# Short-Run Costs and Output Decisions

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1 Semester-I Course: 01 (Introductory Microeconomics) Unit IV - The Firm and Perfect Market Structure Lesson: Short-Run Costs and Output Decisions Lesson Developer: Jasmin Jawaharlal Nehru University Institute of Lifelong Learning, University of Delhi 1

2 Table of Contents Short-Run Costs and Output Decisions Learning Outcomes Introduction Short-Run Costs Fixed Costs Total Fixed Costs Average Fixed Costs Variable Costs Marginal Cost Shape of Marginal Cost Curve in the Short-Run Total Variable Costs and Marginal Costs : Graphical Representation Average Variable Cost Average Variable Cost and Marginal Cost: Relationship Total Cost Average Total Cost Profit Maximization, revenues and costs Total Revenue Marginal Revenue Profit Maximization The Short Run Supply Curve Conclusion Summary Practice Questions Glossary Institute of Lifelong Learning, University of Delhi 2

3 Short-Run Costs and Output Decisions Learning Outcomes This lesson revolves around the cost of production and the output decisions of the firms. Profit maximizing firms aim at minimizing the cost that they incur in production. After having gone through the chapter, the reader should be able to understand various concepts related to short-run costs like fixed costs, variable costs, average and marginal costs and the relation between the two. The chapter discusses the demand curve and how the price is determined in a perfectly competitive set up. Also, the short-run supply curve for a perfectly competitive firm and the factors on which it depends has been discussed. The lesson is followed by a set of practice questions to help the reader, better understand the concepts discussed in this lesson. Introduction It can be reiterated that, a profit maximizing firm is always on the lookout for the production techniques that minimize the cost of production. We continue to analyze the case of a perfectly competitive firm, which takes the prices to be fixed both in the market for the final product and the market for factors of production. The cost of production depends on the production technique, the quantity of inputs that are used in producing the output and the input prices. As we know profit of a firm is determined by revenue and costs, both the aspects are equally important to be analyzed. Figure 1 shows the decisions that the firms have to take and the elements that help the firms make such decisions. In this lesson, the short run costs and the supply curve of the perfectly competitive firm have been discussed. Institute of Lifelong Learning, University of Delhi 3

4 Short-Run Costs Short-Run can be defined as the time period where one or more of the factors of production of a firm are fixed and the exit and entry of the firms from the industry is constrained. Firms in the short-run can be said to have two types of cost: Fixed and Variable costs. Fixed costs are the costs that do not depend on the level of production, these costs are incurred even if the output is zero. Variable costs vary with the level of output. So the sum of fixed and variable costs gives total costs. Where TC is total costs, TVC is total variable costs and TFC is total fixed costs. Fixed Costs To produce any output at all, the factory has to incur costs on the inputs which are fixed in nature in the short-run. These inputs include building for the factory, furniture, machinery etc. Costs of this nature are called fixed costs. The proportion of fixed costs in the total costs differs from one firm to the other. In this chapter, we assume that two inputs are used in production: labor and capital. Usually, capital is seen as a fixed input in the short-run while labor is seen as a variable input. But, it is safe to assume that capital has both a fixed and a variable component. There is always some capital that can be bought in the short-run as well. Let s say that Sam wants to set up a factory to manufacture shoes. He will buy land to set up factory, machines will be required. These costs are fixed in the short run. The Institute of Lifelong Learning, University of Delhi 4

5 monthly electricity bill and the salary of can also be called fixed costs. The costs on raw material are variable costs. As the production rises, more administrative staff may be required, computers for them to work with, may be required. So, the firm might add to its capital even in the short run. Total Fixed Costs As stated previously these are the costs that do not vary with the output. Fixed costs are also referred to as overheads. If Sam incurred a fixed cost of Rs in setting up a factory, this cost stays the same at all levels of output. Part a of figure 2 shows the graph of total fixed cost. Since in the short run fixed costs cannot be controlled by the firm they are also called sunk costs. Average Fixed Costs Average fixed cost is computed by dividing the total fixed cost by the total number of units of output. If total output is given by Q, Average fixed cost is given by following equation: The graph for average fixed cost (AFC) is shown in part b of figure 2. If the fixed costs are Rs , the average fixed cost when the firm produces a single unit of output is Rs When the firm produces 2 units of output the average fixed cost is Rs When the firm produces 5 units of output the average fixed cost is Rs It can be said that the average fixed cost falls as the output rises. The fixed cost is spread over the units of output produced. This phenomenon is also called spreading overhead. The average fixed cost is a downward sloping curve and the average fixed cost Institute of Lifelong Learning, University of Delhi 5

