Notes on Chapter 10 OUTPUT AND COSTS

Notes on Chapter 10 OUTPUT AND COSTS PRODUCTION TIMEFRAME There are many decisions made by the firm. Some decisions are major decisions that are hard to reverse without a big loss while other decisions are small ones that could be easily changed. All decisions are aimed to achieve the main goal of the firm: maximizing economic profit. The use of resources implies cost of production. In order to lower the cost of production the firm must know how many resources are needed to produce a given level of output. The challenge to the managers is to choose the right level of output and cost that maximize economic profit. To study the relationship between a firm output decisions and its cost, we must distinguish between two decisions time frames. The short-run (SR) The SR is time frame in which some inputs are fixed while others are variable. Fixed inputs are such as building, capital, plant and organization and variable inputs are such as labor, raw materials and energy. To increase the output in the SR, a firm must increase the quantity of the variable input. SR decisions can easily be reversed. The firm for example can increase or decrease its output in the SR by increasing or decreasing the amount of labor to employ. The long-run (LR) The LR is a time frame in which all its resources are variable. To increase the output in the LR, a firm is able to change its technology, capital, plant as well as its labor. 1

LR decisions are not easily reversed. Once a decision is made the firm usually must live with it for some time. A sunk cost is a cost that is incurred by the firm and cannot be changed. If a firm s plant has no resale value, the amount paid for it is a sunk cost. Sunk costs are irrelevant to a firm s decisions. THE SHORT RUN PRODUCTION FUNCTION The total amount of output produced by a firm is a function of the levels of input used by the firm. Production function refers to a technological relationship between different combinations of inputs (factors of production) and the maximum amount of output that can be produced within a given period of time, assuming a fixed level of technology. The production function illustrates the relationship between output (Q) and inputs of labor (L), capital (K), land (N), and the entrepreneurship (E): Q = f (L, K, N, E) To simplify the production function, let us assume the production process requires only two inputs labor and capital. Since we are in the short-run, at least one input must be fixed. We will assume that the capital is fixed while the firm can change the amount of labor. Thus, the production function becomes: Q = f (L, K) The production function in this simple form, where labor is the only input that can be changed, is sometimes referred to as the total product of labor (TP L ). To increase the quantity in the SR, a firm must increase labor. We describe the relationship between Q and L by using the following related concepts: 1. Total product (TP L ) 2. Marginal product (MP L ) 3. Average product (AP L ) 2

Total Product (TP L ): Total product is the total output produced in a given period. It shows the output capacity of the firm. Total product captures the relationship that exists between the maximum level of output that can be produced by a firm and the quantity of labor used in production, holding other inputs and technology constant. TP is similar to the production possibilities frontier (PPF): o It separates the attainable output level from the unattainable level of output. All points that lies above the curve are unattainable, while points that lie on the curve or below it are attainable. o Points on TP curve are technologically efficient. Technological efficiency is producing the maximum output attainable from any combination of inputs. o Points below the curve are inefficient. They produce less output from a given input o In other words, inefficiency is the use of more inputs than necessary to produce a given output. Inefficiency leads to higher cost. L TP L MP L AP L 0 0 -- -- 1 5 5 5 2 14 9 7 3 30 16 10 4 44 14 11 5 50 6 10 6 50 0 8.33 7 48-2 6.86 8 43-5 5.38 9 36-7 4 AP, MP MP TP L 3

TP curve shows how output changes as the quantity of labor changes. A careful inspection of the table and the figure above indicates that output initially increases more rapidly as the quantity of labor increases (the shape of the TP curve starts steep), but this increase gets smaller and smaller as L increases (the curve become less steep). The steeper the slope of the TP curve, the greater is the MP. Marginal Product: Marginal product (MP) is a short-run production function that shows how much each additional worker contributes to output. MP is defined as the change in total output that results from the use of one additional unit of a variable input, holding other inputs constant MP L = Change in total output Change in the quantity of labor TP = = L Q L MP is the slope of the TP curve We plot MP L at the mid points between labor input to emphasize that it is the result of changing input. MP L increases until reaches maximum then start to decrease until reaches zero and after that starts to become negative. Almost every production process has two features: initially, (1) increasing marginal returns (IMR), and then (2) Diminishing marginal returns (DMR), eventually. Increasing marginal returns (IMR) IMR occurs when every additional worker adds more to the total product than the previous one. Thus, the MP of an additional worker exceeds the MP of the previous worker. IMR arise from the increase in specialization, teamwork and division of labor in the production process. 4

