THE THEORY AND ESTIMATION OF COST

Chapter 7

The Theory and Estimation

of Cost

Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-2

Chapter Outline

• Importance of cost in managerial decisions• Definition and use of costs in economic analysis• Relationship between production and cost• Short-run cost function• Long-run cost function• Learning curve• Economies of scope and scale• Supply chain management• Ways companies have cut costs to remain

competitive


Learning Objectives

• Define the cost function and the difference between the short and long run

• Distinguish between economic cost and accounting cost

• Explain how the concept of relevant cost is used in economic analysis

• Define total, variable, average and fixed cost• Explain the linkage between the production and

cost function• Provide reasons for the existence of economies of

scale and scope


Importance of Costin Managerial Decisions

• Ways to contain or cut costs popular during the past decade

– Most common: reduce number of people on the payroll

– Consolidation of shared services– Outsourcing components of the business– Mergers and consolidation (usually with a

reduction in employees)


Definition and Use of Cost in Economic Analysis

• Relevant cost: a cost that is affected by a management decision

• Historical cost: cost incurred at the time of procurement

• Opportunity cost: amount or subjective value that is forgone in choosing one activity over the next best alternative


Definition and Use of Cost in Economic Analysis

• Incremental cost: varies with the range of options available in the decision

• Sunk cost: does not vary in accordance with decision alternatives


Relationship Between Production and Cost

• Cost function is simply the production function expressed in monetary rather than physical units

• We assume the firm is a ‘price taker’ in the input market



• Total variable cost (TVC) = the cost associated with the variable input, found by multiplying the number of units by the unit price

• Marginal cost (MC) = the rate of change in total variable cost

– The law of diminishing returns implies that MC will eventually increase

MP

W

Q

TVCMC



Plotting TP and TVC illustrates that they are mirror images of each other

When TP increases at an increasing rate, TVC increases at a decreasing rate


Short-run Cost Function

• Short-run cost function assumptions:

– the firm employs two inputs, labor and capital– the firm operates in a short-run production period

where labor is variable, capital is fixed– the firm produces a single product– the firm employs a fixed level of technology



• More short run cost function assumptions.

– the firm operates at every level of output in the most efficient way

– the firm operates in perfectly competitive input markets and must pay for its inputs at a given market rate (it is a ‘price taker’)

– the short-run production function is affected by the law of diminishing returns



• Standard variables in the short-run cost function:

– Quantity (Q) is the amount of output that a firm can produce in the short run

– Total fixed cost (TFC) is the total cost of using the fixed input, capital (K)




– Total variable cost (TVC) is the total cost of using the variable input, labor (L)

– Total cost (TC) is the total cost of using all the firm’s inputs,

TC = TFC + TVC




– Average fixed cost (AFC) is the average per-unit cost of using the fixed input K AFC = TFC/Q

– Average variable cost (AVC) is the average per-unit cost of using the variable input L AVC = TVC/Q




– Average total cost (AC) is the average per-unit cost of all the firm’s inputs AC = AFC + AVC = TC/Q

– Marginal cost (MC) is the change in a firm’s total cost (or total variable cost) resulting from a unit change in output MC = DTC/DQ = DTVC/DQ



• Graphical example of the cost variables



• Important observations

– AFC declines steadily– when MC = AVC, AVC is at a minimum– when MC < AVC, AVC is falling– when MC > AVC, AVC is rising

The same three rules apply for average cost (AC) as for AVC



Two critical relationships:

• Productivity and cost are inversely related.

• The marginal cost pulls average either up or down depending on if it is above or below average.



• A reduction in the firm’s fixed cost would cause the average cost line to shift downward

• A reduction in the firm’s variable cost would cause all three cost lines (AC, AVC, MC) to shift downward.





• Alternative specifications of the Total Cost function (relating total cost and output)

– cubic relationship:as output increases, total cost first increases at a decreasing rate, then increases at an increasing rate



• Alternative specifications of the Total Cost function (relating total cost and output)

– quadratic relationship: as output increases, total cost increases at an increasing rate

– linear relationship: as output increases, total cost increases at a constant rate


Long-run Cost Function

• In the long run, all inputs to a firm’s production function may be changed

– Because there are no fixed inputs, there are no fixed costs

– The firm’s long run marginal cost pertains to returns to scale

– In general, at first firms achieve increasing returns to scale, then as they mature they have constant returns, then they may experience decreasing returns to scale





• When a firm experiences increasing returns to scale:

– a proportional increase in all inputs increases output by a greater proportion

– as output increases by some percentage, total cost of production increases by some lesser percentage



• Economies of scale: situation where a firm’s long-run average cost (LRAC) declines as output increases

• Diseconomies of scale: situation where a firm’s LRAC increases as output increases

• In general, the LRAC curve is u-shaped.



• Reasons for long-run economies of scale:

– specialization of labor and capital– prices of inputs may fall with volume discounts in

firm’s purchasing– use of capital equipment with better price-

performance ratios– larger firms may be able to raise funds in capital

markets at a lower cost– larger firms may be able to spread out

promotional costs



• Reasons for diseconomies of scale:

– Scale of production is not optimal for the total market demand

– Transportation costs tend to rise as production grows, due to handling expenses, insurance, security, and inventory costs



• In long run, the firm can choose any level of capacity

• Once it commits to a level of capacity, at least one of the inputs must be fixed. This then becomes a short-run problem.

• The LRAC curve is an envelope of SRAC curves, and outlines the lowest per-unit costs the firm will incur over a range of output.




Learning Curve

• Learning curve: line showing the relationship between labor cost and additional units of output

– A downward slope indicates additional cost per unit declines as the level of output increases because workers improve with practice.

– The production process also improves as engineers and other development personnel gain more experience.


Learning Curve

• Learning curve: measured in terms of percentage decrease in additional labor cost as output increases

Yx = Kxn

Yx = units of factor or cost to produce the xth unit

K = factor units or cost to produce the Kth (usually first) unit

x = product unit (the xth unit)n = log S/log 2S = slope parameter


Economies of Scope

• Economies of scope: reduction of a firm’s unit cost by producing two or more goods or services jointly rather than separately

– Closely related to economies of scale


Supply Chain Management

• Supply chain management (SCM): efforts by a firm to improve efficiencies through each link of a firm’s supply chain from supplier to customer

– transaction costs are incurred by using resources outside the firm

– coordination costs arise because of uncertainty and complexity of tasks

– information costs arise to properly coordinate activities between the firm and its suppliers





• Ways to develop better supplier relationships

– strategic alliance: firm and outside supplier join together in some sharing of resources

– competitive tension: firm uses two or more suppliers, thereby helping the firm keep its purchase prices under control


Ways Companies Cut Costs to Remain Competitive

• the strategic use of cost

• reduction in cost of materials

• using information technology to reduce costs

• reduction of process costs


Ways Companies Cut Costs to Remain Competitive

• relocation to lower-wage countries or regions

• mergers, consolidation, and subsequent downsizing

• layoffs and plant closings

• reductions in fixed assets


Global Application

• Discussion example: Li & FungIs this the model of a global business?

– Operating in 40 countries around the world– Outsourcing the entire supply chain


Summary

• Virtually all management decisions must consider the impact on costs.

• The short run cost function has fixed costs, in the long run, all costs are variable.

• The law of diminishing returns also affects costs.

• Firms may experience economies of scope and scale and benefit by the learning curve.

THE THEORY AND ESTIMATION OF COST

Business

cost cost function

cost function short

economic cost

cost total variable

cost variablescopyright

total cost tc

average cost acas

short run total fixed