Foundation of Economic Analysis3250:600

Instructor: Richard W. Stratton

Meets: Thursday 5:20 – 7:50 pm

CAS 134

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Administration

This Week’s AssignmentsFarnham Chapter 5 (SR costs), Chapter 6 (LR costs)Homework 4 – due next week

Next Week’s AssignmentsFarnham Chapter 7 (Perfect competition)Homework 5 - attempt

Decision Tree

Decision Tree

Introduction Short Run Production Short Run Costs Discussion

Long Run Costs

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Introduction – net benefit

Why are we interested in cost functions?

Decisions depend on net benefits of alternative courses of action

What are the relevant costs?Opportunity costsMarginal costs

Decision Tree

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Introduction – net benefit

Net benefit is the additional benefit received from an activity

Accounting profitTotal revenue – explicit costs

Economic profitTotal revenue – (explicit + implicit costs)

Group activity distinguishing between accounting and economic profit

Decision Tree

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Introduction – net benefit

Benefits determined by Revenue functionMarket structure – demand facing firmOur topic for next 2 weeks

Costs determined byProduction function Input pricesTo which we now turn

Decision Tree

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Introduction

Definition of production functionShort run versus long runFixed inputsVariable inputs

Decision Tree

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Introduction - definition

Production function is the relationship of how resources (inputs) can be converted to outputsLabor (L)Capital (K)Land (R)Entrepreneurship (En) Intermediate inputs (M)

Simplify – focus on L and K

Decision Tree

),,,,( MEnRKLfQx

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Introduction - definition

Production is a flow!Efficiency

Technical efficiencyEconomic efficiency

Given enough time all inputs can be changed to affect output

But some take longer than others

Decision Tree

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Introduction - definition

Short runThe amount of at least one input cannot

be changedThe amount of at least one input is fixedSome input amounts can vary

Long runAll input amounts can be changedAll input amounts can vary

Decision Tree

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Introduction - definition

Simplify – focus on L and K

Short runAssume Capital fixedAssume Labor can vary

Long runAssume Labor and Capital can vary

Decision Tree

),( KLfQx

),( KLfQx

);( KLfQx

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Introduction – Lasting Ideas

Costs derived from productionCost are a function of input pricesCost are a function of input

productivity

Input substitution is important

Sunk costs are irrelevant

Decision Tree

Decision Tree

Introduction Short Run Production Short Run Costs Discussion

Long Run Costs

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Short Run Production

Short run production functionLaw of variable proportions

Diminishing returnsTotal productAverage productMarginal product

Decision Tree

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Short Run Production

Proposition: As the amount of labor increases, capital

fixed, output will at some point increase at a decreasing rate Output may actually decline

Groups – is there a way to quickly test this proposition?

Decision Tree

);( KLfQx

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Short Run Production

SuggestionPaper airplane production in a men’s

room stall

Diminishing returnsLaw of variable proportions

Decision Tree

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Short Run Production

Important measures Total product – total production per unit of

time [TP or Q] Average product – production per unit of

variable input TP / L or Q / L

Marginal product – additional production from one addition unit of variable input Change TP / Change L or Q / L

Decision Tree

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Short Run Production (algebra)

Total Product

Average Product – TP/L

Marginal Product – TP/L

);( KLfQx 32 3333.05.410 LLLTPQx

23333.05.410 LLAPL

20.1910 LLMPL

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Short Run Production (table)

K Labor TP AP MP MP 10.00 01.00 014.17 14.17 18.00 14.17 10.00 02.00 035.33 17.67 24.00 21.17 10.00 03.00 061.50 20.50 28.00 26.17 10.00 04.00 090.67 22.67 30.00 29.17 10.00 04.50 105.75 23.50 30.25 15.08 10.00 05.00 120.84 24.17 30.00 15.08 10.00 06.00 150.01 25.00 28.00 29.17 10.00 06.75 170.03 25.19 25.19 20.02 10.00 07.00 176.18 25.17 24.00 06.15 10.00 08.00 197.35 24.67 18.00 21.17 10.00 09.00 211.52 23.50 10.00 14.17 10.00 10.00 216.70 21.67 00.00 05.18 10.00 11.00 210.88 19.17 -12.00 -05.82

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Short Run Production (graph)

