AAEC 2305AAEC 2305Fundamentals of Ag Fundamentals of Ag

EconomicsEconomics

Chapter 4Chapter 4

Costs, Returns, and Profit Costs, Returns, and Profit MaximizationMaximization

IntroductionIntroduction

A manager’s goal is to determine how A manager’s goal is to determine how much to produce in order to maximize much to produce in order to maximize profits.profits.

In Chapter 3, we established Stage II is the In Chapter 3, we established Stage II is the rational stage of pdn, but price information rational stage of pdn, but price information (cost) is necessary to determine at which (cost) is necessary to determine at which point in Stage II to produce.point in Stage II to produce.

Profit is affected not only by how much is Profit is affected not only by how much is produced, but also by the costs of produced, but also by the costs of generating that pdn.generating that pdn.

ObjectiveObjective

Objective of Chapter 4 is to introduce Objective of Chapter 4 is to introduce cost and revenue relationships into cost and revenue relationships into production to evaluate profit production to evaluate profit maximization.maximization.

Combine what we know about the Combine what we know about the physical pdn process with input price physical pdn process with input price information to examine relationship information to examine relationship between costs of production and level between costs of production and level of output produced.of output produced.

AssumptionsAssumptions

1) Firms seek to maximize π1) Firms seek to maximize π 2) One product, one pdn method2) One product, one pdn method 3) One variable input, all others 3) One variable input, all others

are fixed or held constantare fixed or held constant 4) Perfect Information4) Perfect Information 5) Price taker5) Price taker

Cost DefinitionsCost Definitions

Costs of Pdn or Economic Costs: The Costs of Pdn or Economic Costs: The payments that a firm must make to payments that a firm must make to attract inputs and keep them from attract inputs and keep them from being used to produce other products.being used to produce other products.• Explicit Costs - Normal out of pocket costs Explicit Costs - Normal out of pocket costs

of inputs used in pdnof inputs used in pdn• Implicit Costs- Costs associated with Implicit Costs- Costs associated with

inputs owned by the firm (i.e., inputs owned by the firm (i.e., opportunity costs - ex., land)opportunity costs - ex., land)

Fixed vs. Variable CostsFixed vs. Variable Costs

Fixed Costs: Costs which do not vary Fixed Costs: Costs which do not vary with the level of pdn - These costs are with the level of pdn - These costs are associated with the fixed factors of associated with the fixed factors of pdn.pdn.• Incurred regardless whether any output is Incurred regardless whether any output is

producedproduced Variable Costs: Costs that vary as the Variable Costs: Costs that vary as the

output level changes - These costs are output level changes - These costs are associated with variable factors of pdn.associated with variable factors of pdn.

Cost Relationships in PdnCost Relationships in Pdn

Costs Based on Total OutputCosts Based on Total Output 1) Total Fixed Costs (TFC)1) Total Fixed Costs (TFC) 2) Total Variable Costs (TVC)2) Total Variable Costs (TVC) 3) Total Costs (TC) 3) Total Costs (TC)

TFC (overhead costs) - costs of TFC (overhead costs) - costs of inputs (implicit & explicit) that are inputs (implicit & explicit) that are fixed in the SR & do not change as fixed in the SR & do not change as the output level changes.the output level changes.

Cost Relationships in PdnCost Relationships in Pdn

TVC - costs of inputs (implicit & TVC - costs of inputs (implicit & explicit) that are variable in the SR, and explicit) that are variable in the SR, and change as output level changes.change as output level changes.• Calculated by summing the cost of each Calculated by summing the cost of each

variable input usedvariable input used

TVC = (PTVC = (PX1X1XX11) + (P) + (PX2X2XX22) + . . . . + ) + . . . . + (P(PXnXnXXnn))

• For One Variable Input:For One Variable Input:

TVC = PTVC = PXXXX

Cost Relationships in PdnCost Relationships in Pdn

TC - sum of TFC & TVCTC - sum of TFC & TVC TC = TFC + TVCTC = TFC + TVC

Total Cost CurvesTotal Cost Curves(Assume TFC = $10 and P(Assume TFC = $10 and Pxx = 4 = 4

0 0 $10 $0 $10 1 2 $10 $4 $14 2 5 $10 $8 $18 3 9 $10 $12 $22 4 11 $10 $16 $26 5 12 $10 $20 $30 6 11 $10 $24 $34

