Production and Cost in the Firm CHAPTER 7 © 2003 South-Western/Thomson Learning

Cost and Profit In economics, we assume that producers try to maximize profit  this provides the motivation for their behavior Firms transform resources into products in their attempt to accomplish this objective They must make plans while confronting uncertainty about Consumer demand Resource availability Intentions of other firms in the industry

Explicit and Implicit Costs To hire resources, producers must pay resources at least their opportunity costs For most resources, the cash payments approximate their opportunity cost However, some resources are owned by the firm or the firm’s owners  there are no direct cast payments Whether hired in resource markets or owned by the firm, all resources have an opportunity cost

Explicit and Implicit Costs Explicit costs Refer to the firm’s actual cash payments for resources  wages, rent, taxes, etc. Implicit costs The opportunity costs of using resources owned by the firm or provided by the firm’s owners Require no cash payment and no entry in the firm’s accounting statement, which records its revenues, explicit costs, and accounting profits

Alternative Measures of Profit A particular example may help to clarify the distinction between explicit and implicit costs and the alternative measure of profit that are used Wanda Wheeler currently earns $50,000 in her current job She decides to start her own business She withdraws $20,000 from her savings account, hires and assistant and uses a spare bay in her garage that had been renting for $1,000 a year Exhibit 1 shows the results after the first year

Exhibit 1: Accounts of Wheeler Dealer 2001 Total revenue $105,000 Less explicit costs: Assistant's salary -21,000 Material and equipment -20,000 Equals accounting profit $64,000 Less implicit costs: Wanda's forgone salary 50,000 Forgone interest on savings -1,000 Forgone garage rental -1,200 Equals economic profit $11,800 Accounting profit equals total revenue minus explicit costs  used to determine a firm’s taxable income However, this ignores the opportunity cost of Wanda’s own resources Her forgone salary of $50,000 Annual interest of $1,000 from the savings used to start the business Rental income of $1,200 Economic profit equals total revenue minus all costs, both explicit and implicit Accounting profit of $64,000 less implicit costs of $52,200  economic profit of $11,800

Normal Profit There is one other profit measure to consider: the accounting profit required to induce the firm’s owners to employ their resources in the firm Alternatively, the accounting profit just sufficient to ensure that all resources used by the firm earn their opportunity cost  normal profit Recall that the accounting profit = $64,000 Normal profits = $50,000 + $1,200 + $1,000 = $52,200  normal profit  $11,800 is an economic profit

Fixed and Variable Resources Resources can be divided into two categories Variable resources can be varied quickly to change the output rate Fixed resources are those resources which cannot be easily changed This provides us the distinction between the short run and the long run Short run  at least one resource is fixed Long run  all resources are variable

Short Run and Long Run Output can be changed in the short run by adjusting variable resources However, the size, or scale of the firm is fixed in the short run In the long run, all resources can vary The length of the short and long run differs from industry to industry because the nature of production differs

Law of Diminishing Marginal Returns For the present, suppose we focus on the short-run link between resource use and the rate of output Suppose the company’s fixed resources are already in place and consist of a warehouse, a moving van, and moving equipment The only variable resource is labor Exhibit 2 provides our illustration

Exhibit 2: Short-Run Relationship Units of Labor and Tons of Furniture Moved Units of the Total Marginal Variable Product Product Resource (tons moved (tons moved (worker-days) per day) per day) 0 0 - 1 2 2 2 5 3 3 9 4 4 12 3 5 14 2 6 15 1 7 15 0 8 14 -1 Labor measured in worker-days (1 worker for one day) Output measured in tons of furniture moved per day. Tons of furniture moved, or total product, at each level of employment is shown in the center column Relationship between the amount of resources employed and total product is called the firm’s production function. Last column shows the marginal product of each worker

Law of Diminishing Marginal Returns As more of a variable resource is combined with a given amount of a fixed resource, marginal product eventually declines This is the most important feature of production in the short run  dictates the shape of the production function and the cost curves

Total and Marginal Product Curves Exhibit 3 illustrates the relationship between total product and marginal product The values used in these figures are derived from the data presented in Exhibit 2

Exhibit 3: Total and Marginal Product (a) Total Product Because of increasing marginal returns, marginal product increases with each of the first three workers  total product is increasing at an increasing rate. 15 Total Total product (tons/day) product 10 5 However, once decreasing returns set in – adding the 4th worker – marginal product declines  total product continues to increase but at a decreasing rate. 5 10 (b) Marginal product Workers per day Increasing Marginal returns Diminishing but Positive marginal returns Negative Marginal returns 5 4 Marginal product (tons/day) As long as marginal product is positive, total product increases  where marginal product turns negative, total product starts to fall. 3 2 Marginal product 1 5 10 Workers per day

