1517 cost-theory and estimation of cost

Chapter 8Chapter 8The Theory

and Estimation

of Cost Managerial Economics:

Economic Tools for Today’s Decision

Makers, 4/e By Paul Keat and Philip Young

2003 Prentice Hall Business Publishing Managerial Economics, 4/e Keat/Young

Before We Start…Group Presentation

• So popular?Q = aLbK1-b or c

• b+c > 1 IRTS• b+c = 1 CRTS• b+c < 1 DRTS

• Short Run Analysis: MPK = c Q/K & MPL = b Q/L

• b & c are elasticities of K & L factors

• LogQ=loga+blogL+clogK + dlogT where T technology


The Theory and Estimation of Cost

• Definition of Cost• The Short Run Relationship Between

Production and Cost• The Short Run Cost Function

• The Long Run Relationship Between Production and Cost• The Long Run Cost Function

• The Learning Curve


Definition of Cost

• A cost is relevant if it is affected by a management decision. • Historical cost is incurred at the time of

procurement• Replacement cost is necessary to replace

inventory• Are historical costs relevant?


Definition of Cost

• There are two types of cost associated with economic analysis• Opportunity cost is the value that is

forgone in choosing one activity over the next best alternative

• Out-of-pocket cost is actual transfer of value that occur

• Which cost is relevant?


Definition of Cost

• There are two types of cost associated with time• Incremental cost varies with the range

of options available in the decision making process.

• Sunk cost does not vary with decision options.

• Is sunk cost relevant?


SR Relationship Between Production and Cost

• A firm’s cost structure is related to its production process.• Costs are determined by the production

technology and input prices.• Assuming that the firm is a “price taker” in

the input market.



• Total variable cost (TVC) is associated with the variable input• Assume w=$500

per unit (price-taker)

Total Input (L) Q (TP) MP

TVC (wL)

0 0 01 1,000 1,000 5002 3,000 2,000 1,0003 6,000 3,000 1,5004 8,000 2,000 2,0005 9,000 1,000 2,5006 9,500 500 3,0007 9,850 350 3,5008 10,000 150 4,0009 9,850 -150 4,500



• TP and TVC are mirror images of each other

Kings Dominion Example



• Total cost (TC) is the cost associated with all of the inputs. It is the sum of TVC and TFC.• TC=TFC+TVC

• Marginal Costs• Average Costs

Tool Set for Production Cost

Analysisvs.

Production Process Analysis



• Marginal cost (MC) is the change in total cost associated a change in output.

QTCMC

QTVC

QTVC

QTFC

QTVCTFC

QTCMC

0)(



• Add marginal cost to the table

Total Input (L) Q MP

TVC (wL) MC

0 0 01 1,000 1,000 500 0.502 3,000 2,000 1,000 0.253 6,000 3,000 1,500 0.174 8,000 2,000 2,000 0.255 9,000 1,000 2,500 0.506 9,500 500 3,000 1.007 9,850 350 3,500 1.438 10,000 150 4,000 3.339 9,850 -150 4,500



• Observe that:• When MP is

increasing, MC is decreasing.

• When MP is decreasing, MC is increasing.

Total Input (L) Q MP

TVC (wL) MC

0 0 01 1,000 1,000 500 0.502 3,000 2,000 1,000 0.253 6,000 3,000 1,500 0.174 8,000 2,000 2,000 0.255 9,000 1,000 2,500 0.506 9,500 500 3,000 1.007 9,850 350 3,500 1.438 10,000 150 4,000 3.339 9,850 -150 4,500



• The relationship between MP and MC is

MPw

MPw

QLw

QLw

QTVCMC

1

Law of diminishing returns implies that MC will eventually increase! Why?


The Short Run Cost Function

• Average total cost (ATC) is the average per-unit cost of using all of the firm’s inputs (TC/Q)• Average variable cost (AVC) is the

average per-unit cost of using the firm’s variable inputs (TVC/Q)

• Average fixed cost (AFC) is the average per-unit cost of using the firm’s fixed inputs (TFC/Q)



• Add ATC = AFC + AVC to the table



• ATC = AFC + AVC


The Short Run Cost Function• Production cost graph or map is



• Important Map Observations• AFC declines steadily over the range of

production. Why?

• In general, ATC is u-shaped. Why?

• MC intersects the minimum point (q*) on ATC. Why?



• Important Map Observations• What is the economic significance of q*?



• Average total cost (ATC) is the average per-unit cost of using all of the firm’s inputs (TC/Q)• At Q* - ATC is minimized or inputs

are used most efficiently given the production function

Going at 55 MPH



• A change in input prices will shift the cost curves.• If fixed input costs

are reduced then ATC will shift downward. AVC and MC will remain unaffected. Computer

Chip Case



• A change in input prices will shift the cost curves.• If variable input

costs are reduced then MC, AVC, and AC will all shift downward.

Airline Industry Case



• Yahoo Group Discussion• What is different

about dot.com businesses?

Irrational Exuberance


The LR Relationship Between Production and Cost

• In the long run, all inputs are variable.• What makes up LRAC?


The Long-Run Cost Function

• LRAC is made up for SRACs• SRAC curves represent

various plant sizes• Once a plant size is

chosen, per-unit production costs are found by moving along that particular SRAC curve



• The LRAC is the lower envelope of all of the SRAC curves.• Minimum efficient scale is the lowest

output level for which LRAC is minimized

Is LRAC a function of market size?What are implications?



• Reasons for Economies of Scale…Increasing returns to scaleSpecialization in the use of labor and capital

• Economies in maintaining inventory• Discounts from bulk purchases• Lower cost of raising capital funds• Spreading promotional and R&D costs

Management efficiencies



• Reasons for Diseconomies of Scale… Decreasing returns to scale Input market imperfections Management coordination and control problems


The Learning Curve

• Measures the percentage decrease in additional labor cost each time output doubles.• An “80 percent” learning

curve implies that the labor costs associated with the incremental output will decrease to 80% of their previous level.


The Learning Curve

• A downward slope in the learning curve indicates the presence of the learning curve effect • Why? Workers improve their

productivity with practice• The learning curve effect shifts the

SRAC downward


Production Cost Homework

• Page 378 • Problem 10

1517 cost-theory and estimation of cost

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