The Theory and Estimation of Cost - UW–Madison Econ Chapter 7 -- Cost Curves.pdf · Chapter 7 The...

Chapter 7The Theory and Estimation of

Cost Managerial Economics: Economic

Tools for Today’s Decision Makers, 5/e By Paul Keat and Philip Young

2006 Prentice Hall Business Publishing Managerial Economics, 5/e Keat/Young

The Theory and Estimation of Cost

• The Importance of Cost in Managerial Decisions• The Definition and Use of Cost in Economic Analysis• The Relationship Between Production and Cost

• DUALTIY: Inverse (Mirror) Functions.• The Short Run Cost Function• The Long Run Cost Function• The Learning Curve• Economies of Scope• Economies of Scale: the Short Run Versus the Long Run• Supply Chain Management• Ways Companies Have Cut Costs to Remain Competitive


Learning Objectives• Define the cost function and explain the difference

between a short-run and a long-run cost function.• Explain the linkages between the production function

and the cost function.• Distinguish between economic cost and accounting

cost.• Explain how the concept of relevant cost is used in the

economic analysis of cost.• Define short-run total cost, short-run variable cost, and

total fixed cost and explain their relationship to each other.


Learning Objectives• Define average cost, average variable cost, and

average fixed cost and explain their relationship to each other in the short run. Do the same for average cost and average variable cost in the long run.

• Compare and contrast the short-run cost function and the long-run cost function and explain why economies of scale is considered to be a long-run phenomenon.

• Provide at least four reasons for the existence of economies of scale.


The Importance of Costin Managerial Decisions

• Ways to contain or cut costs over the past decade:• Most common: reduce number of people on

the payroll.• Outsourcing components of the business.• Merge, consolidate, then reduce headcount.

• “Neutron Jack” Welch (GE): Leave only buildings.


The 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.

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

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


The Relationship Between Production and Cost

• Cost function is simply the production function expressed in monetary rather than physical units.• Mirror Image.• Inverse Functions:

• Recall MCQ = PL/MPL Inverse of MP !!!

• Assume the firm is a “price taker” in the input market.



• Total Variable Cost (TVC): the cost associated with the variable input, determined 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.

MPW

QTVCMC =∆

∆=



• 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.


The Short-Run Cost Function• For simplicity the following assumptions are made:

• 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 uses the inputs to produce a single product.• The firm operates with a fixed level of technology.• 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” in the input markets.

• The short-run production function is affected by the law of diminishing returns.


The Short-Run Cost Function• Standard variables in the short-run cost

function:• Quantity (Q): the amount of output that a firm can

produce in the short run.• Total fixed cost (TFC): the total cost of using the

fixed input, capital (K)• Total variable cost (TVC): the total cost of using the

variable input, labor (L)• Total cost (TC): the total cost of using all the firm’s

inputs, L and K.TC = TFC + TVC


The Short-Run Cost Function• Standard variables in the short-run cost function:

• Average fixed cost (AFC): the average per-unit cost of using the fixed input K.AFC = TFC/Q

• Average variable cost (AVC): 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 using all the firm’s inputs.AC = AFC + AVC = TC/Q

• Marginal cost (MC): the change in a firm’s total cost (or total variable cost) resulting from a unit change in output.MC = ∆TC/∆Q = ∆TVC/∆Q


The Short-Run Cost Function

• Graphical example of the cost variables



• Important Observations• AFC declines steadily over the range of

production.• 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.



• 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.



Decrease Fixed Costs Decrease Variable Costs



• Alternative specifications of the Total Cost function (Hmwk 2-3 !!!):• Most commonly: specified as a cubic relationship

between total cost and output• As output increases, total cost first increases at a

decreasing rate, then increases at an increasing rate.• Quadratic relationship

• As output increases, total cost increases at an increasing rate.

• Linear relationship• As output increases, total cost increases at a constant rate.


The 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.• First, increasing returns to scale.• As firms mature, they achieve constant returns,

then ultimately 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.


The Long-Run Cost Function• Reasons for long-run economies:

• Specialization in the use of labor and capital.• Prices of inputs may fall as the firm realizes volume

discounts in its 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 than smaller firms.• Larger firms may be able to spread out promotional

costs.



• Reasons for Diseconomies of Scale:• Scale of production becomes so large that it

affects the total market demand for inputs, so input prices rise.

• Transportation costs tend to rise as production grows.• Handling expenses, insurance, security, and

inventory costs affect transportation costs.


The 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.


The Learning Curve• Learning Curve: line showing the relationship between labor

cost and additional units of output.• Downward slope indicates additional cost per unit declines as

the level of output increases because workers improve with practice.

• Measured in terms of percentage decrease in additional labor cost as output doubles.

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 2• S = Slope parameter


The Learning Curve


Economies of Scope

• Economies of Scope: reduction in unit cost by producing two or more goods or services jointly rather than separately.

• Closely related to economies of scale.• Second Derivative Cost Concept:

• ∂2Cost/∂Q1∂Q2 = ∂MC1/∂Q2 < 0 ???• Does MC1 decline with increased

production of Q2 ??? If so, SCOPE !!!


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.

• Includes all internal and external activities required to fulfill a customer’s demand.

• Transaction costs are incurred by using resources outside the firm.

• Coordination costs arise because of uncertainty and complexity of tasks.

• Information costs arise because information is essential to the proper coordination of activities between the firm and its suppliers.


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.


Supply Chain Management


Ways Companies Have 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• Relocation to Lower-Wage Countries or

Regions• Mergers, Consolidation, and Subsequent

Downsizing• Layoffs and Plant Closings

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