Econ 1011 (Chapter IV)

1. INTRODUCTION TO ECONOMICS (ECON 1103) By: MICHAEL T.(MSc.) Dire Dawa University College of Business and Economics Department of Economics April, 2022

2. CHAPTER FOUR CHAPTER FOUR THE THEORY OF PRODUCTION AND COST April 12, 2022 By: Michael T. 2

3. OUTLINE 4.1 Theor y of Production  Basic Concepts of Production  Production function  Production with one variable input 4.2 Theor y of Cost  Basic Concepts of Cost  Short run Cost of Production  Relationship between Short-run Production and Cost Curves  The Least Cost Rule April 12, 2022 By: Michael T. 3

4. 4.1 T H E O RY O F P RO D U C T I O N Basic Concepts of Production  Raw materials yield less satisfaction to the consumer by themselves. In order to get better utility from raw materials, they must be transformed into outputs.  Production: is the process of transforming or converting resources (or inputs) into commodities (or outputs). It can also be defined as an act of creating value or utility.  Precisely, production is the process of combining inputs to make outputs. Input Production Output April 12, 2022 By: Michael T. 4

5.  Inputs: are anything that can be used in the production of goods and services. All inputs used in production are broadly classified into four categories: land, labor, capital and entrepreneurship.  Inputs can also be divided into two main groups- fixed and variable inputs. Fixed Inputs  Fixed inputs are those inputs whose quantity cannot readily be changed when market conditions indicate that an immediate adjustment in output is required. In other words, fixed inputs are those inputs whose quantity remain fixed for a given period of time.  Skilled labor, land, factory buildings, heavy capital equipment, are some examples of fixed inputs because their quantity cannot be changed or manipulated easily in a short period of time. 5 April 12, 2022 By: Michael T.

6. Variable Inputs  An input whose quantity can be changed during the period under consideration is known as a variable input. In other words, variable inputs are those inputs whose quantity can be altered(increased or decreased) almost instantaneously in response to desired changes in output.  That is, their quantities can easily be diminished when the market demand for the product decreases and vice versa. The best example of variable input include raw materials, unskilled labor, power, fuel, transportation, etc. Output: refers anything that comes from the given production process. The end products of the given production process are outputs which could be tangible (goods) or intangible (services) 6 April 12, 2022 By: Michael T.

7. Production Period  In economics production periods is classified into two categories: the short-run and the long-run. 1. Short Run Production Period  In economics, short run refers to a period of time in which the quantity of at least one input is fixed. In other words, short run is a time period which is not sufficient to change the quantities of all inputs so that at least one input remains fixed.  Here it should be noted that short run periods of different firms have different durations. Some firms can change the quantity of all their inputs within a month while it takes more than a year for other types of firms. April 12, 2022 By: Michael T. 7

8. 2. Long Run Production Period  The term long run refers to the production time period during which all factors of production can be varied or all inputs are variable. Long-run is the period during which the size of the plant can be changed. A firm can install a new plant or raise a new factory building. Thus, all the factors are variable in the long-run.  It may be noted that the distinction between the short-run and the long- run does not correspond to a specific calendar period, such as a month or a year. It is rather based on the possibility of input adjustments.  In a very simple language, short run doe not refer to relatively short period of time like a year or less than a year, and long run doe not refer to period of time greater than a year or 5 year. April 12, 2022 By: Michael T. 8

9. Production Function  A production function shows the technical relationship between the different combinations of inputs used in a given production and output.  It shows the maximum output that can be produced with fixed amount of inputs and the existing technology. It can be expressed in tabular or graphic form or by a mathematical formula.  The production function is written mathematically as: Q = f(X1, X2, X3,....., Xn) Where X1, X2, X3,..., Xn are different types of inputs and Q is amount of output produced. April 12, 2022 By: Michael T. 9