Diminishing marginal returns (DMR) DMR occurs when the MP of an additional worker is less than the MP of the previous worker. DMR is observed in SR because we add more and more of the variable input to the fixed input. As more workers are added to a fixed machine, for example, there is less and less for the additional worker to do and the gains from specialization and the division of labor is getting less and less. Because DMR exists eventually in every production process in the SR it is called the law of diminishing returns Law of diminishing returns: As a firm uses more and more of a variable input with a given quantity of a fixed input, the MP of the variable input eventually diminishes (decline). The Relationship between MP L and TP L Because of IMR, TP increases initially at increasing rate. Then, because of DMR, TP increases at decreasing rate. The point that TP change its increase from increasing at increasing rate to increasing at decreasing rate (i.e., the point where DMR start its course) is called the turning point. When TP L is at its turning point MP L is at its maximum, o If MP L > 0, TP L is increasing o If MP L = 0, TP L is at its maximum o If MP L < 0, TP L is decreasing Exercise: (True or False): TP decreases when MP decreases. Exercise: Why the law of diminishing returns does not apply in long run? In long run, firm can increase the availability of space and capital to keep up with the increase in the variable input. 5

Exercise: How many workers a firm should hire if it can hire all workers it wanted at zero wage (i.e., the workers are volunteers)? The firm should hire enough workers to produce where MP = 0 Exercise: Find the MP L from the labor and output data in the following table: Total and Marginal Product from Hiring Labor Labor TP L MP L 0 0 2 200 4 500 6 700 8 800 Notice that even though output rises from zero to 200, marginal product is only 100. This is because the firm hired two more workers and we want to know how much output would rise if they only hired one additional worker. Exercise: Could the law of diminishing returns be applied to the marginal product of capital (MP K )? The answer is yes. If the capital is the variable input, marginal product of capital (MP K ) is the change in the firm s output as a result of one unit change in capital, keeping labor and other inputs fixed. Law of DMR also hold for capital that means if firm uses more capital with fixed input, MP of capital eventually declines. 6

Average Product (AP) The relationship between the quantity of input and total output can also be represented through the average product of labor (AP L ). The average product is defined as the ratio of total product to the quantity of labor. AP is the total product per unit of labor TP Q AP L = = L L Economists expect that the AP may initially rises but will ultimately decline as a result of the law of diminishing returns. The average product of labor shows labor productivity. Productivity refers to the output produced per unit of input. For example, output per hour of labor. Productivity of any input depends on the amount of other resources available to it. It increases when the ratio of output per unit of input increases Greater labor productivity means higher output per worker. Labor productivity will increase if capital per worker increases. The Relationship between MP L and AP L AP, MP Usually, MP L reaches the max before AP L As more labor is employed AP L increases until It reaches the maximum then starts to decline MP curve cuts the AP curve at the point of its maximum. If MP > AP, AP is increasing an additional L* worker adds more to output than the average worker is producing. In this case, the average has to increase. If MP = AP, AP is at maximum an additional worker adds the same amount of output as the average worker is producing. In this case, the average stays the same and it is at maximum. MP AP L 7

If MP < AP, AP is decreasing an additional worker adds less to output than the average worker is producing. In this case, the average has to decrease. Marginal Grade and GPA To see the relationship between AP and MP think about your "marginal grade" of any additional course and your GPA: o GPA when marginal grade > GPA o GPA when marginal grade < GPA o GPA is constant when marginal grade equals GPA 8

