Cost Analysis and Estimation Chapter 8

Chapter 8 OVERVIEW Economic and Accounting Costs Role of Time in Cost Analysis Short-run Cost Curves Long-run Cost Curves Minimum Efficient Scale Firm Size and Plant Size Learning Curves Economies of Scope Cost-volume-profit Analysis

Economic and Accounting Costs Historical Versus Current Costs Historical cost is the actual cash outlay. Current cost is the present cost of previously acquired items. Opportunity Costs Foregone value associated with current rather than next-best use of an asset. Replacement cost is expense of replacing productive capacity using current technology. Explicit and Implicit Costs Explicit costs are cash expenses. Implicit costs are noncash expenses.

Economic and Accounting Costs Explicit costs - require an outlay of money, payment to non owners for resources: paying wages paying rent paying interest Implicit costs - do not require a cash outlay, opportunity cost: the owner’s time lost wages the owner’s property forgone rental income the owner’s money forgone interest income

Economic and Accounting Costs Shoe Co. Revenue $300,000 Worker Wages $100,000 Explicit Rent Expense $50,000 Explicit Leather Cost $100,000 Explicit Explicit Cost $250,000 Accounting Profit $50,000 Superintendent $100,000 Principal $50,000 Teacher $30,000 Implicit - $50,000 Economic Loss $0 Economic Profit Economic Profit $20,000 Accounting profit - total revenue minus total explicit costs Economic profit - total revenue minus total costs (includes explicit and implicit costs) Accounting profit ignores implicit costs and it’s always higher than economic profit. Copyright 2009 eStudy.us michael.roberson@eStudy.us

Economic and Accounting Costs Short Run - a time period when at least one input is fixed Cost for a fixed input is termed Fixed Cost Factory Special equipment Land Long Run - A time period when all inputs are variable firms can build more factories, or sell existing ones In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (the factory size with the lowest ATC)

Role of Time in Cost Analysis Incremental Cost Incremental cost is the change in cost tied to a managerial decision. Incremental cost can involve multiple units of output. Marginal cost involves a single unit of output. Sunk Cost Irreversible expenses incurred previously. Sunk costs are irrelevant to present decisions.

Short-run Cost Curves Short-run Cost Categories Total Cost = Fixed Cost + Variable Cost For averages, ATC = AFC + AVC Marginal Cost, MC = ∂TC/∂Q Short-run Cost Relations Short-run cost curves show minimum cost in a given production environment.

Short-run Cost Curves - Fixed Cost (TFC) 𝑀𝐶= ∆𝑇𝐶 ∆𝑄 costs that don’t vary as output changes AV𝐶= 𝑇𝑉𝐶 𝑄 AT𝐶= 𝑇𝐶 𝑄 AF𝐶= 𝑇𝐹𝐶 𝑄 - Variable Cost (TVC) costs that do vary as output changes - Total Cost (TC) TC = TFC + TVC - Marginal Cost (MC) the cost of producing one more output (Q) Q 1 2 3 4 5 6 7 8 9 TFC TVC TC MC AFC -- $10.00 $5.00 $3.33 $2.50 $2.00 $1.67 $1.43 $1.25 $1.11 AVC -- $4.00 $3.50 $3.67 $4.50 $5.60 $7.83 $10.57 $14.00 $18.00 ATC -- $14.00 $8.50 $7.00 $7.60 $9.50 $12.00 $15.25 $19.11 $10 $0 $10 $14 $17 $21 $28 $38 $57 $84 $122 $172 $10 $4 $7 $11 $18 $28 $47 $74 $112 $162 $4 $3 $4 $7 $10 $19 $27 $38 $50 Copyright 2010 eStudy.us michael.roberson@eStudy.us

Short-run Cost Curves Calculation Equations at Q = 6 𝑀𝐶= ∆𝑇𝐶 ∆𝑄 = 𝑇𝐶 1 − 𝑇𝐶 0 𝑄 1 − 𝑄 0 $57−$38 6−5 = $19 1 =$19 𝐴𝐹𝐶= 𝑇𝐹𝐶 𝑄 $10 6 =$1.67 𝐴𝑉𝐶= 𝑇𝑉𝐶 𝑄 $47 6 =$7.83 𝐴𝑇𝐶= 𝑇𝐶 𝑄 $57 6 =$9.50 𝐴𝑇𝐶=𝐴𝐹𝐶+𝐴𝑉𝐶 $9.50=$1.67+7.83 Copyright 2010 eStudy.us michael.roberson@eStudy.us

Short-run Cost Curves $ MC $19.00 ATC AVC $9.50 $1.67 AFC $7.83 Q 1 2 4 5 6 7 8 9 The MC curve intersects the ATC curve at minimum average total cost. when MC < ATC, ATC falls as Q rises when MC > ATC, ATC rises as Q rises Copyright 2010 eStudy.us michael.roberson@eStudy.us

Short-run Cost Curves 𝑀𝐶= ∆𝑇𝐶 ∆𝑄 = 𝑤𝑎𝑔𝑒 𝑀𝑃 𝑙 = $75 25 =$3 MC 10 25 50 65 75 80 $ Q Minimum Marginal Cost corresponds to maximum Marginal Product Suppose an accountant earns $75 / hour and her marginal productivity is: $7.50 $3.00 MP wage MC Third hour 25 Fourth hour 15 Fifth hour 10 Sixth hour 5 $75 $3 $5 $7.5 $15 MP 1 2 3 4 5 6 Labor Q / Labor 25 10 𝑀𝐶= ∆𝑇𝐶 ∆𝑄 = 𝑤𝑎𝑔𝑒 𝑀𝑃 𝑙 = $75 25 =$3 Copyright 2010 eStudy.us michael.roberson@eStudy.us

Long-run Cost Curves Long-run total cost curves show minimum total cost in an ideal environment. Economies of Scale Increasing returns to scale imply falling average costs. Constant returns to scale implies constant average costs. Decreasing returns to scale implies rising average costs.

