 We will start discussion on the second part of this model that is theory of cost now onwards. So, in the previous part we discussed about theory of production in the case of long run short run. Then how the input-output relationship and focus from now onwards is on the second part of this model which talks about theory of the cost. Here again we do the analysis from the short run and long run perspective. Before that we will see that how what is the motivation for studying this cost of production, how it is generally getting used in the business decision and how it leads to profit or maybe how it is used as the optimization problem in case of the minimization of the cost. So, to start with the session we will talk about the production cost. Then the types of cost mainly in the accounting sense and in the case of the economic analysis. Then we will talk about the cost and output relationship and finally, we will talk about the short run cost analysis. Essentially the relationship between the average cost that is average variable cost, average fixed cost, marginal cost and then we will see that how from the total cost we derive the different kind of the average cost. So, to start with we will see that what is the need or what is the motivation to study this production cost. So, business decision if you look at they are generally taken based on the monetary values of input and output. So, if you remember in the very fast model when we discussed about the need of business or maybe the business problems, all the activity which gives some monetary or non-monetary value we call them as the economic activity. And when it comes to business the sole motive is profit, then the decisions are generally taken based on the monetary values of input and output. The quantity of input multiplied by their respective unit price will give the monetary value or the cost of production. So, the quantity of inputs may be labor, the quantity of inputs may be capital, the quantity of inputs may be raw material, may be it is technology, may be it is time. In all these cases when it gets multiplied, the quantity get multiplied with the respective price or respective unit price that gives the monetary value or the cost of the production. So, what is this importance of production cost? In all business decision essentially in case of if you look at specifically related to the profitability or especially those decision which concern the location of weak points in the production management, cost minimization, finding the optimal level of output, determination of price and dealer's margin and estimation of cost in the business operation, these are certain may be the these are certain coordinates or these are certain points where there is importance to analyze or importance to calculate the production cost. So, in generic sense production cost or need for production cost comes to take any kind of business decision, but specially those decision which talks about the location of weak points in production management, cost minimization, finding the optimal level of output and what is your optimal level of output where maximum output can be produced at the minimum of cost, determination of price. So, if you know market in case of market price, cost of production is one of the important component or may be that is the base of the market price, dealer's margin that generally the profit comes to the when it change from the producer to dealer, the market price changes and what should be the dealer's margin that based on the cost of production and estimation of cost in the business operation. So, these are the specific decisions in that case again the cost of production is may be the analysis of cost of production is required. Then we will see the we will categorize the cost into two category, category one where the concept used for accounting purpose or though in the accounting perspective and some analytical cost concept that used in the economic analysis of business activity. So, category of cost strictly one for the accounting sense and second when generally we use a different kind of cost for economic analysis. May be there is overlapping when you take the categorization in both these cases in case of accounting sense and in case of economic analysis sense there may be overlapping, but still there is some categorization some kind of some different kind of cost that has been analyzed by taking the accounting purpose and taking the economic analysis purpose. To start with we will talk about that whatever the categorization or whatever the different kind of cost comes under the accounting cost concept or may be the accounting domain. So, the first is the first type comes here is the opportunity cost and actual or explicit cost. So, one is opportunity cost and second one is the actual or explicit cost. So, if you remember when we discuss this may be the different concept that is getting used in managerial economics, then we spend a couple of minutes I think on opportunity cost and opportunity cost is nothing but the cost benefit associated with the next best alternatives. So, opportunity cost can be seen as the expected returns from the second best use of an economic resources which is foregone due to scarcity of resources. So, let us go back to the initial decision of or initial discussion on opportunity cost, how opportunity cost comes into picture is resources are scarce and that is the reason the resources cannot be used for all this activity. Generally, the producer makes a priority list and where to spend the or where to use the resources and generally they use the resources on a specific activity. Now, the concept of opportunity comes opportunity cost comes here with the fact that if the same resources could have been used for the other activity what would have been the benefit that is strictly the opportunity cost for this present activity. So, the benefit what would have been received from the other activity by using the same kind of resources that is the opportunity cost of using this resources. So, opportunity cost can be seen as the expected return from the alternate use or the expected return from the next best alternatives and that is the opportunity cost of the present activity. Then the second one is the actual and explicit cost. Actual or explicit cost are those out of pocket cost for the labour, materials, machines, plant buildings and other factor of production. So, one is opportunity cost which generally derived from the benefit from the next best alternative and explicit cost or the out of pocket cost is labour, materials like whatever the firms or whatever the producer spending on labour, whatever the producer spending on materials, the building cost, plant building, other factor of production or strictly whatever the cost incurs for the different inputs getting used in the production that is the actual or the explicit cost. So, the first category of cost comes under the accounting purposes opportunity cost and the actual or explicit cost. Then we will come to the second category which is business and business cost and the full cost. All the expenses incurred to carry out the business are referred as the business cost. So, typically if you look at this is nothing but the explicit cost or the actual