CHAPTER 9 COST ANALYSIS 2 nd Semester, S.Y 2013 – 2014

1. CHAPTER 9 COST ANALYSIS 2nd Semester, S.Y 2013 – 2014

2. Chapter Outline • What is a cost? • The Firm • Short Run vs. Long Run • Fixed and Variable Inputs • Cost Function • Short Run Production Costs • Fixed Cost • Variable Cost • Total Cost • Marginal Cost • Average Costs • Cost Curves: An Analysis • Isocost Line • Isocost Equation • Isocost Map • Cost Minimization Problem • Long Run Costs • Economies and Diseconomies of Scale

3. Short Run Only some inputs (e.g. labor) can be adjusted Not enough time to adjust all inputs (such as capital) Long Run long enough time to adjust all inputs (capital as well as labor) Short Run vs. Long Run When economists examine firms over time they must define the Short Run and Long Run.

4. Fixed Cost • It is the cost of the fixed input that does not depend on the quantity of output produced. • It does not vary as output changes and that must be paid even if output is zero. These are payments that the firm must make in the short run, regardless of the level of output. • Fixed costs are those that are spent and cannot be changed in the period of time under consideration. • In the long run, there are no fixed costs since all inputs (and therefore their costs) are variable. • In the short run, a number of inputs and their costs will be fixed

5. Sunk costs are costs that have been incurred and cannot be recovered. An example is the cost of R&D to a pharmaceutical company to develop and test a new drug and then, if the drug has been proven to be safe and effective, the cost of marketing itrepresents the sunk costs. Whether the drug is a success or a failure, these costs cannot be recovered and thus are sunk. Fixed versus Sunk Costs

6. Variable Cost • It is the cost of the variable input that depends on the quantity of output produced. • This consists of costs that are zero when output is zero and vary as output changes. These costs relate to the costs of variable inputs. Examples include wages for hourly workers, electricity, fuel, and raw materials.

7. Shutting Down Fixed Costs and Variable Costs Shutting down doesn’t necessarily mean going out of business. By reducing the output of that factory to zero, the company could eliminate the costs of raw materials and much of the labor. The only way to eliminate fixed costs would be to close the doors, turn off the electricity, and perhaps even sell off or scrap the machinery. Fixed or Variable? How do we know which costs are fixed and which are variable? Over a very short time horizon—say, a few months—most costs are fixed. Over such a short period, a firm is usually obligated to pay for contracted shipments of materials. Over a very long time horizon—say, ten years—nearly all costs are variable. Workers and managers can be laid off (or employment can be reduced by attrition), and much of the machinery can be sold off or not replaced as it becomes obsolete and is scrapped.

8. Total Cost • It is thewhole amount of payments to all inputs used in producing a given quantity of output. • This is the sum of fixed cost and variable cost at each level of output. It is expressed by the following equation:

9. Total Cost Schedule / Curve • The total cost schedule shows the variable cost, fixed cost, and total cost for various output quantities. • The total cost curve shows how total cost (measured on the vertical axis) depends on the quantity of output (measured on the horizontal axis).. The total cost curve slopes upward because total cost increases as the quantity of output increases.

10. Total Cost Function The total cost of production can be thought of as a function , where it is the cost of producing outputs. The cost function describes the relationship of output and cost. It is expressed by the equation: where is fixed cost, is variable cost and is output or quantity produced.

11. Let’s Check Your Understanding! 1. Suppose the fixed cost of production for a commodity is P12,000, the variable cost is P25. Determine the cost equation. • 2. Determine or derive the cost function given the cost data on the table. • 3. A donut shop has a fixed cost of P5, 000 per day and a variable cost of P6 per donut. How many donuts can be produced for a total daily cost of P11 000.

12. Marginal Cost Marginal cost is the change in total cost when one additional unit of output is produced.Stated differently, marginal cost is the ratio of the change in total cost to a one-unit change in output. Written as a formula: Because fixed cost does not change as the firm’s level of output changes, marginal cost is equal to the increase in variable cost or the increase in total cost that results from an extra unit of output. Therefore, marginal cost is

13. Average Cost Average fixed cost (AFC) is the total fixed cost divided by the quantity of output produced. Written as a formula Average variable cost (AVC) is total variable cost divided by the quantity of output produced. Written as a formula: Average total cost (ATC)is sometimes referred to as per-unit cost. It is the total cost divided by the quantity of output produced. Written as a formula: 12-13

