Cost Analysis and Estimation

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1 Please Read: Cost Analysis and Estimation Chapter 9 Economies of of Scale and Software Production Economies of of Scale and Scope in in Telecommunications Economies of of Scale in in Automobile Accessories 7 8 Chapter 9 OVERVIEW What Makes Cost Analysis Difficult Opportunity Cost Incremental and Sunk Costs in Decision Analysis Short-run and Long-run Costs Short-run Cost Curves Long-run Cost Curves Minimum Efficient Scale Learning Curves Economies of Scope Cost-volume-profit Analysis historical cost current cost replacement cost opportunity cost explicit cost implicit cost incremental cost profit contribution sunk cost cost function short-run cost functions long-run cost functions short run long run planning curves Chapter 9 KEY CONCEPTS operating curves fixed cost variable cost short-run cost curve long-run cost curve economies of scale cost elasticity capacity minimum efficient scale multiplant economies of scale multiplant diseconomies of scale learning curve economies of scope cost-volume-profit analysis breakeven quantity 9 10 What Makes Cost Analysis Difficult? Link Between Accounting and Economic Valuations Accounting and economic costs often differ. Historical Versus Current Costs Historical cost is the actual cash outlay. Current cost is the present cost of previously acquired items. Replacement Cost Cost of replacing productive capacity using current technology. Opportunity Cost Opportunity Cost Concept Opportunity cost is foregone value. Reflects second-best use. Explicit and Implicit Costs Explicit costs are cash expenses. Implicit costs are noncash expenses

2 Incremental and Sunk Costs in Decision 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 and Long-run Costs How Is the Operating Period Defined? At least one input is fixed in the short run. All inputs are variable in the long run. Fixed and Variable Costs Fixed cost is a short-run concept. All costs are variable in the long run What Are Cost Functions? All cost functions are a combination of two pieces of information: 1) the production function. 2) the input prices. Changes in either of these pieces of information will change the cost function. That is, cost functions get their shapes from the shape of the production function and the input prices. Production and Cost Related I Constant returns to the variable input in the production function results in a linear variable cost function Production and Cost Related II Decreasing returns to the variable input in the production function results in a curvilinear variable cost function which increases at an increasing rate Production and Cost Related III Increasing returns to the variable input in the production function results in a curvilinear variable cost function which increases at an decreasing rate

3 Cost Curves Cost = sum of (P( inputs * Q inputs ) Short-Run Cost Curves Q inputs includes fixed and variable inputs Fixed Costs - sum of all Pi*Qi for fixed inputs Variable Costs - sum of all Pi*Qi for variable inputs These cost cost functions are are exactly those those in in the the Stack Diagram. Figure Total Cost Total cost (TC) = TFC + TVC (vertical addition of TFC and TVC curves) Total Cost Function for a Production System Exhibiting Increasing, Then Decreasing, Returns to to Scale Total Total Cost Cost Function Function Total Total Product Product Function Function Figure Total Cost Curve Derived Total Cost Curve Derived Production Function Cost Cost Function Production Function Each Each unit unit of of labor labor costs costs $160 $

4 MPX APX Total Cost Curve Derived Quantity of Output Stage I Stage II Stage III Cost Cost Function Production Function Variable cost curve is is derived from the production function and an assumption about the price of of the input (labor s price is is $160 per unit in in this example). The Stack Diagram Shows the Relationship Between Production and Cost! (short-run) run) $ (C) $ (D) TC = a + bq - c Q 2 + dq 3 Q3 Q2 Q1 Q2 Q3 DAR DMR TVC = bq - c Q 2 + dq 3 TFC = a Quantity of Output Q1 MC = b - 2cQ + 3d Q 2 ATC = a + b - cq + d Q 2 Q AVC = b - cq + d Q 2 AFC = a Q X 3 X 2 X 3 X 2 X 1 Q = bx + c X 2 - dx 3 Units of Variable Input (X) AP X = b + cx - d X 2 Units of Variable Input (X) X 1 MP X = b + 2cX - 3d X 2 (A) (B) Q3 Q2 Q1 Quantity of Output Marginal and Average Cost Curves Long-run Cost Curves Economies of Scale Long-run cost curves show minimum cost in an ideal environment The Effect of Scale (This is the Long Run!) if you expect 10 customers, you will build a smaller facility than if you expect 100 customers Effect of Scale In short-run run,, firm takes size as a given, and tries to solve the problem of the "optimal combination of inputs." In long-run run,, when nothing is fixed, optimal size might be larger or smaller

5 The shape of the LRAC Why Does It Decline At First? Greater Specialization Ability to Use More Advanced Technologies Opportunity to Take Advantage of Lower Costs Lower Administrative Costs Per Unit Advances in Management Technology Why Does It Eventually Increase? People Problems Key Steps In Estimating Cost Functions Definition of Cost relevant cost data Correction for Price Level Changes perhaps using separate price indices Relating Cost to Output distinguish costs that vary (and those that don t vary) Matching Time Periods Controlling Product, Technology, and Plant fixed definition of product, technology, and scale Length of Period and Sample Size large number of observations desired but... Real Long Run Average Cost Data Evidence of Economies and Diseconomies of Scale Increasing Returns to Scale Soft Drink Industry Grain Production Decreasing Returns to Scale Electric Power Generation Cost Elasticity and Economies of Scale Cost elasticity is ε C = C/C Q/Q. ε C < 1 means falling AC, increasing returns. ε C = 1 means constant AC constant returns. ε C > 1 means rising AC, decreasing returns

