chapter 9 cost analysis 2 nd semester, s.y 2013 – 2014

BACHELOR OF ARTS IN ECONOMICS Econ 111 – ECONOMIC ANALYSIS

Pangasinan State UniversitySocial Science Department – PSU Lingayen

CHAPTER 9COST ANALYSIS2nd Semester, S.Y 2013 – 2014



A. What is a cost?B. The FirmC. Short Run vs. Long Run D. Fixed and Variable InputsE. Cost FunctionF. Short Run Production Costs

a. Fixed Costb. Variable Costc. Total Costd. Marginal Coste. Average Costs

G. Cost Curves: An AnalysisH. Isocost LineI. Isocost EquationJ. Isocost MapK. Cost Minimization ProblemL. Long Run CostsM. Economies and Diseconomies of Scale

Chapter Outline



When economists examine firms over time they must define the Short Run and Long Run.

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



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.

o In the long run, there are no fixed costs since all inputs (and therefore their costs) are variable.

o In the short run, a number of inputs and their costs will be fixed

Fixed Cost



Fixed versus Sunk Costs

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 it represents the sunk costs.

Whether the drug is a success or a failure, these costs cannot be recovered and thus are sunk.



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.



Fixed Costs and Variable Costs

Shutting DownShutting 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.



Total Cost

It is the whole 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:



OutputFixed Cost

Variable Cost

Total Cost

0 P400 0 4001 P400 200 6002 400 400 8003 400 600 1,0004 400 800 1,2005 400 1,000 1,4006 400 1,200 1,6007 400 1,400 1,8008 400 1,600 2,0009 400 1,800 2,200

10 400 2,000 2,400

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.

0 2 4 6 8 10 120

500

1000

1500

2000

2500

3000

400600

8001000

12001400

16001800

20002200

2400

Total Cost



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.



Let’s Check Your Understanding!

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.

2. Determine or derive the cost function given the cost data on the table.

1. Suppose the fixed cost of production for a commodity is P12,000, the variable cost is P25. Determine the cost equation.

OutputFixed Cost

Variable Cost

Total Cost

0 P400 0 4001 P400 200 6002 400 400 8003 400 600 1,0004 400 800 1,2005 400 1,000 1,4006 400 1,200 1,6007 400 1,400 1,8008 400 1,600 2,0009 400 1,800 2,200

10 400 2,000 2,400



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



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



Total Output

Fixed Cost(FC)

Variable Cost (VC)

Total Cost (TC)

Marginal Cost (MC)

Average Fixed Cost

(AFC)

Average Variable

Cost (AVC)

Average Total Cost

(ATC)

0 100 0 100 -- -- -- --

1 100 50 150 50 100 50 150

2 100 84 184 34 50 42 92

3 100 108 208 24 33 36 69

4 100 127 227 19 25 32 57

5 100 150 250 23 20 30 50

6 100 180 280 30 17 30 47

7 100 218 318 38 14 31 45

8 100 266 366 48 13 33 46

9 100 325 425 59 11 36 47

10 100 400 500 75 10 40 50

11 100 495 595 95 9 45 54

12 100 612 712 117 8 51 59

Costs of Production



FC, VC and TC Curves

0 2 4 6 8 10 12 140

100

200

300

400

500

600

700

800

100

150184

208 227250

280318

366

425

500

595

712

0

5084

108 127150

180218

266

325

400

495

612

100 100 100 100 100 100 100 100 100 100 100 100 100

Fixed Cost Variable Cost Total Cost

TOTAL OUTPUT

FC

, V

C,

TC

TCTotal Output

Fixed Cost(FC)

Variable Cost (VC)

Total Cost (TC)

0 100 0 100

1 100 50 150

2 100 84 184

3 100 108 208

4 100 127 227

5 100 150 250

6 100 180 280

7 100 218 318

8 100 266 366

9 100 325 425

10 100 400 500

11 100 495 595

12 100 612 712

VC

FC



MC, AFC, AVC and ATC Curves

0 2 4 6 8 10 12 140

20

40

60

80

100

120

140

160

150

92

69

5750 47 45 46 47 50

5459

5042

3632 30 30 31 33 36

4045

51

100

50

3325

20 17 14 13 11 10 9 8

50

34

2419

2330

38

48

59

75

95

117

Marginal Cost -- Average Fixed Cost --

Average Variable Cost -- Average Total Cost --

TOTAL OUTPUT

MC

, A

FC

, A

VC

, A

TC

Total Output

Marginal Cost (MC)

Average Fixed Cost (AFC)

Average Variable

Cost (AVC)

Average Total Cost (ATC)

0 -- -- -- --

1 50 100 50 150

2 34 50 42 92

3 24 33 36 69

4 19 25 32 57

5 23 20 30 50

6 30 17 30 47

7 38 14 31 45

8 48 13 33 46

9 59 11 36 47

10 75 10 40 50

11 95 9 45 54

12 117 8 51 59

MC

ATC

AVC

AFC



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. Because the 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



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



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.