10.  If the quantity of at least one input remains fixed, the above mentioned production function is called short run production function.  But if all the inputs are variable, then the production function is called long run production function. April 12, 2022 By: Michael T. 10

11. Production Function with One Variable Input  In this section, we will focus on a production process in which there are only two factors of production; labor and capital, where capital is the fixed factor and labor is the variable factor.  Given the assumptions of short run production, here the firm can increase its output only by increasing the amount of labor it uses. Hence, its production function can be given by: Q f (L )  The above function shows different levels of output the firm can produce by efficiently utilizing different units of labor and the fixed capital. April 12, 2022 By: Michael T. 11

12. Total Product, Average & Marginal Product ♠ Before we take up a detailed analysis of production function with one variable input, lets clarify the three concepts used to explain input- output relationship. These are 1. Total Product (TP) 2. Average Product (AP) and 3. Marginal Product (MP) 1. Total Product ♦ Refers to the total amount of output that can be produced by efficiently utilizing specific combinations of the variable input and fixed input. April 12, 2022 By: Michael T. 12

13. Table 4.1: Hypothetical Schedule of TP, MP and AP ♦ The above table shows that increasing the variable input (while some other inputs are fixed) can increase the total product only up to a certain point and output tends to decline if we employ more and more unit of the variable input beyond the carrying capacity of the fixed input. ♦ In general, the TP function in the short-run follows a certain trend: It initially increases at an increasing rate, then increases at a decreasing rate, reaches a maximum point, and eventually falls as the quantity of the variable input rises. April 12, 2022 By: Michael T. 13

14. 2. Average Product ♦ Average product of an input(AP): is the level of output that each unit of input produces, on the average. In other words, it tells us the mean contribution of each variable input to the total product. ♦ Mathematically, average product is the ratio of total output to the number of the variable input. TP AP  L ♦ As the amount labor increase combined with the fixed inputs, average product of labor first increases, reaches its maximum value and eventually declines( See the previous table and Figure 4.2). April 12, 2022 By: Michael T. 14

15. 3. Marginal Product ♦ Marginal Product(MP): is the measure of change in total product resulting from the use of one unit more of a variable input assuming other inputs being constant. For instance, the change in total output resulting from employing additional worker (holding other inputs constant) is the Marginal Product of Labor (MPL).   TP  Q   MP  L L ♦ Marginal product of labor measures the contribution of each additional unit of labor employed to the total output. ♦ MPL measures the slope of the total product curve at a given point. April 12, 2022 By: Michael T. 15

16. ♦ Like average product, the marginal product of the variable input first increases, reaches its maximum and then decreases to the extent of being negative as we employee more and more units of variable inputs. Figure 4.2: TP, AP and MP Curves April 12, 2022 By: Michael T. 16

17. Relationship Between TP, AP and MP The Relationship between MP and AP The patterns of average product and marginal product curves are similar.  When MP > AP, this means that AP is rising When MP = AP, this means that AP is at maximum When MP < AP, this means that AP is falling. The Relationship between TP and MP  When MP increases, TP increases at an increasing rate When MP declines, TP increases at a diminishing rate When MP becomes zero, TP reaches its maximum  When MP becomes negative, TP begins to decline. April 12, 2022 By: Michael T. 17

18. The Law of Diminishing Marginal Return  Also known as ‘the law of variable proportions’. The Law of Variable Proportions states that as successive units of a variable input(say, labor) are added to a fixed input (say, capital or land), beyond some point the extra, or marginal product that can be attributed to each additional unit of the variable resource will decline.  More precisely, the LDMR states that increasing the amount of a variable input is combined with fixed inputs, eventually the contribution of each additional amount of the variable input to the total output (MP) declines. April 12, 2022 By: Michael T. 18