Costs in the Short Run There are two kinds of costs in the short run Fixed costs pay for fixed resources and must be paid even if no output is produced  do not vary when output varies In our example the fixed costs are assumed to be $200 Variable cost is the cost of variable resources – labor in our example – and vary with the amount of labor employed in the production process  as more labor is employed, output and variable cost both increase The firm can hire labor at $100 per worker day  variable cost equals $100 times the number of workers hired

Exhibit 4: Short-Run Cost Data Tons Moved Fixed Variable Marginal per Day cost Workers Cost Total Cost Cost (q) (FC) per Day (VC) TC=FC+VC MC=TC/ q (1) (2) (3) (4) (5) (6) $0 $200 0 $0 $200 - 2 200 1 100 300 50.00 5 200 2 200 400 33.33 9 200 3 300 500 25.00 12 200 4 400 600 33.33 14 200 5 500 700 50.00 15 200 6 600 800 100.00 Notice that fixed costs – column (2) – remain constant at $200 per day regardless of output. Column (3) shows the amount of labor needed to produce each rate of output based on the the productivity figures introduced previously. The variable and total cost associated with each level of output are shown in columns (4) and (5), respectively. TC = FC + VC Since total cost is the opportunity cost of all resources employed by the firm, it includes a normal profit but not an economic profit. Marginal cost is provided in the last column. Marginal cost is simply the change in total cost divided by the change in output  MC = ΔTC / Δq Changes in MC reflect changes in marginal productivity of the variable resource employed

Marginal Cost and Marginal Productivity When the firm experiences increasing marginal returns – marginal product is increasing – the marginal cost decreases When the firm experiences diminishing marginal returns – marginal product begins to decline – the marginal cost of output increases Exhibit 5 provides a graphical illustration of our cost curves

Exhibit 5: Total and Marginal Cost Curves ( (a) Total cost curve Since total cost does not vary with output, the fixed cost curve is a horizontal line at $200. $1,000 Total cost Variable cost is zero when output is zero  the variable cost curve starts at zero, then increases slowly then sharply. Total dollars Variable cost 500 The total cost curve sums the variable and fixed cost curves. Fixed cost Fixed cost 200 Marginal cost declines until the 9th unit of output and then increases reflecting labor’s increasing and then diminishing marginal returns. 3 6 9 12 15 Tons per day (b) Marginal cost curve $100 The change in total cost resulting from a one-unit change in production equals marginal cost  the slope of the total cost curve at each rate of output equals the marginal cost at that rate of output. Cost per ton 50 Marginal cost 25 3 6 9 12 15 Tons per day

Summary The total cost curve can be divided into two sections, based on what happens to marginal cost Because of increasing marginal returns from labor, marginal cost at first declines  total cost initially increases by successively smaller amounts  total cost curve gets flatter Because of diminishing marginal returns from labor, marginal cost starts increasing  a steeper total cost curve

Summary Marginal cost is the key to economic decisions made by firms The firm operating in the short run has no control over its fixed cost, but, by, varying output, the firm can alter its variable cost and hence its total cost Marginal cost indicates how much total cost will increase if one more unity is produced and how much total cost will drop if production declines by one unit

Average Cost in the Short Run The average cost per unit of output is another of the useful cost measures There are average cost measures corresponding to variable cost, fixed cost and variable cost Exhibit 6 provides a detailed listing of the variable costs for our example

Exhibit 6: Short Run Cost Data Tons Moved Variable Marginal Average Average per Day Cost Total Cost Cost Variable Cost Total Cost (q) (VC) TC=FC+VC MC=TC/ q AVC=VC/q ATC=TC /q (1) (2) (3) (4) (5) =(2) / (1) (6)=(3) / (1) 0 $0 $200 $0.00 - 2 100 300 50.00 $50.00 $150.00 5 200 400 33.33 40.00 80.00 9 300 500 25.00 33.33 55.55 12 400 600 33.33 33.33 50.00 14 500 700 50.00 35.71 50.00 15 600 800 100.00 40.00 53.33 Average variable cost, AVC, equals variable cost divided by output  AVC = VC / q Average total cost, ATC, equals total cost divided by output  ATC = TC / q Both average variable cost and average total cost first decline as output expands, then increase

Marginal and Average Cost The relationship between marginal and average cost is also important When marginal cost is below or less than average cost it pulls average cost down When marginal cost is above or higher than average cost it pulls average cost up Exhibit 7 depicts this relationship

Exhibit 7: Average and Marginal Cost Curves Marginal cost declines as output expands because of increasing marginal returns to labor  so long as marginal cost is below average cost, average cost falls as output expands. The distance between the average variable and total cost gets smaller as output increases because average fixed costs decline as output increases $150 125 n o Marginal cost t 100 r e p t s 75 At higher rates of output, marginal cost increases o C Average total cost 50 Average variable cost Where marginal cost exceeds average cost, marginal cost pulls up the average. 25 0 5 10 15 Tons per day Because marginal cost first pulls down average cost and then pulls up average cost, each average cost curve has a U shape. Notice also that the rising marginal cost curve intersects both the average variable and total cost curves at their minimums.