6 tends to zero as the output rises. Table 1 shows the data on the short-run total fixed costs and average fixed costs of a firm. Let s say the total fixed cost in the short-run is Rs The total fixed cost stays the same for all levels of output, while the average fixed cost falls as the output rises. Table 1: Total fixed cost and the average fixed cost in the short run Output Total fixed cost (Rs.) Average fixed cost (Rs.) Variable Costs Total Variable Costs: It is the sum of all those costs that vary with the level of output in the short-run. Additional output is produced by employing more inputs and the additional cost incurred will depend on the additional quantity of inputs and their prices. As we have discussed, out of all the production techniques available, the firm chooses the one that produces the required level of output at the minimum cost. The total variable cost incurred with different production techniques, to produce the required level of output, can be compared. A firm can choose a labor intensive or a capital intensive technique. This choice depends on its scale of production in the present. A small-scale firm, with low level of capital might want to choose a labor intensive technique. The information that the labor is relatively cheap or expensive might not play much of a role in such a choice. Similarly a firm operating on a large scale, with a large stock of capital, might go with a capital intensive technique. The graph of total variable cost shows the total variable cost as a function of the firm s level of production. It needs to be reiterated that the total variable cost depends on the production technique used and the input prices. Table 2 shows a comparison of two production techniques for producing output. The production technique 1 is more capital intensive than the production technique 2. We look at the capital that is variable in nature. The firm also deals with the capital that is fixed in nature. Let s assume that the price of a unit of labor is Rs.2 per unit and the price of capital is Rs.4 per unit. Institute of Lifelong Learning, University of Delhi 6

7 Table 2: Comparison of production techniques for different level of outputs Output Technique Units of input required Total Variable Cost Capital (K) Labor (L) 1 unit of output unit of output unit of output As the table shows, to produce one unit of output, the labor intensive technique 2 involves the lowest cost. To produce 2 units of output, again the labor intensive technique is the least costly. But for 3 units of output, the capital intensive technique 1 should be used since it involves the least cost. Figure 3 shows the graph of the levels of output and the corresponding total variable cost, where an assumption is made that the firm uses the cost minimizing production technology. The total variable cost curve, therefore, shows the cost of production of the level of output, using the cost minimizing production technology. Marginal Cost Marginal cost is the rise in the total cost due to an additional unit of production. The marginal costs largely represent the change in the variable costs since, it s the variable Institute of Lifelong Learning, University of Delhi 7

8 costs that change with the output while the fixed costs do not. For instance if the total cost to produce 3 toys is Rs.150 while 4 units are produced by incurring Rs.175 as the total cost, the marginal cost to produce the 4 th unit is Rs.25. Table 3 shows the marginal cost extracted from the data on the total variable cost. Marginal cost of producing an extra unit of output is obtained by taking difference between the total variable costs. The marginal cost of producing the third unit will be given by subtracting the total variable cost incurred in producing 2 units of output from the total variable cost incurred in producing three units of output. Table 3: Marginal Cost and Total Variable Cost Units of Output Total Variable Costs (Rs.) Marginal Costs (Rs.) As the table shows the marginal costs can be easily derived from the total variable costs. The Shape of the Marginal Cost Curve in the Short Run The law of diminishing returns, operates in the short run. The law of diminishing returns states that beyond a particular point, if additional units of a variable input are employed along with fixed inputs, the marginal product of the variable input falls. This also has an implication that in the short run, since the firm is operating at a given scale of production, the marginal cost starts rising with the output beyond a point of production. This can be illustrated with an example. Suppose a person owns a small scale business of printing cards. If he has one printing machine, as he goes on employing more labor, he will find that the marginal product of labor falls after a particular point. This indicates that due to the fixed capacity the marginal product of the variable input falls and hence greater units of variable input will have to be used to produce additional unit of output. Hence, the marginal cost will go up as the production continues. Each additional unit is more costly to produce. Thus, the diminishing returns indicates rising marginal cost. Part a of figure 4 shows the graph for marginal product, while part b shows the marginal cost. Institute of Lifelong Learning, University of Delhi 8