6 Minimum Efficient Scale Competitive Implications of Minimum Efficient Scale MES is the minimum point on the LRAC curve. Competition is most vigorous when: MES is small in absolute terms. MES is a small share of industry output. Disadvantage to less than MES scale is modest. Transportation Costs and MES Terminal, line-haul and inventory costs can be important. High transport costs reduce MES impact Multi-plant Economies and Diseconomies of Scale Multi-plant economies are cost advantages from operating several plants. Multi-plant diseconomies are cost disadvantages from operating several plants. Figure Economics of Multi-plant Operation: an Example Plant Size and Flexibility Figure

7 There may be economies to multiplant operation Consider first a single plant firm: P = $940 $0.02Q MR = TC = $250,000 + $40Q + $0.01Q MC = TR Q TC Q = $940 $0.04Q = $40 + $0.02Q Demand Function Cost Cost Function 2 To Profit Maximize in the single plant firm: MR = MC $940 $0.04Q = $40Q + $0.02Q $0.06Q = $900 Q = 15,000 Optimal Optimal single single plant plant size size 44 See See Pg Pg At At this Profit Maximizing Point (15,000 units): P = $940 $0.02Q P = $940 $0.02(15,000) P = $640 and π = $6,500,000 Profits with a single plant To gain insight into whether multiple plants might be reasonable AC for a single plant must be examined Assume same cost conditions apply Assume no other multiplant economies or diseconomies Now examine the the same firm when considering multiple plants by by finding the minimum of of average cost: TC AC = Q TC = $250,000 + $40Q + $0.01Q $250,000 + $40Q + $0.01Q AC = Q AC = $250,000Q 1 + $40 + $0.01Q 2 2 See See Pg Pg This firm (considering multiplant operations) finds minimum of of AC: MC = AC $40 + $0.02Q = $250,000Q 250,000Q ,000 Q = 0.01 Q = 5,000 = 0.01Q MES Plant 1 + $40 + $0.01Q 7

8 But, this does not imply that the the firm should use three 5000 unit plants and produce 15,000 units to to maximize profits! Profits were maximized at at Q=15,000 under the assumption that both marginal cost and marginal revenue were equal to to $640. However, if if the the firm uses 5,000 size plants the the marginal costs will be be lowered and the the new profit maximizing level of of production will be be greater than 15,000! The Real Answer MC = $40 + $0.02Q MC = $40 + $0.02(5,000) MC = $140 MR = MC $940 $0.04Q = $140 Q = 20,000 Use 4 plants of of 5,000 unit capacity and profits will equal $8,000, See See page page Learning Curves Learning Curve Concept Learning causes an inward shift in the LRAC curve. Learning curve advantages are often mistaken for economies of scale effects. Learning Curve Example Strategic Implications of the Learning Curve Concept When learning results in 20% to 30% cost savings, it becomes a key part of competitive strategy. Figure 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. Cost-volume-profit Analysis Cost-volume-profit Charts Cost-volume-profit analysis shows effects of varying scale. Breakeven analysis shows zero profit points of cost coverage

9 Firm Goal: Maximize Profit Profit(π)= Total Revenue minus Total Cost π =TR-TC Approach to Profit Maximization Set marginal cost equal to marginal revenue MC = MR MC = ΔTC ΔTP MR = ΔTR ΔTP Why? Linear Cost-Volume-Profit Chart Breakeven and Operating Leverage (Firm A) Figure 9.12 Figure 9.13a Breakeven and Operating Leverage (Firm B) Breakeven and Operating Leverage (Firm C) Figure 9.13b Figure 9.13c 61 Once breakeven is is achieved, profits rise faster in in cas C than in in case A or or B. 62 9

10 Generalized Break-even even (Assumptions?) Profit Maximization Using Break- even Analysis (Three Steps) The derivative of TC (which is the slope of total cost) is called marginal cost. The derivative of TR (which is the slope of total revenue) is called marginal revenue. When the slopes of total revenue and total cost are equal, profit is maximized: i.e., MR = MC Where Would This Competitive Firm Choose to Operate? Two Important Points Produce where MC = MR We will see that: MC curve is the supply curve (above average variable cost) Profit in the Graph π = TR - TC < -divide by Q Avg. π =AR ATC; but AR = Price Avg. π =P ATC π and the Shutdown Point π and the shutdown points Shutdown Point: The shutdown point is the intersection of marginal cost and average variable cost

11 Shutdown Point Short run (Lower)(or... MC = AVC) when MC below AVC Why? With a shutdown losses are equal TFC If operation is, losses are greater (not even variable costs can be covered) You must at least cover your variable costs (and perhaps contribute to fixed costs) The Supply Curve is the Marginal Cost Curve For a Competitive Firm Nursing Cost Estimate See data on page

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