cost. So, this is similar to the actual cost or the real cost and include all the payments and the contractual obligation made by the firm together with the book cost of the depreciation on plant and equipment. So, business cost is nothing but the actual cost. It is similar to the real cost also and include all the payments and the contractual obligation made by the firm together with the book cost of depreciation on plant and equipment. So, part one is actual cost, the obligation that is made by the firm and part two is the book cost that includes the depreciation of the plants and the depreciation of the machinery. So, may be what on the basis of the lifetime of the plant, lifetime of the machinery the depreciation is being calculated and that is also a part of the may be the business cost. Now, what is the need of this business cost? This business cost is used in calculating the business profit and losses and for filling return for income tax and other legal purpose. So, typically this is book cost, business cost used in calculating the business profit and losses and for filling returns for income tax and other legal purpose. So, if you look at this the official kind of cost which add the actual real cost, depreciation of plant and equipment and generally used for the income tax and the other legal purpose. And what is full cost? Business cost is one what is kind of a formal cost which includes the book cost and the depreciation and in compare to that we have full cost which includes the business cost, opportunity cost, normal profit while normal profit represent a necessary minimum earning addition to the opportunity cost which a firm must remain in business. So, full cost includes generally in a somehow we can call it also a market price which includes the business cost plus the opportunity cost what is the next best alternative use of this resources what have been used for producing this plus the normal profit because normal profit is required for the producer to remain in the business. If they are setting of a market price which is just equal to the business cost then there is no profit and for them it is difficult to stay in the market and that is the reason full cost includes the business cost plus the opportunity cost and normal profit because normal profit is required for the producer to stay in the business. So, business cost is one what is which is a kind of a formal or official cost which talks about the actual or real or the explicit cost plus the depreciation of planted equipment in comparison to that we have full cost which includes the business cost, opportunity cost and also the normal profit and normal profit is necessary because this is the minimum earning to the producer to remain in the business. Then we will take the third category of cost which cost is the explicit or implicit or we can call it also imputed cost. So, explicit and implicit cost and this cost are falling under business cost and are those enter in the books of account. So, explicit cost is one which falls under the business cost and are those enter in the book of account payment for wages, salaries, materials, insurance premium, depreciation charges are the example of explicit cost. So, whatever the cost incur for paying the wages and salaries, materials cost, insurance premium, depreciation charges are the example of the explicit cost. This cost involves a cash payment are recorded in the accounting practices. All this cost involves a cash payment are recorded in the accounting practice and in compared to that we have implicit cost. So, explicit cost is basically the input cost and the payment is the cash and that is a part of the accounting book and implicit or the imputed cost is one. Those cost that do not involve the cash outlay or the payment or do not appear in the business accounting system are referred to the implicit or imputed cost. Cost do not involve cash outlay or the cash payments do not appear in the business accounting system it is not in the credit debit and since it is not involve any cash outlay business accounting or it is not a part of business accounting system this is generally known as the implicit or the imputed cost. So, if it is not a part of business accounting system if it is does not involve the cash payment then this is not a formalized kind of cost and that is the reason this is the implicit cost. This is also not taken implicit cost are also not taken into account during calculation of the loss and profit and that is quite obvious if it is not a part of the business accounting system then obviously, this is not a part of the loss or the profit and this explicit and implicit cost together form the economic cost. Then what is implicit cost over here we can take an example of suppose the owner is the producer or the owner is the manager. So, if the owner is working as a manager then generally the resources is getting used freely there is no cost associated with that, but there is a cost associated with this because owner is has some market value and if he is working in some other places maybe he has getting incur some cost the firm or the producer has to incur some cost for it and that is the reason this is part of the implicit cost for this present activity and explicit and implicit cost together they form the economic cost. Then we will take a fourth category of cost in the accounting purpose that is out of pocket and book cost. Expenditure item that involve cash payment cash transfer both recurring and non-recurring are referred to in economic as the out of pocket cost. So, all the expenditure what the firm incurs all the expenditure what the producer incur that involve cash payment or the cash transfer both recurring and non-recurring are referred in economics as the out of pocket cost. All the explicit cost including wages, rent, interest, cost of material, maintenance, transport expenditure and the like are in the classification. So, if you look at this out of pocket includes wages which is recurring and also it is it is recurring actually it is recurring it is on a continuous basis till the production is on the labor is going to get used by the producer and the wages are going to be paid rent till the time the production operation is there you need to pay the rent for using the lend interest till the time production operation is on you need money to invest on it and you need to pay the interest for it cost of material till the time production operation is on you need to use material for the production process and that also incurs on a payment basis maintenance transport expenditure. So, if the production operation is on all these inputs are all on a recurring basis and the producer has to continuously spend on it these are all part of out of pocket cost. Now, we will see what is book cost. So, out of pocket cost is all explicit cost which occurs reoccur on a continuous basis that is the out of pocket cost. Then what is book cost? Some actual business cost which do not involve the cash payment but a provision it is made in books of account and they are taken into account while finalizing the profit and loss account such cost are known as the book cost. So, book cost how it is different from the implicit cost if you look at implicit cost they do