Costs in the Long Run Thus far we have focused on how costs vary as the rate of output expands in the short run for a firm of a given size In the long run, all inputs that are under the firm’s control can be varied  there are no fixed costs The long run is not just a succession of short runs

Costs in the Long Run The long run is best thought of as a planning horizon In the long run, the choice of input combinations is flexible, but that flexibility is available only to firms that have not yet acted on their plans Firms plan for the long run, but they produce in the short run

Long-Run Average Cost Curve Suppose that, because of the special nature of technology in the industry, a firm must choose among only three possible sizes Small Medium Large Exhibit 8 presets this simple case

Exhibit 8: Short-Run Cost Curves and the Long-Run Planning Curve The long-run average cost curve connects portions of the three-short run average cost curves that are lowest for each output rate  S,a,b, and L' Cost per unit The appropriate size or scale for the new plant depends on how much the firm wants to produce. S L' M M' Cost per unit S' L For example, if q is the desired rate of output in the long run, the average cost per unit is lowest with a small plant. If the desired output rate is q', the medium plant size ensures lowest cost. a b Output per period q q q' q a b Generally, for any output less than qa average cost is the lowest when the plant is small, for output rates between qa and qb, for the medium plant, and when output exceeds qb, the large plant has the lowest average costs.

Long-Run Average Cost Curve Now suppose there are many possible plan sizes Exhibit 9 presents a sample of short-run average total cost curves shown in pink The long-run average cost curve, shown in red, is formed by connecting the points on the various short-run average cost curves that represent the lowest per-unit cost for each rate of output

Exhibit 9: Family of Many Short-Run Cost Curves Forming a Firm’s Long-Run Planning Curve Each of the short-run average cost curves is tangent to the long-run average cost curve, or planning curve. 10 9 0 Output per period q q' ATC 1 2 3 4 5 6 7 8 Long-run average cost a b c $11 If we could display enough short-run cost curves, we would have a different plant size for each rate of output. Cost per unit These points of tangency represent the least-cost way of producing each particular rate of output, given the technology and resource prices.

Exhibit 9: Family of Many Short-Run Cost Curves Forming a Firm’s Long-Run Planning Curve The short-run average total cost ATC1 is tangent at point a  the least-cost way of producing output rate q is with the plant size associated with ATC1 ATC ATC 10 1 ATC ATC 9 $11 2 a b ATC 10 ATC 8 3 9 ATC c 7 ATC 4 ATC 6 ATC 5 Long-run average cost Cost per unit Note that other output rates along ATC1 have a lower average cost of production. 0 Output per period q q'

Exhibit 9: Family of Many Short-Run Cost Curves Forming a Firm’s Long-Run Planning Curve If the firm decides to produce q', it could select the plant associated with ATC1 ATC ATC 10 1 ATC ATC 9 2 $11 a b ATC 10 ATC 8 3 9 ATC c 7 However, average cost is lower with a larger plant. With ATC2, the average cost of producing q' would be minimized at $9 per unit at point c ATC 4 ATC 6 ATC 5 Long-run average cost Cost per unit 0 Output per period q q'

Economies of Scale Notice that the long-run average curve is U-shaped The U-shape here is a result of economies and diseconomies of scale Economies of scale imply that long-run average costs decline as output expands while diseconomies of scale imply that long-run average costs increase as output increases

Economies of Scale A larger size often allows for larger, more efficient, machines and allows workers a greater degree of specialization  Production techniques such as the assembly line can be utilized only if the rate of output is large enough Typically, as the scale of the firm increases, capital substitutes for labor and complex machines substitute for simpler machines

Diseconomies of Scale As a firm expands, diseconomies of scale, eventually take over  long-run average cost increase as output expands As the amount and variety of resources employed increase, so does the task of coordinating all these inputs However, as the work force grows, additional layers of management are needed to monitor production

Diseconomies of Scale In the thicket of bureaucracy that develops, communications may get mangled The more levels of management there are in an organization, the more difficult it is for top management to communicate with those that perform most of the production tasks

Constant Long-Run Average Costs It is possible for average cost to neither increase nor decrease with changes in firm size In these situations, the firm experiences constant long-run average costs Exhibit 10 presents a firm’s long run average cost curve, which is divided into segments reflecting all these possibilities

Exhibit 10: A Firm’s Long-Run Average Cost Curve The rate of production must reach quantity A for the firm to achieve the minimum efficient scale, which is the lowest rate of output at which long-run average cost is a minimum. Cost per Unit Long-run average cost A B Output per period Economies of scale Constant average cost Diseconomies of scale From output A to rate B, average cost is constant. Beyond output rate B, diseconomies of scale increase long-run average cost.

Economies and Diseconomies of Scale at the Firm Level Thus far we have focused on a particular plant However, a firm could also be a collection of plants And it is possible that economies and diseconomies of scale can exist at the firm level as well as the plant level