9 Hence, in the short run where the firm is constrained to operate at a particular scale of production, since one or more factors of production are fixed, this brings about diminishing returns to the variable inputs and this limits the capacity of production of the firm. As the firm moves towards its capacity limit, successive units of variable input face a fall in their marginal product, implying that the marginal cost increases with the output in the shortrun. Total Variable Costs and Marginal Costs: Graphical representation Figure 5 shows the graph for total variable costs and the marginal costs. The marginal cost curve is a U-shaped curve. It declines up to a particular point of production and then starts rising as the firm approaches its capacity limit. The graph shows that the marginal cost falls till the firm reaches the 1000 units output mark. Beyond this level of output the marginal costs start rising. The total variable cost curve on the other hand has a positive slope, since the total variable costs rise with output. The slope of the total variable cost curve is given by the marginal cost. The slope of the total variable cost curve can be computed by taking the ratio of the change in total variable cost and the change in the quantity. Marginal cost is the change in the total variable cost due a unit change in the output. Hence, the marginal cost can be called the slope of the total variable cost. Slope of TVC = = = MC Institute of Lifelong Learning, University of Delhi 9

10 Before reaching the 1000 unit output mark the total variable cost increases at a decreasing rate as the marginal cost is declining, i.e. the total variable cost curve is flatter. However, beyond 1000 units of output, the marginal cost rises. The total variable cost starts rising at an increasing rate and its curve becomes steeper. This relation between the total variable cost and marginal cost becomes clear, if one goes through table 4. Table 4: Short-Run Costs Output TVC MC AVC ( TFC TC AFC ( ) ATC ( ) ( ( ) Institute of Lifelong Learning, University of Delhi 10

11 As we can see that the marginal cost falls till the 4th unit of output, beyond this point the marginal cost begins to rise. Total variable cost rises consistently with the output and the rate of increase in the total variable cost, as mentioned before, is explained by the marginal cost. Average Variable Cost (AVC) Average variable cost is the ratio of total variable cost and the total number of units of output. If total output is given by Q, then the average variable cost can be computed as follows: Average variable cost is also shown in table 4. Average Variable Costs and Marginal Costs Average and Marginal costs are also related like the way average and marginal product are related. When the marginal cost is below the average variable cost, the average variable cost tends to decline towards the marginal cost and when the marginal cost is above the average variable cost, the average variable cost again rises towards the marginal cost. The average variable cost is not as quick to change as the marginal cost, in fact the average variable cost follows the movements in marginal cost with a lag. Figure 6 shows the relation between average variable cost and marginal cost. At lower levels of production the marginal cost falls, at a particular point of production say 100 units, the marginal cost is at its lowest, as the marginal cost falls the average variable cost also follows this decline. After 100 units of output the diminish returns phenomenon sets in and the marginal cost begins to rise, however, the average variable cost continues to fall until 150 units of output, since the marginal cost is still below it. At 150 units of output the average variable cost is at its Institute of Lifelong Learning, University of Delhi 11

12 minimum and the marginal cost has risen to match the average variable cost. Beyond this level of output the marginal cost surpasses the average variable cost. Once the marginal cost exceeds the average variable cost, the average variable cost also begins to rise. Let s say that the minimum of marginal cost is at Rs.5, at 100 units of output. At the minimum of marginal cost, the average variable cost is Rs.6. After reaching a minimum of Rs.5 the marginal cost starts rising and meets the average variable cost at its minimum of Rs.5.5, at 150 units of output. After 150 units of output since marginal cost exceeds the average variable cost, it pulls with it the average variable cost too. Total Costs Total cost (TC) is the sum of total fixed costs (TFC) and the total variable costs (TVC). Figure 7 shows the graph for total cost, total fixed cost and total variable cost. The total cost curve is just a vertically (upward) shifted version of the total variable cost. The vertical difference between the total cost and the total variable cost curve at all levels of output is given by the total fixed cost. In the figure the total fixed cost is shown at the level of Rs Institute of Lifelong Learning, University of Delhi 12