SHORT RUN COST FUNCTIONS The production decision has to be based not only on the capacity to produce (the production function) but also on the costs of production (the cost function). The most desirable rate of output to produce is the one that maximizes total profit. To produce more output in the SR, a firm must employ more of its variable input (the labor), which means that it must increase its cost. We describe the relationship between output and cost by using three cost concepts: 1. Total cost (TC) 2. Marginal cost (MC) 3. Average cost (AC) Total costs (TC) Total cost (TC) is the market value of all factors of production used to produce goods or services. This cost may be explicit, paid for directly, or implicit, not paid for directly but estimated via opportunity costs including the cost of entrepreneurship, which is the normal profit. Even in the short-run, total costs remain the sum of explicit and implicit costs. However, in the short-run it is actually more useful to divide total costs into two other types of costs because there are two different types of inputs in the short run: variable inputs that the firm can change and fixed inputs that the firm cannot change. Thus, total cost contains both total fixed cost and total variable cost. TC = TFC + TVC 9

Total Fixed Cost (TFC) TFC is the cost of the fixed inputs that the firm uses in production. It does not vary with the changes in the output, even when output equals zero. Examples of such fixed costs include rent, annual license fees, mortgage payments, interest payments on loans, the cost of basic plant and equipment. There is no way to avoid fixed costs in the short run. TFC > 0 even if Q = 0 Total Variable Cost (TVC) TVC is the cost of the variable inputs that the firm uses in production. It varies when the rate of output changes. Labor costs, raw material costs and energy costs are examples of variable costs. TVC is equal to zero when no output is produced and increases with the level of output. Since TC = TFC + TVC, in the short run, when Q =0, TVC = 0 TC = TFC In short run, changes in TC will result only from changes in the TVC. TVC gives TC its shape. Costs Total Costs Graphically The diagram contains a graph of a total fixed cost curve. Since total fixed costs are the same at all levels of output, a graph of the total fixed cost curve is a horizontal line. The total variable cost curve increases as output increases. Initially, it is expected to increase at an increasing rate (since marginal productivity increases initially, TC TVC TFC Q 10

the cost of additional units of output decline). As the level of output rises, however, variable costs are expected to increase at a decreasing rate (as a result of the law of diminishing marginal returns). Since total cost equals the sum of total variable and total fixed costs, the total cost curve is just the vertical summation of the TFC and TVC curves. Marginal Cost Marginal cost (MC) is the increase in total costs associated with a one-unit increase in output. TC MC = TP TC = Q TVC = Q Since the TC consist of the sum of TFC and TVC, TC can only change if either of these two changes. But we know that TFC does not change. Thus, the only possible source for a change in TC is a change in TVC. Diminishing returns in production cause MC to increase as the rate of output increases. The shape of MC curves reflects the law of diminishing returns. Diminishing returns exist because in the short run some resources are fixed. Average (per-unit) Costs One of the most common costs is average, or per-unit, cost. Average cost can be divided into: TC TC Q = = TFC + TVC TFC TVC + Q Q ATC = AFC + AVC 11

The following table and diagram present all of the cost functions Q TFC TVC TC MC AFC AVC ATC 0 10 0 10 0 0 0 0 1 10 8 18 8 10 8 18 2 10 14 24 6 5 7 12 3 10 18 28 4 3.33 6 9.33 4 10 21 31 3 2.5 5.25 7.75 5 10 25 35 4 2 5 7 6 10 31 41 6 1.67 5.17 6.83 7 10 40 50 8 1.43 5.71 7.14 8 10 50 60 10 1.25 6.25 7.5 9 10 65 75 15 1.11 7.22 8.33 10 10 90 100 25 1 9 10 AFC, AVC, ATC MC ATC AVC AFC Q Falling AFC: To understand why average fixed costs always decline one must simply recall two important facts. First, total fixed costs are always constant regardless of the level of output. Second, to calculate average fixed costs we simply divide total fixed costs by output. Hence, as the firm s output rises we are dividing the same number total fixed costs by an increasing output. The result, average fixed cost, must fall as output rises and as the fixed cost is spread over more output. 12