not appear in the business accounting system they are not being calculated in case of loss and profit and in the similar line what is book cost there are some actual business cost. So, this is explicit it is not implicit and this is how it is different from the implicit cost. Some actual business cost which do not involve cash payment, but that provision is made in the books of account that they are taken into accounting when finalizing the loss and profit and such cost are known as the book cost and these are somehow payment made by the firm to the itself. Suppose the manager is the owner manager is taking a salary. Obviously, the salary is a part of business accounting system calculated as the part of loss and profit and that is why this is known as the book cost. So, any cost which is a part of business accounting system which is which is considered in calculating loss and profit that is a part of book cost and also this the actual business cost may not involve a direct cash payment may be the firm of remuneration is non cash or it is in kind, but still it appear in the accounting system and it is being taken during loss and profit calculation that is the reason it is known as the book cost and here it makes a difference between the implicit cost and the book cost that implicit cost never appears in the business accounting system and they are not being taken into account when the calculation of loss and profit. Then, we will come to the second part of the category of cost and the second part of the category of cost is on the basis of the economic analysis of business activity. So, till now all the categorization whatever we did that is on the basis of accounting purpose strictly keeping the business accounting system in the mind, but the this categorization what we are going to discuss now this is specifically the analytical cost concept that is used in the economic analysis of business activity. So, the first one is fixed variable cost then we will discuss about the total average and marginal cost, then the short run and long run cost, incremental and song cost, historical and replacement cost and finally we will discuss about the private and the social cost. So, to start with we will discuss about the fixed cost and variable cost. So, there are two types of factors one is fixed factor another is the variable factor. So, cost that are fixed in volume for a certain level of output that is generally known as the fixed cost. So, suppose to produce 100 units of output the K is fixed. So, the K is suppose the machine capital is the machine and to produce 100 units of output there is only requirement of one machinery. So, in this case the cost also remains same up to 100 units of output and that is why this is part of the fixed cost because cost that are fixed in volume for certain level of output that is as the fixed cost. So, they do not vary with the output they remain constant regardless of the level of output. So, whatever may be the output change in the output whether if it is 60 units, if it is 80 units, if it is 100 units still it is the same level of output the fixed cost is remain constant. It includes the cost of managerial and administrative staff, depreciation of machinery, land and maintenance these are the part of the fixed cost. Like administrative staff or the managerial staff whether you produce 100 units, whether you produce 120 units, whether you produce 200 units it is the same there is no difference in the level of fixed cost because you are going to produce all these unit of output with the same fixed unit of the input. So, input are not getting change obviously the cost will not change. So, suppose the administrative staff irrespective of it whether its producer is producing 180, 60 the administrative staff has to come for 8 hours there is no change in the salary not increase not decrease. So, the cost incur through the salary that remain constant and that is the reason we consider the cost associated with the administrative expenses as the fixed cost of production. It is normally a short term concept because in the long run all cost must vary. If you remember in case of production analysis we discuss that in the long run all the variables has to be all the inputs has to be variable in order to increase the output and that is the reason fixed cost are generally a short term concept. Then we will discuss about the variable cost. Variable cost are those that vary with the variation in output and whenever there is a variation in the output that leads to a variation in the input and if there is a variation in the input that leads to the variable cost. It includes cost of raw materials, running cost of fixed capital such as fuel, repairs, routine maintenance expenditure, direct labour charges associated with the output level and the cost of all other input that may vary with the level of output. So, variable cost are those that vary with the variation in output includes cost of raw material, running cost of fixed capital such as fuel, repairs, routine maintenance expenditure, direct labour charges associated with the output level and the cost of all other input that may vary with the level of output. So, if you look at in the long run all the cost has a variable because all the factors are the all the inputs are variable. Total average and marginal cost. The total cost refers to the total expenditure on the production of goods and services. It includes both explicit and implicit cost. The explicit cost themselves are made of the fixed and variable cost. So, total cost is the total expenditure on the production of goods and services. It includes both explicit and implicit cost. The explicit cost themselves are made of a fixed and the variable cost. Total average and marginal cost. So, in that context we will talk about the average cost. Average cost is obtained by dividing the total cost by total output. So, average cost is nothing but the cost per unit of output. So, average cost is total cost divided by the Q. Q is the number of unit of output and TC is the total cost. So, average cost is the per unit cost of the output. Total cost is the sum total of expenditure made on the production of goods and services. And what is marginal cost? Whenever the concept of marginal comes it is the addition to the total cost when you are producing one more additional unit of output. So, marginal cost is the difference between the total cost in the previous unit of production and the current unit of production. So, marginal cost is the addition to the total cost and account of producing one additional unit of a product. It is the cost of marginal unit produced. Marginal cost is the change in the total cost with respect to change in the Q and it is del TC by del Q where TC is the total cost and Q is the unit of output. So, MC is the marginal cost. Marginal cost is the change in the total cost by change, open change in the quantity and that leads to del that is the change in the TC with respect to del Q that is change in the output. Then we will discuss about the short run and long run cost. So, short run cost are cost we change as desired output changes size of the firm remaining constant. This cost are often referred as the variable cost and long run cost on the other hand