14. Costs of Production

15. FC, VC and TC Curves VC FC

16. MC, AFC, AVC and ATC Curves MC ATC AVC AFC

17. FC, VC and TC Curves • Fixed Cost • FC curve is always constant. Increasing output does not change FC. • It is the vertical distance between the TC and the TVC. • Variable Cost • VC increases as level of output changes. • Becausethe TFC curve does not vary with output, the shape of the VC . • Total Cost • TC curve slopes upward because total cost increases as the quantity of output increases. The curve gets steeper as output increases due to diminishing returns to labor. • Total cost curve has the same shape with VC curve. 12-17 12-17

18. Average Cost Curves • Average fixed cost (AFC) • The average fixed cost curve is downward sloping because increasing output decreases AFC • AVC curves are U-shaped • Average variable cost (AVC) • At first, the AVC curve falls, then it rises. Thus, the AVC curve is U-shaped. • Average total cost (ATC) • At first, the ATC curve falls because its component parts—AVC and AFC—are falling output continues to rise, the AVC curve begins to rise, while the AFC curve falls continuously. Eventually, the rise in the AVC curve is greater than the fall in the AFC curve, which causes the ATC curve to rise in a U-shaped pattern. 12-18 12-18

19. Average Cost Curves • The U-shape of ATC and AVC curves is due to: • When output is increased in the short run, it can only be done by increasing the variable input • The law of diminishing productivity causes marginal and average productivities to fall • As average and marginal productivities fall, average and marginal costs rise • The marginal cost curve goes through the minimum points of the ATC and AVC curves.

20. Marginal Cost Curve • Marginal Cost • MC curve slopes upward, reflecting diminishing returns to the variable input • The marginal cost (MC) curve decreases at first as output expands, eventually reaches a minimum, and then rises as output increases. • The MC curve intersects both the average variable cost (AVC) curve and the average total cost (ATC) curve at the minimum point on each of these cost curves.

21. Let’s Check Your Understanding! The following table is composed of production and cost items of a firm. Suppose the unit cost of capital and labor are P10 and P20 respectively. Fill in the missing columns.

22. Let’s Check Your Understanding! The following table is composed of production and cost items of a firm. Suppose the unit cost of capital and labor are P10 and P20 respectively. Fill in the missing columns.

23. Let’s Check Your Understanding! 1. Complete the following cost data by filling in the missing values.

24. Let’s Check Your Understanding! 1. Complete the following cost data by filling in the missing values.

25. Let’s Check Your Understanding! 1. JNE Firm has the following cost information. Fill in the missing values. JNE Firm’s Costs Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost (FC) (VC) (TC) (MC) (AFC) (AVC) (ATC) (1) (2) (3) (4) (5) (6) (7) • 0 50 0 -- -- -- -- • 1 50 50 • 2 50 78 • 3 50 98 • 4 50 112 • 5 50 130 • 6 50 150 • 7 50 175 • 8 50 204 • 9 50 242 • 10 50 300 • 11 50 385

26. Let’s Check Your Understanding! 1. JNE Firm has the following cost information. Fill in the missing values. JNE Firm’s Costs Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost (FC) (VC) (TC) (MC) (AFC) (AVC) (ATC) (1) (2) (3) (4) (5) (6) (7) • 0 50 0 50 -- -- -- -- • 1 50 50 100 50 50 50 100 • 2 50 78 128 28 25 39 64 • 3 50 98 148 20 16.7 32.7 49.3 • 4 50 112 162 14 12.5 28 40.5 • 5 50 130 180 18 10 26 36 • 6 50 150 200 20 8.3 25 33.3 • 7 50 175 225 25 7.1 25 32.1 • 8 50 204 254 29 6.3 25.5 31.8 • 9 50 242 292 38 5.6 26.9 32.4 • 10 50 300 350 58 5 30 35 • 11 50 385 435 85 4.5 35 39.5

27. The Relationship Between Marginal Cost and Average Cost Costs per unit The marginal cost curve goes through the minimum point of both the ATC and AVC curves MC ATC AVC Q

28. The Relationship Between Marginal Cost and Average Cost • If MC > ATC, then ATC is rising • If MC > AVC, then AVC is rising • If MC < ATC, then ATC is falling • If MC < AVC, then AVC is falling • If MC = AVC and MC = ATC, then AVC and ATC are at their minimum points 12-28

29. The Relationship Between Marginal Product and Marginal Cost Costs per unit MC AVC If marginal product is rising, marginal cost is falling Q If average product is falling, average cost is rising Output per worker AP of workers MP of workers Q

30. The Long Run Cost-Minimization Problem We now turn to a fundamental problem that all firms face: how to select inputs to produce a given output at minimum cost. Cost-minimization problem is the problem of finding the input combination that minimizes a firm’s total cost of producing a particular level of output. Cost-minimizing firmis a firm that seeks to minimize the cost of producing a given amount of output. For simplicity, we will work with two variable inputs: labor (measured in hours of work per year) and capital (measured in hours of use of machinery per year).

