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Lecture 5Econ 340H

Managerial Economics

Cost Theory & Analysis

Christopher Michael

Trent UniversityDepartment of Economics

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• Meaning and Measurement of Cost

• Short-Run Cost Functions• Long-Run Cost Functions

Topics

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The Importance of Cost Analysis» Managers seek to produce the highest quality

products at the lowest possible cost.» Firms that are satisfied with the status quo find

that competitors arise that produce at lower costs and drive them out of business.

» The advantages once assigned to being a large firm (economies of scale and scope) have NOT provided the advantages of flexibility and agility found in some smaller companies.

» Cost analysis is helpful in the task of finding lower cost methods to produce goods and services.

Overview

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There a number of cost concepts in business.

• Opportunity Cost – value of next best alternative use.

• Explicit vs. Implicit Cost – actual prices paid vs. opportunity cost of owner-supplied resources.

Meaning and Measurement of Costs

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Accounting vs. Economic Cost

• Accounting costs involve explicit historical costs. They attempt to use the same rules for different firms, so we can compare firm performance.

• Economic costs are based on making decisions. These costs can be both implicit and explicit.» A chief example is that economic costs include the

opportunity costs of owner-supplied resources such as time and money, which are implicit costs.

» Economic Profit =

Total Revenues - Explicit Costs - Implicit Costs

» Both explicit and implicit costs make economic profit lower than accounting profit

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• Depreciation Cost Measurement. Accounting depreciation (e.g., straight-line depreciation) tends to have little relationship to the actual loss of value» To an economist, the actual loss of value is the true cost

of using machinery. • Inventory Valuation. Accounting valuation depends on its

acquisition cost» Economists view the cost of inventory as the cost of

replacement.• Unutilized Facilities. Empty space may appear to have

"no cost”» Economists view its alternative use (e.g., rental value) as

its opportunity cost.

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• Sunk Costs -- already paid for, or there already exists a contractual

obligation to pay• Incremental Cost - - extra cost of

implementing a decision = TC of a decision

• Marginal Cost -- cost of last unit produced = TC/Q

SHORT-RUN COST FUNCTIONS

1. TC = FC + VC fixed & variable costs

2. ATC = AFC + AVC = FC/Q + VC/Q

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AFC

Q

Q

1.

2. AVC

3.

QAFC

AVC

ATC

MC

MC intersects lowest point of AVC and lowest point of ATC.

When MC < AVC, AVC declinesWhen MC > AVC, AVC rises

Short-Run Cost Graphs

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Relationships Among Cost & Production FunctionsWhen Factor Markets Are Perfectly Competitive

• AP & AVC are inversely related. (ex: one input)

• AVC = WL /Q = W/ (Q/L) = W/ APL

» As APL rises, AVC falls

• MP and MC are inversely related

• MC = dTC/dQ = W dL/dQ = W / (dQ/dL) = W / MPL

» As MPL declines, MC rises

prod. functions

cost functions

MPL

L

MC

AP

AVC

Q

Q

cost

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Let there be a cubic VC function:

VC = 0.5 Q3 - 10 Q2 + 150 Q 1. find AVC from the VC function above.

2. find minimum variable cost output from AVC.

3. and find MC from the VC function

A1: AVC = 0.5 Q 2 -10 Q + 150 (divide by Q)

A2: Minimum AVC is where dAVC/dQ = 0dAVC / dQ = Q - 10 = 0

Q = 10, so AVC = 100 @ Q = 10

A3: MC= dVC/dQ= 1.5 Q2 - 20 Q + 150

Problem

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Long-Run Cost Functions• All inputs are variable in the long

run• LAC is long-run average cost

» ENVELOPE of SAC curves

• LMC is FLATTER than SMC curves

• The optimal plant size for a given output Q2 is plant size 2. (A SR concept.)

• However, the optimal plant size occurs at Q3, which is the lowest cost point overall. (A LR concept.)

Q

LAC

LMCSAC2

SMC2

Q2 Q3

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Long-Run Cost Function (LAC) Envelope of SAC curves

Q

SAC-small capital

SAC-med. capital

SAC-big capital

LAC--Envelopeof SRAC curves

Avg Cost

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Economists think that the LAC is U-shaped

• Downward section due to:» Product-level economies which include specialization

and learning curve effects.

» Plant-level economies, such as economies in overhead, required reserves, investment, or interactions among products (economies of scope).

» Firm-level economies which are economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi-product firms.

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• Flat section of the LAC» Displaces constant returns to scale» The minimum efficient scale (MES) is the smallest scale at which

minimum per unit costs are attained.

• Upward rising section of LAC is due to:» diseconomies of scale. These include transportation costs,

imperfections in the labour market, and problems of coordination and control by management.

» The maximum efficient scale (Max ES) is the largest scale before which unit costs begin to rise.

» Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to performance.

CRS region

MES Max ES

DRS

LAC

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Q Suppose we have the following info:

TC = 200 + 5Q - 0.4Q2 + 0.001Q3

MC = 5 - 0.8Q + 0.003Q2

1. FIND fixed cost

2. FIND AVC function

3. FIND AVC at Q = 10

4. If FC rises $500, what happens to the average variable cost function?

Problem

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TC = 200 + 5Q - 0.4Q2 + 0.001Q3

MC = 5 - 0.8Q + 0.003Q2

1. FIND fixed cost

Answer: FC = 200, the intercept in the TC curve.

2. FIND AVC function

Answer: VC = 5Q - 0.4Q2 + 0.001Q3

So AVC = 5 - 0.4Q + 0.001Q2 (Divide VC by Q)

3. FIND AVC at Q = 10.

Answer: Substitute Q = 10 into the AV C function. AVC = 5 - 0.4(10) + 0.001(102) = 5 – 4 + .1 = 1.1

4. If FC rises $500, what happens to the average variable cost function?

Answer: No change, since AVC does NOT include fixed cost.