19. Note that: This law operates only if technology does not change The law starts to operate after the MP curve reaches its maximum  This law is universal because the tendency of diminishing return is all pervading, and so it applies sooner or later in every field of production. Example: Suppose that the short-run production function of a certain cut- flower firm is given by: Where L is labor input and K is fixed capital input (K=5). a) Determine the average product of labor (APL) function. b) At what level of labor does the TP of cut-flower reach the maximum? c) What will be the maximum achievable amount of cut-flower production? April 12, 2022 By: Michael T. 19

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21. S t a g e s o f P r o d u c t i o n  The short-run production function (with one variable input) can be divided into three distinct stages of production. We may use Figure 4.3 below to explain these stages. Stage I ♠ It goes from the origin to the point where the APL is maximum, which is the equality of MPL and APL. ♠ The producer should not limit himself at this stage. ♠ In this stage MPL is greater than APL i.e., each additional unit of labor is contributing more than the average product. As a result of that APL increases. This stage is not an efficient region of production though the MP of variable input is positive. April 12, 2022 By: Michael T. 21

22.  The reason is that in this stage the variable input employed is relatively too small so as to efficiently run the fixed input. Thus, there is underemployment of variable input and underutilization of fixed inputs. This is the stage of increasing return to labor. Figure 4.3: The three stages of production April 12, 2022 By: Michael T. 22

23. Stage II  This stage is the efficient region of production.  It ranges from the point where APL is at its maximum (MPL=APL) to the point where MPL is zero.  In this stage additional inputs are contributing positively to the total product and MP of successive units of variable input is declining. Here, as the labor input increases by one unit, output still increases but at a decreasing rate. This is because the marginal product of labor diminishes.  Hence, the efficient region of production is where the marginal product of the variable input is declining but positive. Thus, the second stage of production is termed as the stage of diminishing marginal returns. April 12, 2022 By: Michael T. 23

24. Stage III  This stage starts from the point where TP reach maximum to the right ( whenever MP is negative). Obviously, a rational firm should not operate in stage III because additional units of variable input are contributing negatively to the total product (MP of the variable input is negative).  In a very simple language, we can say that in this stage, the producer must stop its production. This is because the contribution of additional unit of labor to the total output(MPL) becomes negative.  The cause of negative marginal returns is the fact that the volume of the variable inputs is quite excessive relative to the fixed input. April 12, 2022 By: Michael T. 24

25.  Hence, in this stage there is overemployment of variable inputs and over utilization of fixed inputs.  Thus, in this region the total product curve slopes downwards.  This stage is also known as the stage of negative marginal returns to the variable input. Thus, it can be concluded that a rational producer should operate in stage II where both the average product and the marginal product are positive but declining. For the sake of convenience, we can represent the three stages of production in tabular form as follows: April 12, 2022 By: Michael T. 25

26. CONCLUSION ♠ ♠ It is obvious that no ‘rational’ firm will choose to operate either in in Stage I or in Stage III. In Stage I the firm is underutilizing its fixed capacity, so in this stage marginal product of variable input rises (i.e., each additional unit of the variable factor contributes more to output than the earlier units). It is therefore profitable for the firm to keep on employing additional units of the input. ♠ In Stage III, the firm over utilizes its fixed capacity. It is therefore inadvisable to use any additional units. Even if the cost of variable input is zero, it is still unprofitable to move into Stage III. It can, thus, be concluded concluded that Stage II is the only relevant range for a rational firm. April 12, 2022 By: Michael T. 26

27. Table 4.2: Summary of Stages of Production Stage Total Product Marginal Product Average Product Initially TP increases at an MP increases at a decreasing AP continuously I increasing rate and subsequently rate, reaches maximum and increases & reaches at a diminishing rate starts to decline the maximum Increase at diminishing rate, and From the maximum Continues to decline and II eventually reaches the maximum begins to decline eventually becomes zero Continues to decline Begins to decline Negative III but is always positive April 12, 2022 By: Michael T. 27