31. Isocost Line • Isocostline • represents a set of combinations of labor and capital that yield the same total cost (TC) for the firm. • a graph that shows all possible combinations of labor and capital that can be purchased for a given total cost. • An isocost line is analogous to a budget line from the theory of consumer choice. • The long-run cost-minimization problem for a firm that uses two inputs: labor and capital. Each input has a price. The price of a unit of labor services—also called the wage rate—is . This price per unit of capital services is .

32. Isocost Line Consider, for example, a case in which per labor-hour, per machine-hour, and per month. The 100 thousand isocost line is described by the equation , which can be rewritten as More generally, for an arbitrary level of total cost TC, and input prices and , the equation of the isocost line is

33. Isocost Line Slope of Isocost Line is CAPITAL LABOR

34. Isocost Map Isocost Lines (Map) As we move to the northeast in the isocost map, isocost lines correspond to higher levels of total cost. All isocost lines have the same slope. It is expressed by . IL2 IL3 IL1

35. Isocost Map

36. Cost Minimization Producing a Given Output at Minimum Cost Isocost curves describe the combination of inputs to production that cost the same amount to the firm. Isocost curve C1 is tangent to isoquant q1 at A and shows that output q1 can be produced at minimum cost with labor input L1 and capital input K1. Other input combinations-L2, K2 and L3, K3-yield the same output but at higher cost.

37. Choosing Inputs Input Substitution When an Input Price Changes Facing an isocost curve C1, the firm produces output q1 at point A using L1 units of labor and K1 units of capital. When the price of labor increases, the isocost curves become steeper. Output q1 is now produced at point B on isocost curve C2 by using L2 units of labor and K2 units of capital.

38. Choosing Inputs Recall that in our analysis of production technology, we showed that the marginal rate of technical substitution of labor for capital (MRTS) is the negative of the slope of the isoquant and is equal to the ratio of the marginal products of labor and capital: It follows that when a firm minimizes the cost of producing a particular output, the following condition holds: We can rewrite this condition slightly as follows:

39. Cost Minimization with Varying Output Levels Expansion pathis a curve passing through points of tangency between a firm’s isocostlines and its isoquants. The Expansion Path and Long-Run Costs • To move from the expansion path to the cost curve, we follow three steps: • Choose an output level represented by an isoquant. Then find the point of tangency of that isoquant with an isocost line. • From the chosen isocost line determine the minimum cost of producing the output level that has been selected. • Graph the output-cost combination.

40. Long-run versus Short-run Cost Curves Long-run average cost curve (LAC) Curve relating average cost of production to output when all inputs, including capital, are variable. Short-run average cost curve (SAC) Curve relating average cost of production to output when level of capital is fixed. Long-run marginal cost curve (LMC) Curve showing the change in long-run total cost as output is increased incrementally by 1 unit.

41. Economies and Diseconomies of Scale • As output increases, the firm’s average cost of producing that output is likely to decline, at least to a point. • This can happen for the following reasons: • If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive. • 2. Scale can provide flexibility. By varying the combination of inputs utilized to produce the firm’s output, managers can organize the production process more effectively. • 3. The firm may be able to acquire some production inputs at lower cost because it is buying them in large quantities and can therefore negotiate better prices. The mix of inputs might change with the scale of the firm’s operation if managers take advantage of lower-cost inputs.

42. At some point, however, it is likely that the average cost of production will begin to increase with output. • There are three reasons for this shift: • At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs effectively. • Managing a larger firm may become more complex and inefficient as the number of tasks increases. • The advantages of buying in bulk may have disappeared once certain quantities are reached. At some point, available supplies of key inputs may be limited, pushing their costs up. Economies and Diseconomies of Scale

43. Economies and Diseconomies of Scale • Economies of scale • Situation in which output can be doubled for less than a doubling of cost. • Diseconomies of scale • Situation in which a doubling of output requires more than a doubling of cost. Increasing Returns to Scale: Output more than doubles when the quantities of all inputs are doubled. Economies of Scale: A doubling of output requires less than a doubling of cost.

44. Long- Run Cost Curves Long-Run Cost with Economies and Diseconomies of Scale The long-run average cost curve LAC is the envelope of the short-run average cost curves SAC1, SAC2, and SAC3. With economies and diseconomies of scale, the minimum points of the short-run average cost curves do not lie on the long-run average cost curve.