13 Average Total Cost Average cost is the cost per unit of output produced. It is the ratio of the total cost and the total output. The average can be calculates as: + Where Q = Level of output ATC = Average Total Cost AFC = Average Fixed Cost AVC = Average Variable Cost Or, For example in table no. 4, the total cost for 4 units of output is Rs.1037 so the average total cost is Rs Figure 8 shows the curves for average total cost, average variable cost, average fixed cost and marginal cost. Both the average total cost and the average variable cost curves are U- shaped due to the operation of the law of diminishing returns in the short run. The minimum point of average variable cost curve lies to the left of the minimum point of the average cost curve. This is because average total cost is the sum of average variable cost and the average fixed cost. Average variable cost falls with an increase in output till point B. After this point the average variable cost rises, but the average cost continues with its decline due to the fact that the rise in the average variable cost is offset by the fall in average fixed cost, initially. However when the rise in the average variable cost supersedes the fall in the average fixed cost, it pulls up the average total cost with it. As the output rises, the average variable cost tends to approach the average total cost but these two Institute of Lifelong Learning, University of Delhi 13

14 curves do not meet. The relationship between the average total cost and the marginal cost is similar to the one that marginal cost shares with the average variable cost. The average total cost follows the marginal cost curve but, it is not as quick to change as the marginal cost. In fact the average total cost lags behind the marginal cost more as compared to the average variable cost. As is evident in the figure, the marginal cost falls till it reaches its minimum point, A. beyond this point it rises and cuts the average variable cost and the average total cost at their respective minimum points, B and C. Hence the marginal cost brings about changes in the average costs. Institute of Lifelong Learning, University of Delhi 14

15 Important Cost Concepts Accounting Costs These are explicit costs in terms of payment of wages and raw materials. These occur in the firm s books of account. Economic Costs These include both the explicit and implicit or imputed costs. The opportunity costs of various inputs are included in the economic costs. Private Costs These are the costs that are taken into account by a firm that indulges in the production process. Social Costs These are the costs of commodity production that are inflicted on the society in terms of environment degradation and increasing pollution. Unfortunately, these costs are not taken into account by the firms that are engaged in production. Opportunity Cost Opportunity cost is the cost of the second best alternative that is foregone. This is because the resources are scarce and a particular resource can be put to multiple alternative uses. Profit Maximization, Revenues and Costs It has been continuously discussed that profit maximization is a objective of a firm and profit is the difference between the total revenues and total costs. To expand profit a firm might want to raise the price above per unit cost of production, but then it might lose out on demand and run out of the business. Profits in the industry will entice competitors to get in the industry which will bring down the overall profit. It is important to understand how a firm decides what quantity of output to produce. Let s stick to the discussion of perfectly competitive market. A perfectly competitive firm is a price taker. The price is determined by the market forces of demand and supply in the industry. Since the firm is a miniscule part of the market, the market consisting of many sellers and buyers, it cannot influence this market price. The firm faces a perfectly elastic demand curve at the equilibrium market price in the short run. It won t be able to sell Institute of Lifelong Learning, University of Delhi 15

16 anything if it charges a price above the market price since there are too many competitors in the market and it is irrational to sell at a price less than the market price. Figure 9 shows a perfectly competitive set up. The market price of Rs.10 is determined by demand and supply forces at the industry level. The demand curve at this price is horizontal and perfectly elastic. Total Revenue Total revenue is the quantity of output that is sold multiplied by the price at which it is sold. For example if a firm sells 600 dolls in a month at the price of Rs.50, the total revenue is Rs (Rs.50 X 600). A perfectly competitive firm charges a fixed price, for whatever quantity of output it sells. So the total revenue is simply P X Q. Where P is the price per unit and Q is the quantity of output sold. Marginal Revenue Marginal revenue is the rise in the total revenue when one more unit of output is sold. For example if 6 buckets are sold for Rs.500 and 7 buckets are sold for Rs.600, the marginal revenue for the seventh bucket is Rs.100. Marginal revenue can be computed as: Or, Marginal revue for the nth unit ( ) = Since a perfectly competitive firm charges the same price for each unit of output sold, the marginal revenue for each unit is the market price (P). Hence, the marginal revenue curve is also horizontal like the demand curve at the equilibrium price. Institute of Lifelong Learning, University of Delhi 16