Production Function

000.00

050.00

100.00

150.00

200.00

250.00

00.00 02.00 04.00 06.00 08.00 10.00 12.00

TP

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Short Run Production (graph)

Production Function

00.00

05.00

10.00

15.00

20.00

25.00

30.00

35.00

00.00 02.00 04.00 06.00 08.00 10.00 12.00

AP

MP

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Short Run Production (graph)Production Function

000.00

050.00

100.00

150.00

200.00

250.00

00.00 02.00 04.00 06.00 08.00 10.00 12.00

TP

Production Function

00.00

05.00

10.00

15.00

20.00

25.00

30.00

35.00

00.00 02.00 04.00 06.00 08.00 10.00 12.00

AP

MP

Diminishing Returns

TP maximum

Decision Tree

Introduction Short Run Production Short Run Costs Discussion

Long Run Costs

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Short Run Costs

Opportunity Cost (explicit, implicit) Net benefit Accounting and economic profit

SR Total Costs Fixed Variable Total

SR Average Costs Fixed Variable Total

Marginal Cost

Decision Tree

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Opportunity Cost

As we have seen the real cost of an activity is the most valued activity sacrificed!

Opportunity CostExplicit costs Implicit costs

Decision Tree

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Short Run Total Costs

If we know how much of each input is required for production Production function

And the cost per unit of inputs Input costsK = $50/unitL = $100/unit

We can calculate SR Total Costs

Decision Tree

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Short Run Total Cost

Total Cost TC = FC + VC FC = $50 * 10 = $500 VC = $100 * L

Fixed costs constant Variable costs

Increase at decreasing rate Increase at increasing rate

);( KLfQx

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Short Run Average Cost

Average Total Cost ATC = AFC + AVC AFC = TFC / Q AVC = TVC / Q

AFC always declining AVC U shaped

Decline, reach minimum, increase

ATC U shaped Decline, reach minimum, increase

);( KLfQx

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Short Run Marginal Cost

Marginal Cost Change in TC per unit change in Q Change in VC per unit change in Q TC / Q = VC / Q

MC U shaped Decline, reach minimum, increase

);( KLfQx

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Short Run Costs (table)

TP TFC TVC TC AFC AVC ATC MC0 $500 $0 $500

14 $500 $100 $600 $35.71 $7.14 $42.86 $7.14 35 $500 $200 $700 $14.29 $5.71 $20.00 $4.76 62 $500 $300 $800 $8.06 $4.84 $12.90 $3.70 91 $500 $400 $900 $5.49 $4.40 $9.89 $3.45

121 $500 $500 $1,000 $4.13 $4.13 $8.26 $3.33 150 $500 $600 $1,100 $3.33 $4.00 $7.33 $3.45 175 $500 $700 $1,200 $2.86 $4.00 $6.86 $4.00 197 $500 $800 $1,300 $2.54 $4.06 $6.60 $4.55 212 $500 $900 $1,400 $2.36 $4.25 $6.60 $6.67 217 $500 $1,000 $1,500 $2.30 $4.61 $6.91 $20.00

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Short Run Total Cost (graph)

Total Cost Functions

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

$1,600

0 50 100 150 200 250

TC

TFC

TVC

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Short Run Costs (graph)

Average and Marginal Cost Functions

$0.00

$5.00

$10.00

$15.00

$20.00

$25.00

$30.00

$35.00

$40.00

$45.00

0 50 100 150 200 250

ATC

AVC

AFC

MC

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Short Run Costs (stylized)

Q

$ MC

ATC

AVC

AFC

Q1 Q2

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Short Run Costs (stylized)

Production Function

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00

AP

MP

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Short Run Costs (stylized)

Decision Tree

Introduction Short Run Production Short Run Costs Discussion

Long Run Costs

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Discussion - Short Run Cost

Constant MC MP constant TC / Q = VC / Q constant

TC and VC are straight lines

Impact on AVC? AVC constant and equal to MC

Impact on ATC? ATC always declining

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Discussion - Short Run Cost

Decreasing MC MP increasing TC / Q = VC / Q decreasing

Additional units cost less than current units If current unit profitable, wouldn’t more

units also be profitable? Depends on revenue!

AVC always declining ATC always declining

Decision Tree

Introduction Short Run Production Short Run Costs Discussion

Long Run Costs