28. Effect of Technological Change on Production Function  So far, we assume that technology is unchanged. But what will happen to our production function if there is technological advancement?  As stated in chapter one, technological advancement make our limited resources more productive. This means we can produce:  More output from the existing level of inputs, or  The existing level of output by using less of the inputs  Generally, technological advancement shifts the total product curve up implying that we can produce more of a product than before. April 12, 2022 By: Michael T. 28

29. Figure 4.8: Effects of Technological Progress on Production Function Graphically, the effect of technological advancement is shown with an upward shift of the production function. This shift shows that the same output may be produced by using fewer factor inputs, or more output may be obtained with the same inputs. April 12, 2022 By: Michael T. 29

30. Exercise: 1 Complete the following table: Exercise: 2 Copy and complete the following table: Exercise: 3 Calculate MRTSLK for each combination given in the following table: April 12, 2022 By: Michael T. 30

31. 4.2 T H E O RY O F C O S T Basic Concepts of Cost  In the previous section we have seen the relationship between inputs and output, and the basic concepts of production. Here in this section we will discuss about the basic concepts of cost and its relation with production.  Basically, production and cost are interrelated terms and concepts.  Production with out cost is impossible, and cost without production is economically meaningless.  Precisely, cost function is derived from production function. April 12, 2022 By: Michael T. 31

32.  To produce goods and services, firms need factors of production or simply inputs. To acquire these inputs, firms have to buy them from resource suppliers. Cost is, therefore, the monetary value of inputs used in the production of an item(goods and services). Social Cost vs. Private Cost  We can identify two types of cost of a product: Social cost and Private cost. Private Cost: refers to the cost of producing an item to the individual 1. producer. In other words, private cost refers the cost of production incurred by an individual firm in producing a commodity. April 12, 2022 By: Michael T. 32

33. Social Cost: refers to cost of producing an item to the society. In 2. other words, social cost refers to the cost that the society has to bear on account of production of a commodity. ♠ Social cost is a wider concept than private cost. ♠ It is the sum total of the cost incurred by the producers of goods and services (private cost), and the cost experienced by those who have to suffer because of the production of the commodity in terms of external cost. ♠ Thus, Social Cost = Private Cost + External Cost ♠ Social cost differs from private cost to the extent of external cost. April 12, 2022 By: Michael T. 33

34. ♠ ‘External Cost’ is the cost that is not borne by the firm, but is incurred by other members of the society or the entire society. Such costs are termed external costs from the firm’s point of view and social costs from society’s point of view. Note: ♠ These external costs are not taken into account by the individual producers and, therefore, they are not part of the private cost. ♠ Generally, this social cost is realized due to the fact that most resources used for production purpose are scarce and some production process, by their nature, emit dangerous chemicals, bad smell, etc. to surrounding society. April 12, 2022 By: Michael T. 34

35. ♦ For example, when a certain beer factory wants to produce beer in Ethiopia, the society as a whole also incurs a cost. Because, the next- best alternative of the raw material (such as barely) used for the production of beer is sacrificed. ♦ When the beer factories buy barley from the market, the amount of barely available for consumption by society may be reduced and the price may become dearer. Hence, the production of beer imposes an indirect cost on the society, moreover, by its nature; the production of beer emits bad chemicals to the environment, which pollutes waters, air, etc. ♦ Therefore, to control the understandable consequences of the production process on the environment and their property, the society incurs cost. This cost is known as Social Cost. April 12, 2022 By: Michael T. 35

36. Economic Cost vs. Accounting Cost  Private cost of production can be measured in to two ways. 1. Economic Cost: refers cost of all inputs used to produce an item. The producer may buys part of the inputs from the market. The producer may also use his/her own inputs which are not purchased from the market.  Economic cost classified in to two: Explicit Cost and Implicit Cost. Explicit Cost: Actual payments made by a firm for purchasing or A. hiring resources (or factor services) from the factor-owners or other firms (from outside suppliers of input) are called explicit costs.  Thus, examples of explicit costs are: payments for raw materials and power; wages to the hired workers; rent for the factory building; interest on borrowed money; etc. April 12, 2022 By: Michael T. 36