Note that AFC decreases at a decreasing rate. It approaches the horizontal axis but never equal to zero. Note that the vertical distance between the ATC and the AVC curve is equal to AFC (since AFC+AVC = ATC). Because the difference between ATC and AVC equals AFC and because as output rises AFC is getting closer and closer to zero, then the vertical distance between ATC curve and AVC curve is getting smaller and smaller as total output increases. MC and the U-shape of ATC (and AVC) Curves: AFC always declines as output rises. It does not matter whether MC is rising or falling, AFC is always falling. Thus, MC and AFC are simply not related. The one has no impact on the other. However, MC is related to ATC and AVC. These relationships exist because MC is calculated from either TC or TVC as discussed earlier. We calculate MC by taking the change in either TC or TVC and dividing that change by the change in output. The MC curve starts below ATC curve and AVC curve, but rises faster than both of them. MC always intersects both ATC and AVC curves from below at their minimum points. MC curve gives ATC and AVC their U-shape o If MC < ATC, ATC is decreasing, o If MC > ATC, ATC is increasing. o If MC = ATC, ATC at minimum Same thing is applied to AVC o If MC < AVC, AVC is decreasing. o If MC > AVC, AVC is increasing, o If MC = AVC, AVC at minimum Looking at it from the production side, the AVC curve is U-shaped because: 13

1. Initially, marginal product exceeds average product, which brings rising average product and falling AVC. 2. Eventually, marginal product falls below average product, which brings falling average product and rising AVC. The ATC curve is U-shaped for the same reasons. In addition, ATC falls at low output levels because AFC is falling steeply. Relating Costs to Production Recall that the cost curves are U-shaped because they are related to productivity; when productivity rises initially due to the returns to specialization (IMR), costs fall and when productivity eventually falls due to diminishing returns (DMR), costs must rise. The relationship between costs and Productivity is an inverse one; increases in productivity cause costs to fall while decreases in productivity cause costs to rise. MC and AC are mirror image of MP and AP. AP, MP AVC, MC Initially MC and AC decrease because MP and AP increase, but eventually MC and AVC increase because of DMR. MP reaches the max before AP and MC reaches the min before AVC o When MP is increasing, MC is decreasing o When MP is decreasing, MC is increasing o When MP is at its maximum, MC is at its minimum We can say the same thing with regard to AP and AVC o When AP is increasing, AVC is decreasing o When AP is decreasing, AVC is increasing o When AP is at its maximum, AVC is at its minimum MP MC AP L AVC Q 14

When MP intersects AP at its maximum, MC intersects AVC at its minimum. Shifts in the Cost Curves The position of a firm's SR cost curves depends on two factors: 1. Technology 2. Prices of productive resources. 1. Technology A technological change that increases productivity shifts the TP, MP and AP curves upward. With better technology, the same inputs can produce more output. Therefore, technological change lowers costs and shifts the cost curves downward. The relationship between product curves and cost curves have not change with changes in technology. Often, a technological advance results in a firm using more capital (a fixed input) and less labor (a variable input).therefore, fixed costs increase and variable costs decrease. This change in the mix of costs means ATC may increase at low output levels and decrease at high output levels. 2. Prices of Resources The increase of price of fixed input shifts the fixed and total cost curves (TFC, TC, AFC and ATC) upward. The increase in the price of variable inputs shift TVC, TC, AVC, ATC and MC upward but leaves TFC and AFC unchanged. 15

LONG-RUN COSTS The short-run is characterized by fixed inputs and fixed costs as well as variable inputs and variable costs. Long run is a period of time long enough for the firm to change all of its resources or to choose the production capacity that suite market demand for its product. Because there are no fixed inputs in the LR, there are no fixed costs. All inputs and all costs of production are variables in the long run. Long-run average variable costs equal long-run average total costs. There is no fixed cost in the long run The behavior of long-run cost depends upon the firm s production function, which is the relationship between the maximum output attainable and the quantities of both capital and labor. The average cost of producing a given output varies and depends on the firm s plant size. The larger the plant size, the greater is the output at which ATC is at a minimum. LONG-RUN AVERAGE COST (LRAC) The long-run average cost curve is the relationship between the lowest attainable average total cost and output when both the plant size and labor are varied. The long-run average cost curve is a planning curve that tells the firm the plant size that minimizes the cost of producing a given output range. LRAC shows the production efficiency at every level of output because it shows the plant size and the quantity of resources to be used at each level of output to minimize the cost. 16

