost is increasing. When marginal product is equal to average product and at that point average product is maximum corresponding to that marginal cost is equal to the average cost and at this point the average variable cost is also minimum. So, to summarize if you look at the average cost and the marginal cost and average product and the marginal product they are related in a inverse way whenever the average product marginal product is increasing, average cost marginal cost is decreasing, whenever marginal product average product is increasing, marginal cost and average cost is decreasing, marginal cost is equal to average cost at the minimum point of the average cost. So, the relationship is such that if the product is doing well then that has to be at the minimum cost and that is the reason we say that whether it is the case of increasing return, whether it is a case of decreasing return or whether it is a case of the cost and return. So, cost and output relationship are normally determined by the cost function and exited by the cost function whether it is a short term whether it is a long run and the shape of the cost curve depends upon the nature of the cost function which are derived from the actual cost data. So, we will talk about three different kind of cost function typically in the case of a specific in case of the short run cost. So, first one is the linear cost function where it takes a functional form that is T c is equal to a plus b q where this is the fixed cost and this is the total variable cost. Now, how to find out the average cost and marginal cost from here? So, average cost is total cost divided by q. So, total cost divided by q is q is a plus b q by q which comes to a by q plus b. So, average cost is a by q plus b. How we find out the marginal cost? Marginal cost is change in total cost with respect to change in q. So, that way we take the first order derivative of total cost with respect to q and that is d a plus b q with d q which is b d q by d q and you get b as the marginal cost. So, b is marginal cost and average cost is a by q plus b if it is a case of a linear cost function where the cost function takes a functional form of a plus b q. So, a is the intercept which talks about the fixed cost b is the slope and b q is the total variable cost. Then we will see the case of the quadratic cost function and quadratic cost function takes the value that is total cost is a plus b q plus q square. Now, how to find out the average cost here? Average cost is again total cost by q. So, this is a by q plus b q by q plus q square by q. So, that comes to a by q plus b plus q this is the average cost and for marginal cost we need to take the day T c with respect to d q. So, that comes to b plus 2 q. Now, if you take a functional form or if you add a numerical value here total cost is equal to 150 plus 10 q plus q square then in this case in order to find the average cost that is a c is equal to T c by q. So, this comes to this is comes to 0 this is 10 and this is q. So, this comes to 10 plus q is the average cost and to find out the marginal cost that is T 150 plus 10 q plus q square with respect to d q. So, that comes to 10 plus 2 q. So, this is the this is the marginal cost. So, average cost is 10 plus q and marginal cost is 10 plus 2 q then we will take the a cubic cost function and in case of a cubic cost function total cost is a plus b q minus c q square plus d q q. So, average cost is total cost by q which comes to a plus b q minus c q square plus d q q divided by q. So, that comes to a by q plus b minus c q plus d q square and marginal cost will be d a plus b q minus c q square plus d q q with respect to d q. So, that comes to b plus b plus 2 c q plus 3 d q square. Now, if you will take a numerical value with respect to cubic cost function or we can say that total cost is equal to 10 plus 6 q minus 0.9 q square plus 0.05 q q. We can make it two part we can find out what is TFC we can find out what is TBC. So, 10 is TFC because this is the intercept value and this is strictly only the fixed cost not because it is associated with the fixed input and total variable cost is 6 q minus 0.9 q square plus 0.05 q q. So, in order to find AFC here we can take this is as TFC by q. So, this is 10 by q and for ABC we can find out this is TBC by q like 6 q minus 0.9 q square plus 0.05 q q divided by q which comes to 6 minus 0.9 q plus 0.05 q square. Then average total cost is TBC by q that comes to 10 by q plus 0.9 q square plus 0.9 q plus 6 minus 0.9 q plus 0.05 q square and to find the marginal cost that is DTC with respect to DQ. So, that comes to that comes to D10 plus 6 q minus 0.9 q square plus 0.9 q square plus 0.05 q cube. So, that with respect to DQ that comes to 6 minus 1.8 q plus 0.15 q square. So, this is equal to the marginal cost. So, it depends upon the value of marginal cost average cost depends upon that what kind of cost function whether it is a linear cost function whether it is a quadratic cost function and whether it is a cubic cost function. So, we will talk about the long run cost analysis and the economies of scale in the next session and these are the session references the materials that is being followed for preparation of this typical specific session.