Long-run Cost Curves $ Output Short Run Average Cost Long Run Average Cost Diseconomies to Scale Economies to Scale Constant Returns to Scale Output

Cost Elasticities Econ. of Scale Cost elasticity measures the percentage change in cost following a one percent change in output. 𝐸 𝑐 = %∆𝑇𝐶 %∆𝑄 = 𝜕𝑇𝐶 𝜕𝑄 ∙ 𝑄 𝑇𝐶 Cost elasticity measures returns to scale. EC < 1 means increasing returns (falling AC). EC = 1 means constant returns (constant AC). EC > 1 means decreasing returns (rising AC).

Long-run Cost Curves $ Output Long Run Average Cost Min LRAC Least Cost Plant Output

Firm Size and Plant Size Multi-plant Economies and Diseconomies of Scale Multi-plant economies are cost advantages from operating several plants. Multi-plant diseconomies are coordination costs from operating several plants. Plant Size and Flexibility Big plants can offer lower AC. Smaller plants can make it easier to add and /or subtract capacity.

Firm Size and Plant Size Constant costs Declining costs U-shaped costs $ $ $ 𝑄 ∗ 𝑄 𝐹 𝑄 ∗ 𝑄 𝐹 𝑄 ∗ 𝑄 𝐹

Firm Size and Plant Size 𝑃=$940−$0.02𝑄 𝑇𝑅= $940−$0.02𝑄 𝑄=$940𝑄−$0.02 𝑄 2 𝑀𝑅= 𝑑𝑇𝑅 𝑑𝑄 =$940−$0.04𝑄 𝑇𝐶=$250,000+$40𝑄+$0.01 𝑄 2 𝑀𝐶= 𝑑𝑇𝐶 𝑑𝑄 =$40+$0.02𝑄

Firm Size and Plant Size 𝑀𝑅=𝑀𝐶 $940−$0.04𝑄=$40+$0.02𝑄 $0.06𝑄=$900 𝑄=15,000 𝑃=$940−$0.02𝑄=$940−$0.02 15,000 =$640 𝜋=$940𝑄−$0.02 𝑄 2 −($250,000+$40𝑄+$0.01 𝑄 2 ) 𝜋=−$0.03 𝑄 2 +$900𝑄−$250,000 𝜋=−$0.03 15,000 2 +$900(15,000)−$250,000 𝜋=$6,500,000

Firm Size and Plant Size 𝐴𝐶= 𝑇𝐶 𝑄 = $250,000+$40𝑄+$0.01 𝑄 2 𝑄 𝐴𝐶=$250,000 𝑄 −1 +$40+$0.01𝑄 𝑀𝐶=𝐴𝐶 $40+$0.02𝑄=$250,000 𝑄 −1 +$40+$0.01𝑄 $250,000 𝑄 −1 =$0.01𝑄 𝑄 2 = $250,000 0.01 𝑄= $25,000,000 =5,000

Firm Size and Plant Size Average cost is minimized at an output level of 5,000. This output level is the minimum efficient plant scale (MES). Because the average cost-minimizing output level of 5,000 is far less than the single plant profit maximizing activity level of 15,000 units, the profit maximizing level of total output occurs at a point of rising average costs. Thus a multi-plant alternative will reduce cost and increase profits. 𝑀𝐶=$40+$0.02𝑄=$40+$0.02 15,000 =$640 𝑀𝐶=$40+$0.02𝑄=$40+$0.02 5,000 =$140 𝑀𝑅=$140=𝑀𝐶 $940−$0.04𝑄=$140 $0.04𝑄=$800 𝑄=20,000

Firm Size and Plant Size 𝑂𝑝𝑖𝑚𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑙𝑎𝑛𝑡𝑠= 𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑎𝑛𝑡 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝐿𝑒𝑣𝑒𝑙 𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑃𝑒𝑟 𝑃𝑙𝑎𝑛𝑡 𝑂𝑝𝑖𝑚𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑙𝑎𝑛𝑡𝑠= 20,000 5,000 =4 𝑃=$940−$0.02𝑄=$940−$0.02 20,000 =$540 𝜋=𝑇𝑅−𝑇𝐶 𝜋=𝑃∙𝑄−4∙𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑃𝑙𝑎𝑛𝑡 𝜋=$540 20,000 −4($250,000+$40 5,000 +$0.01 5000 2 ) 𝜋=$8,000,000

Economies of Scope Economies of Scope Concept Scope economies are cost advantages that stem from producing multiple outputs. Big scope economies explain the popularity of multi-product firms. Without scope economies, firms specialize. Exploiting Scope Economies Scope economics often shape competitive strategy for new products.