17 Profit Maximization In this analysis we are dealing with a perfectly competitive market structure assuming that the firms aim to maximize the profit. Figure 10 shows the supply and demand in the industry and the corresponding equilibrium price. It also depicts a representative perfectly competitive firm, which takes this price P as fixed. The firm can sell any quantity it wants to at this equilibrium price of Rs.10. but it has to arrive at the profit maximizing level of output. It can be said that one should choose the level of output where the marginal cost is at its minimum. But the firm needs to maximize the difference between total revenue and total cost, not marginal revenue and marginal cost. When the marginal cost is at its minimum, i.e. Rs.4, the marginal revenue is greater than the marginal cost which reflects that the profits are not being maximized. The optimal level of output is greater than the level of output of 10 units where the marginal cost is minimum. At 15 units of output where the average total cost is at its minimum is also not the optimal level, since the marginal revenue is Rs.10 while the marginal cost is Rs.7, profit can be further expanded by producing and selling a greater output. The equality of marginal revenue and marginal cost occur at 20 units of output, profit is maximum here. If the firm produces more than 20 units the marginal cost exceeds the marginal revenue, which reduces the profit. The profit maximizing level of output for a perfectly competitive firm is the one where the price of the output is equal to the short run marginal cost, P = MC. But not all the firms are perfectly competitive, hence the profit maximizing output level is the one where marginal revenue is equal to the marginal cost, MR = MC. A numerical example will help understand the concept stated above in a better manner. Table 5: Profit maximizing output for a perfectly competitive firm Output TFC (Rs.) TVC (Rs.) MC (Rs.) P=MR (Rs.) TR (Rs.) TC (Rs.) Profit (Rs.) Institute of Lifelong Learning, University of Delhi 17

18 As can be seen when the firm produces nothing it incurs a loss. It earns a marginal profit of Rs.10 at the first unit of output which compensates for the previous loss. By producing two units of output and selling it at Rs.25 per unit, it earns a profit of Rs.10. Selling three units brings a profit of Rs.25. The fourth unit brings additional profit of Rs.5, so the fourth unit should be produced as the total profit reaches Rs.30. At the fifth unit diminishing returns make the marginal cost exceed the marginal revenue and this reduces the profit by Rs.5, clearly the fifth unit should not be produced. Hence the profit maximizing level of output is 4 units of the good. The Short Run Supply Curve Suppose the equilibrium price of the product rises, due to a rise in the demand. Suppose the price now becomes Rs.15. At Rs.10, the firm was producing 20 units of output. To produce less than this level or more than it would reduce the profit. At Rs.15 the firm will produce 25 units of output. If due to a further shift of the demand curve the price rises to Rs.30 it will produce 30 units of output. Hence at any equilibrium level of price the marginal cost curve shows the profit maximizing level of output. Thus the upward rising portion of the marginal cost curve is the short run supply curve of a competitive firm. Figure 11 shows the supply curve of the perfectly competitive firm in the short run. Conclusion The available production technique, the quantity of inputs used and the prices of those inputs determine the cost of production. Any firm, big or small, aims at maximizing its profit. The firm would want to minimize the cost it incurs. It is extremely crucial to examine the concept of cost in order to comprehend how a firm takes several decisions related to Institute of Lifelong Learning, University of Delhi 18

19 production and what all factors determine the profit. The importance is not only restricted to the decisions that the firm takes, the costs, as we have seen in the short run analysis, determine the supply curve of a perfectly competitive firm. It is interesting to learn how the law of variable proportions effects production and the costs, and it comes across as if these two concepts are inherently related to each other. Hence the theory of costs is extremely useful to understand the functioning of firms in the market. Summary The chapter throws light on several important concepts. Following points present the summary of the chapter. Production cost depends on the choice of production technique, quantity of inputs used and the input prices. Fixed costs are the costs that do not vary with the level of output. Variable costs vary with the level of output. Total cost is the sum of total fixed cost and total variable cost. Average fixed cost is the ratio of the total fixed cost to the total quantity produced. The average fixed cost as the output produced rises. Marginal cost is the change in the total cost when an additional unit of output is produced. In the short run the production capacity of a firm is fixed because of the fixed inputs which implies that it has to work at a given scale of production. Because of the law of variable proportions, the marginal cost rises beyond a particular point of production. Marginal cost is the slope of the total cost and the total variable cost curve. Average variable cost is the ratio of total variable cost to the total output produced. Marginal cost dries the changes in the average total cost and the average variable cost. It cuts both the average variable cost and average total cost at their respective minimum points. Average total cost is computed by dividing the total cost by the total output. It can also be computed as the sum of average fixed cost and average variable cost. A perfectly competitive firm is a price taker, the demand curve it faces at the equilibrium price set by the market forces of demand and supply is perfectly elastic. Total Revenue is the product of price, per unit of output and the quantity of the good that the firm produces and sells. Marginal revenue is the change in the total revenue due to an additional unit of output is produced and sold. For a perfectly competitive firm, the marginal revenue is the same as the equilibrium price. The a perfectly competitive firm will choose that level of output to maximize its profit, where the upward sloping portion of the marginal cost curve intersects the marginal revenue or the price line. In the case of a perfectly competitive firm this is when P = MC. For any firm the general condition is MR = MC. The short run supply curve for a perfectly competitive firm is given by the upward sloping portion of the marginal cost curve. Institute of Lifelong Learning, University of Delhi 19