are cost incur on firm fixed asset such as plant machinery building and like. So, in case of whatever the cost gets changes with respect to the operational part this is the variable cost and this is considered as the short run cost. Long run cost on the other hand are cost incur on the firm's fixed asset such as plant machinery building and the similar kind of expenses. Then we will talk about the incremental cost and the sunk cost. Now, if you remember in some in when we are introducing different kind of managerial concept we discussed about the marginal analysis and incremental analysis. Incremental analysis is required where the per unit changes is not possible and per unit changes is always captured through the marginal change, but when the per unit change is not possible where there a change is has to be in the chunk or change has to be more than one unit the incremental analysis comes into picture. Corresponding to that actually we get the incremental cost when the change in the input is in a chunk it is not per unit then it is a case of the incremental analysis. So, incremental cost refers to the total additional cost associated with the decision to expand the output or to add a new variety of product and the concept of incremental cost based on the fact that in the real world it is not practicable to employ factors for each unit of output separately due to lack of perfect divisibility of the inputs. It also arises a result of change in the product line, addition, introduction of a new product, replacement of the own out plant and machinery, replacement of old technique of production with new one and the similar kind of expenses. So, now when this incremental cost comes into picture one when the decision is or when the change in in a chunk. So, if you look at suppose a machine has a capability to produce 100 units and if producer requires to produce only 50 units it is not that a machine can be may be divide into 50 units or machine can be divided into two parts which produce only 50 units. The producer has to run the machine and in this case whatever the additional they are doing in order to cost incurring to run the machine even if the capacity to produce is 100 they are producing 50 units this is these are the incremental cost. So, incremental cost generally if you look at it comes into picture because all the inputs they are not perfectly divisible and whenever there is a new initiative may be launching a new product or launching a new product line some replacement activity has to be done and that has to be done in a chunk. In that case generally the incremental cost is incur and the expenses related to all those activity is part of the incremental cost. Next see the second part of this category that is sunk cost. The sunk cost are those costs that cannot be altered increase or decrease by varying the rate of output. So, sunk cost are those cost that cannot be altered increase or decrease by varying the rate of output. Once management decides to make incremental investment expenditure and fund are allocated and spent all proceeding cost are considered to be the sunk cost since they accord to the prior commitment and cannot be reverse recover when there is a change in the market condition or change in the business decision. It is like once the firm or the management decide to make incremental investment expenditure on a new product may be a new product line replacing a existing rail replacing a existing product. Once the expenses or once the funds are being spent then whatever the cost proceeding that that has to be that is considered as the sunk cost because since they accord to the prior commitment and cannot be reverse recover when there is a change in the market condition or the change in the business decision. Then we will come to a category of historical and replacement cost. Historical cost refer to the cost and asset require in the past whereas replacement cost refer to the outlay made for replacing an old asset. So, historical cost refer to the cost and asset acquire in the past the cost associated with that whereas replacement cost refers to the outlay made by replacing an old asset. This concept derive from unstable nature of price behavior when price becomes stable over time other things be equal historical and replacement cost will be at par with each other. So, there is a unstable nature of price behavior that is the reason there is a difference between the historical cost and replacement cost. When price becomes stable over time other things being equal there is there will be no difference between the historical cost and the replacement cost. The difference comes because of the instability nature of the price. 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 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 DC 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 there 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 DC 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 byproduct 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 byproduct 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 firms view point this is external cost, but from the society since even if they are not producing the product they are exposed to the byproduct of the firm byproduct 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 mills 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 where the factory is located and the factory discharging creating a air pollution because of that they are developing a respiratory disease this is the social 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 a 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, 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 a 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 increases as output increases. So, total variable cost is the part 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 that 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 represents the cost and total variable cost is total variable cost is starting from origin and it 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 is 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 of 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 an 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 case of the cost and return. So, cost and output relationship are normally determined by the cost function and exit rate by the cost function whether it is a short run, 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 specifically 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 it takes a 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 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 cubic cost function and in case of 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 by q 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 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 to 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 fixed cost not because it is as 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 0.5 q q. So, 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 6 q minus 0.5 q square 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 0.05 q q. 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 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.