Average Cost Curves



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.

Marginal Cost Curve



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.

Capital Input

Labor Input

TP MP AP FC VC TC MC AFC AVC ATC

4 0 0

4 1 2

4 2 5

4 3 10

4 4 14

4 5 14

4 6 12

4 7 10

4 8 9




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.

Capital Input

Labor Input

TP MP AP FC VC TC MC AFC AVC ATC

4 0 0 40 0 40

4 1 2 2 2.0 40 40 80 10.0 20.0 20.0 40.0

4 2 5 3 2.5 40 100 140 6.7 8.0 20.0 28.0

4 3 10 5 3.3 40 200 240 4.0 4.0 20.0 24.0

4 4 14 4 3.5 40 280 320 5.0 2.9 20.0 22.9

4 5 14 2 2.4 40 240 280 10.0 3.3 20.0 23.3

4 6 12 2 1.7 40 200 240 0.0 4.0 20.0 24.0

4 7 10 0 1.4 40 200 240 0.0 4.0 20.0 24.0

4 8 9 -2 1.0 40 160 200 -10.0 5.0 20.0 25.0




Output FC VC TC MC AFC AVC ATC

3 50 38

4 50 50

9 50 100

10 50 108

16 50 150

17 50 157

22 50 200

23 50 210

27 50 255

28 50 270

32 50 400


1. Complete the following cost data by filling in the missing values.



Output FC VC TC MC AFC AVC ATC

3 50 38 88 16.67 12.66 29.33

4 50 50 100 12.50 12.50 25.00

9 50 100 150 5.56 11.11 16.67

10 50 108 158 5.00 10.80 15.80

16 50 150 200 3.13 9.38 12.51

17 50 157 207 2.94 9.24 12.18

22 50 200 250 2.27 9.09 11.36

23 50 210 260 2.17 9.13 11.30

27 50 255 305 1.85 9.44 11.29

28 50 270 320 1.79 9.64 11.43

32 50 400 450 1.56 12.50 14.06


1. Complete the following cost data by filling in the missing values.



JNE Firm’s Costs

Rate of Fixed Variable Total Marginal Average Average AverageOutput 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

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 AverageOutput 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

1. JNE Firm has the following cost information. Fill in the missing values.




AVC

MC

Q

Costs per unit

ATCThe marginal cost curve

goes through the minimum point of both the ATC and AVC curves

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

The Relationship Between Marginal Cost and Average Cost

12-28



The Relationship Between Marginal Product and Marginal Cost

AVC

Q

MC

Q

Output per worker

Costs per unit

If marginal product is rising, marginal cost is falling

If average product is falling, average cost is rising

MP of workers

AP of workers



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 firm is 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).

The Long Run Cost-Minimization Problem



Isocost Line

Isocost line

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 .



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



Choice Labor Capital Total Cost

A 0 100 P10,000 = P200 (0) + P100 (100)

B 10 80 P10,000 = P200 (10) + P100 (80)

C 30 40 P10,000 = P200 (30) + P100 (40)

D 40 20 P10,000 = P200 (40) + P100 (20)

E 50 0 P10,000 = P200 (50) + P100 (0)

0 10 20 30 40 50 600

20

40

60

80

100

120A

B

C

D

E

Isocost Line

CAPITAL

LABOR

Slope of Isocost Line is



Isocost Map

Choice

Isocost Line 1 Isocost Line 2 Isocost Line 3

Labor Capital Labor Capital Labor Capital

A 0 100 0 200 0 400

B 10 80 20 160 40 320

C 30 40 60 80 120 160

D 40 20 80 40 160 80

E 50 0 100 0 200 0

0 50 100 150 200 2500

50

100

150

200

250

300

350

400

450

Capital

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 IL3IL1



Isocost Map



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.

Cost Minimization



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.



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:

Choosing Inputs



Cost Minimization with Varying Output Levels

Expansion path is a curve passing through points of tangency between a firm’s isocost lines and its isoquants.

The Expansion Path and Long-Run Costs

To move from the expansion path to the cost curve, we follow three steps:

1. Choose an output level represented by an isoquant. Then find the point of tangency of that isoquant with an isocost line.

2. From the chosen isocost line determine the minimum cost of producing the output level that has been selected.

3. Graph the output-cost combination.



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.



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:

1. 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.

Economies and Diseconomies of Scale




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:

1. At least in the short run, factory space and machinery may make it more difficult for workers to do their jobs effectively.

2. Managing a larger firm may become more complex and inefficient as the number of tasks increases.

3. 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 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.




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.

chapter 9 cost analysis 2 nd semester, s.y 2013 – 2014

Documents

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short run

long run fixed

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costs of raw materials

fixed input

fixed costbachelor of

quantity of output