37. Implicit Cost: refers the estimated cost of non purchased inputs. B. The term, implicit cost, refers to the cost/value of self-owned or self employed resources. They are also known as imputed cost because producers do not make payment to others for them.  For instance, rent of his/her own land, interest on his/her own capital, and salary for his/her own services as manager, etc. are implicit costs.  Thus, in economics the cost of production includes the costs of all inputs used in the production process whether the inputs are purchased from the market or owned by the firm himself.  Precisely, total cost of production is the sum of explicit and implicit costs. Economic Cost = Explicit Cost + Implicit Cost April 12, 2022 By: Michael T. 37

38. 2. Accounting Cost: refers the cost(monetary value) of all purchased inputs used in production of goods and services; it ignores the cost of non-purchased (self-owned) inputs.  For accountants, the cost of production includes the cost of purchased inputs only. It considers only direct expenses such as wages/salaries, cost of raw materials, depreciation allowances, interest on borrowed funds and utility expenses (electricity, water, telephone, etc.).  If a producer calculates her cost by considering only the costs incurred for purchased inputs, then her profit will be an accounting profit. Accounting Profit = Total Revenue – Accounting Cost = Total Revenue – Explicit Cost April 12, 2022 By: Michael T. 38

39.  For economist, economic profit will give the real profit of the firm since all costs are taken into account. Economic profit is, therefore, total revenue less economic costs (explicit and implicit costs). Economic Profit = Total Revenue – Economic Cost = Total Revenue – (Explicit Cost + Implicit Cost) Note: Economic profit will give the real profit of the firm since all costs are taken into account. Accounting profit of a firm will be greater than economic profit by the amount of implicit cost.  If all inputs are purchased from the market, accounting and economic profit will be the same. However, if implicit costs exist, then accounting profit will be larger than economic profit. April 12, 2022 By: Michael T. 39

40. C O S T F U N C T I O N ♠ Cost function shows the algebraic relation between the cost of production and various factors which determine it. ♠ Among others, the cost of production depends on the level of output produced, technology of production, prices of factors, etc. Hence, cost function is a multivariable function. ♠ Symbolically, C = f (x, t, pi) Where C - is total cost of production x - is the amount of output produced t - is the available technology of production. Pi- is the price of input April 12, 2022 By: Michael T. 40

41. S h o r t - Ru n C o s t o f P r o d u c t i o n  The basic analytical cost concepts that are used to analyze the cost behavior of a firm are: Total Cost, Average Cost and Marginal Cost. 1 . To t a l C o s t  In the short run inputs are divided in to two: fixed inputs and variable inputs.  Likewise, short run costs are divided in to two: fixed costs and variable costs. 1. Fixed Cost  Fixed Cost: refers to those costs incurred by the firm for the use of all fixed factors. In other words, fixed costs are those costs that do not vary as the firm changes its level of output. April 12, 2022 By: Michael T. 41

42.  This cost is independent of output, i.e., it does not change with change in quantity of output. Thus, fixed cost is also known as overhead cost.  These are costs that must be incurred even if the firm does not produce anything. That is why again fixed cost is often known as ‘unavoidable cost’.  Fixed costs includes:  Salary of administrative (permanent staff)  Interest on borrowed capital,  Rent of the factory buildings,  Expenses for maintenance of buildings  Expenses for building & machineries depreciation and repairs  Expenses for property tax and license fees etc. April 12, 2022 By: Michael T. 42