20 Practice Questions Questions for Review Q.1 What is opportunity cost and why should it be included while computing total economic costs? Q.2 What can be the probable reasons for a shift in the cost curves? [Hint: Technological changes, changes in the input supply] Q.3 Explain elaborately, the relation between the average total cost curve, average variable cost curve and the marginal cost curve. Q.4 Why are the short run average total cost, average variable cost and marginal cost curves U-shaped? Q.5 How are the concepts of production and cost linked to each other? Discuss similarities with respect to the law of diminishing returns also. Q.6 What will happen if the perfectly competitive firm produces a level of output where the Price is not equal to the marginal cost? Q.7 Distinguish between Accounting and Economic costs. In which of these two costs will the normal rate of return to capital be included. Q.8 Why is the marginal revenue, equal to the equilibrium price in the perfect competition? Discuss with an example. Multiple Choice Questions Table Q1: Total Fixed Cost, Total Variable Cost and Total Cost of a Firm (Rs.) Output Total Fixed Cost Total Variable Cost Total Cost Institute of Lifelong Learning, University of Delhi 20

21 Q.1 What is the marginal cost at the 3 rd unit of output? a) 4 b) 2 c) 1 d) 5 Q.2 What is the average fixed cost for 4 units of output? a) 10 b) 5 c) 3.33 d) 2.5 Q.3 What is the average variable cost for 3 units of output? a) 4 b) 3.5 c) 3.66 d) 4 Q.4 Why is the total fixed cost Rs.10 at zero units of output? a) The table shows wrong information, no cost is incurred at zero units of output. b) It is the fixed cost, hence it is incurred even when no output is produced. c) It is the wage paid to the labor. d) All the options are wrong. Q.5 in the above table, the marginal cost schedule is 4,3,4,5. These numbers correspond to each unit of output. Why does the marginal cost fall initially and rises later. a) Presence of fixed factors. b) Law of variable proportions. c) Fixed capacity due to fixed factors. d) All of the above. Correct Answers/Options for the Multiple Choice Questions Question Number Option Q.1 a Q.2 d Q.3 c Q.4 b Q.5 d Institute of Lifelong Learning, University of Delhi 21

23 Glossary Average Fixed Cost: Average fixed cost is the ratio of total fixed cost and the total number of units of output. Average Variable Cost: Average variable cost is the ratio of total variable cost and the total number of units of output. Average Total Cost: Average cost is the cost per unit of output produced. It is the ratio of the total cost and the total output. Fixed Cost: To produce any output at all, the factory has to incur costs on the inputs which are fixed in nature in the short-run. These inputs include building for the factory, furniture, machinery etc. Costs of this nature are called fixed costs. Marginal Cost: Marginal cost is the rise in the total cost due to an additional unit of production. Marginal Revenue: Marginal revenue is the rise in the total revenue when one more unit of output is sold. Total Cost: This is the sum of total variable cost and total fixed cost. Total Revenue: Total revenue is the quantity of output that is sold multiplied by the price at which it is sold. Variable Cost: These are all those costs that vary with the level of output in the short-run. Slope: The change in one variable due to a unit change in the other variable. References Case, Karl E. and Fair, Ray C. (2007), Principles of Economics, Ch.8, 8 th edition, Pearson Education Inc. Institute of Lifelong Learning, University of Delhi 23

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