ACs SRATC4 SRATC1 SRATC2 SRATC3 LRAC a b c Q LR possibilities are determined by all possible SR options. In this case, there are four options of varying size (ATC 1, ATC 2, ATC 3, and ATC 4 ). In the LR, we would choose that plant which yielded the lowest average cost for any desired rate of output. The dark portion of the curve (LRAC) represents these choices. At point a, the plant that results in SRATC 1 is the best choice while at b SRATC 2 is the best. Same thing can be said about point c where the best choice is SRATC 4 Therefore, LRAC is constructed from the lowest short run ATC at each possible level of output. If plants of all sizes can be built, SR options are infinite. In this case, the LRAC curve becomes a smooth U-shaped curve. Each point on the curve represents the lowest production for a plant size best suited to one rate of output. ECONOMIES AND DISECONOMIES OF SCALE To increase its output in the long-run the firm can increase all of its inputs which makes the firm becomes larger. This is referred to as increasing scale of operations. Note that if a firm increased its output in the short-run it would not be increasing its scale because the firm is not increasing all of its inputs. Thus, scale is only a long-run concept. 17

In the short run, no firm experiences economies of scale. There are many options available in the long-run production. One option is the decision to use one large plant. The other option is to use several smaller plants to produce a given amount of output Economies of Scale [or Increasing Returns to Scale (IRS)] Economies of scale refer to the reduction in the minimum average total costs that result from increasing the size (scale) of plant and equipment. If % in output > % input increasing returns to scale. Economies of scale explain why ATC decreases as output increases in LR. A larger scale of production might enable a firm to divide tasks into more specialized activities, thereby increasing labor productivity. Furthermore, a larger scale of operation might enables a company to justify the purchase of more sophisticated (hence, more productive) machinery. These factors help to explain why a firm can experience increasing returns to scale. Constant Returns to Scale (CRS) In some cases, it is not "more efficient" to produce in large-scale plants than in small plants. In such cases, the production process is characterized by constant returns to scale. Constant Returns to Scale means the increase in plant size do not affect minimum average costs. Minimum average (per-unit) costs are identical for small plants and large plants. (% in Q = % input constant returns to scale) Diseconomies of Scale [or Decreasing Returns to Scale (DRS)] Although large plants may be able to achieve greater efficiencies than smaller plants, there is no assurance that they actually will, especially when the plants becomes too large. 18

Diseconomies of Scale occur when an increase in plant size results in reducing operating efficiency. This happens because of the increased cost of managing and coordinating a firm as the size of the firm rises (% in Q < % input decreasing returns to scale) A common source of diseconomies of scale is the growing complexity of management and organizational structure. Efficiency and size do not necessarily go hand in hand. Operating on a larger scale might create certain marginal inefficiency (e.g., management difficulties, communication problems, bureaucratic red tape, rigid corporate structure, anonymity) and hence cause decreasing returns to scale. LR Costs and Economies of Scale: Cost LRAC Economies of Scales Constant Returns to Scales Diseconomies of Scales Q If LRAC decrease as output increase, the firm experiences economies of scale (IMS). The slope of its LRAC curve is negative and the slope of its ATC curve is negative If LRAC increase as output increase, the firm experiences diseconomies of scale (DRS) If LRAC remains constant as output increase, the firm experiences neither economies nor diseconomies of scale (CRS) 19

EXERCISE 1. Fill out the blanks in the following two tables L TP MP AP 0 0 --- --- 1 12 2 28 3 13 4 12 5 2 6 48 7-6 Q TFC TVC TC MC AFC AVC ATC 0 50 --- --- --- --- 1 20 2 80 3 6 4 7.5 5 34 6 70 20

2. 20 Based on the above figure that shows ATC, AVC and MC, answer the following questions 1. What is the MC of the 120th unit of output? 2. What is the ATC of the 120 th unit of output? 3. What is the AVC of the 120 th unit of output? 4. What is the AFC of the 120 th unit of output? 5. At which level of output shown above will AFC be the lowest? 6. What is the TFC of the 100th unit of output? 7. Why does the ATC curve slope downward before the 120 th units of output? 8. Why does the AVC curve start to slope upward after 100 units of output? 9. At which level of output does "increasing marginal returns" end? 10. At which level of output does "diminishing marginal returns" first occur? 21