0

X Y TFC TVC TCX Y TFC TVC TC

Cost Relationships in PdnCost Relationships in Pdn

Costs Based on Per-Unit OutputCosts Based on Per-Unit Output• 1) Average Fixed Costs (AFC)1) Average Fixed Costs (AFC)• 2) Average Variable Costs (AVC)2) Average Variable Costs (AVC)• 3) Average Total Costs (ATC)3) Average Total Costs (ATC)

AFC - Average cost of fixed inputs AFC - Average cost of fixed inputs per unit of outputper unit of output AFC = TFC / YAFC = TFC / Y

Cost Relationships in PdnCost Relationships in Pdn

AVC - Average cost of variable AVC - Average cost of variable inputs per unit of outputinputs per unit of output AVC = TVC / YAVC = TVC / Y

ATC - Average total cost per unit of ATC - Average total cost per unit of outputoutput ATC = TC / YATC = TC / Y

Cost Relationships in PdnCost Relationships in Pdn

MC - Increase in total cost MC - Increase in total cost necessary to produce one more necessary to produce one more unit of outputunit of output MC = ΔTC / ΔY = ΔTVC / ΔYMC = ΔTC / ΔY = ΔTVC / ΔY

Cost CurvesCost Curves(Assume TFC = $10 and P(Assume TFC = $10 and Pxx = 4 = 4

0 0 10 0 10 - - - 1 2 10 4 14 5 2 7 2 2 5 10 8 18 2 1.60 3.60 1.33 3 9 10 12 22 1.11 1.33 2.44 1 4 11 10 16 26 .91 1.45 2.36 2 5 12 10 20 30 .83 1.66 2.49 4 6 11 10 24 34 .91 2.18 3.09 -4

X Y TFC TVC TC AFC AVC ATC MCX Y TFC TVC TC AFC AVC ATC MC

Summary of Relationships Summary of Relationships Between AFC, AVC, ATC, & Between AFC, AVC, ATC, &

MC CurvesMC Curves

AFC is a continuously decreasing AFC is a continuously decreasing function w/ the shape of a rectangular function w/ the shape of a rectangular hyperbolahyperbola

AVC & ATC curves are U-shaped AVC & ATC curves are U-shaped (representing increasing & decreasing (representing increasing & decreasing returns)returns)

The vertical distance between ATC & The vertical distance between ATC & AVC at each output level is equal to AVC at each output level is equal to AFCAFC

Summary of Relationships Summary of Relationships Between AFC, AVC, ATC, & Between AFC, AVC, ATC, &

MC CurvesMC Curves

MC crosses both AVC & ATC from MC crosses both AVC & ATC from below at their respective below at their respective minimumsminimums

ATC is also referred to as Average ATC is also referred to as Average CostCost

Cost Curves & Pdn ProcessCost Curves & Pdn Process

The cost curves are derived The cost curves are derived directly from the pdn process.directly from the pdn process.• Therefore, the pdn function can Therefore, the pdn function can

be transferred directly to the be transferred directly to the cost curvescost curves

APP & AVC and MPP & MC are APP & AVC and MPP & MC are mirror images of each othermirror images of each other

Summary of RelationshipsSummary of Relationships

When MPP > APP (APP is When MPP > APP (APP is increasing) increasing)

MC < AVC (AVC is decreasing)MC < AVC (AVC is decreasing) When MPP = APP (APP is max) When MPP = APP (APP is max)

MC = AVC (AVC is min)MC = AVC (AVC is min) When MPP < APP (APP is When MPP < APP (APP is

decreasing) decreasing) MC > AVC (AVC is increasing)MC > AVC (AVC is increasing)

Mathematical Mathematical RelationshipsRelationships

MC = ΔTC / Δ Y = PMC = ΔTC / Δ Y = PX X / MPP/ MPP

AVC = TVC / Y = PAVC = TVC / Y = PXX / APP / APP

Changes in Input PriceChanges in Input Price

Input Price IncreaseInput Price Increase• The cost of producing each output level The cost of producing each output level

increases - TVC & TC shift upward & left; TFC increases - TVC & TC shift upward & left; TFC remains unchanged - AVC, AC, & MC shift remains unchanged - AVC, AC, & MC shift upward & leftupward & left

Input Price Decrease (or technological Input Price Decrease (or technological innovation increases productivity)innovation increases productivity)• The cost of producing same amount of output The cost of producing same amount of output

decreases - TVC & TC shift downward & right decreases - TVC & TC shift downward & right - AVC, ATC, & MC shift downward & right- AVC, ATC, & MC shift downward & right