43. 2. Variable Cost:  Variable cost refers to the total cost incurred by a firm for the use of the variable factors. Variable costs are all costs which directly vary with the level of output produce.  When output is zero, variable costs are also zero. But, it is rising as more is produced and falling as less is produced. That is why variable cost is also known as ‘avoidable cost’.  In short, variable costs are dependent on the level of output produced.  The variable cost includes cost of raw materials, wages for daily laborers, running(operating) expenses of fixed capital like electricity, fuel, water and taxes such as excise duties, which depend upon the output produced. April 12, 2022 By: Michael T. 43

44.  In general, the short run total cost is given by the sum of total fixed cost and total variable cost. That is, TC = TFC + TVC Table 4.6: Total Fixed Cost, Total Variable Cost, and Total Cost Labor Output (Workers Per Day) (Jumpers Per Day) TFC TVC TC 0 0 25 0 25 1 4 25 25 50 2 10 25 50 75 3 13 25 75 100 4 15 25 100 125 5 16 25 125 150  Based on the definition of the short run cost functions and by looking their value, let‘s see what their shapes look like. April 12, 2022 By: Michael T. 44

45. Total Fixed Cost (TFC):  Total Fixed Cost is denoted by a straight line parallel to the output axis. This is because such costs do not vary with the level of output. Total Variable Cost (TVC):  Total Variable Cost of a firm has an inverse S-shape. In other words, the TVC curve is a positively sloping curve Initially, it increases at a decreasing rate, and then increases at an increasing as total output increases. Note that:  The rate of increase of TVC is not the same throughout.  TVC curve starts from the origin, which shows that when output is zero, total variable cost is also zero. April 12, 2022 By: Michael T. 45

46. Total Cost (TC):  The Total Cost curve is obtained by vertically adding TFC and TVC at each level of output. The shape of the TC curve follows the shape of the TVC curve, i.e. the TC has also an inverse S-shape. But it lies above the origin.  It should be noted that when the level of output is zero, TVC is also zero which implies TC = TFC. The vertical distance between the TVC and TC curves equals the amount of the total fixed cost. Figure 4.9: Behavior of Total Costs April 12, 2022 By: Michael T. 46

47. 2 . A v e r a g e C o s t s  Like Total Cost, Average Cost is also classified into two: I. Average Fixed Cost and II. Average Variable Cost I. Average Fixed Cost (AFC)  Average Fixed Cost is total fixed cost per unit of output.  It is calculated by dividing TFC by the corresponding level of output.  The graph of AFC is rectangular hyperbola shows AFC is continuously declining but can never be zero or negative. April 12, 2022 By: Michael T. 47

48. Table 4.7: Behavior of TC, AC and MC TFC TVC TC MC AFC AVC ATC Labor Output Dollars Per Day Dollars Per Jumper 0 0 25 25 - - - - 1 4 25 25 50 6.25 6.25 6.25 12.5 2 10 25 50 75 4.17 2.5 5 7.5 3 13 25 75 100 8.33 1.92 5.77 7.69 4 15 25 100 125 12.5 1.67 6 8.33 5 16 25 125 150 25 1.56 7.87 9.38 Remember: TC = TFC + TVC MC = ∆TC ÷ ∆Q AFC = TFC ÷ Q AVC = TVC ÷ Q ATC = AFC + AVC ATC = TC ÷ Q April 12, 2022 By: Michael T. 48

49. Note that:  For very small outputs, the average fixed cost is high, and for large outputs it is low. The curve approaches the X-axis but never touches it because the average fixed cost cannot be zero since total fixed cost is positive. Similarly, the AFC curve never touches the Y-axis because total fixed cost has a positive value even at very low levels of output. Figure 4.10: Average Fixed Cost Curve April 12, 2022 By: Michael T. 49

50. II. Average Variable Cost (AVC) Average variable cost is total variable cost per unit of output. It is obtained by dividing total variable cost by the level of output. The short run AVC curve falls initially, reaches its minimum, and then starts to increase. Hence, the AVC curve has U-shape and the reason behind is the law of variable proportions. Figure 4.11: Average Variable Cost Curve April 12, 2022 By: Michael T. 50