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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-3
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-4
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)
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-5
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-6
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-7
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-8
Relationship Between Production and Cost
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-9
Relationship Between Production and Cost
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-10
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-11
Short-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-12
Short-run Cost Function
• 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)
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-13
Short-run Cost Function
• Standard variables in the short-run cost function:
– 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-14
Short-run Cost Function
• Standard variables in the short-run cost function:
– 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-15
Short-run Cost Function
• Standard variables in the short-run cost function:
– 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-16
Short-run Cost Function
• Graphical example of the cost variables
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-17
Short-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-18
Short-run Cost Function
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.
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-19
Short-run Cost Function
• 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.
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-20
Short-run Cost Function
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-21
Short-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-22
Short-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-23
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-24
Long-run Cost Function
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-25
Long-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-26
Long-run Cost Function
• 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.
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-27
Long-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-28
Long-run Cost Function
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-29
Long-run Cost Function
• 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.
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-30
Long-run Cost Function
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-31
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.
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-32
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-33
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-34
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-35
Supply Chain Management
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-36
Supply Chain Management
• 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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-37
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-38
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-39
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
Copyright ©2014 Pearson Education, Inc. All rights reserved. 7-40
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.