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Cost Theory EA Session 7 July 13, 2007 Prof. Samar K. Datta

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Overview Short run costs Long run costs & economies of scale Economies of scope & product transformation curve

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SHORT RUN COSTS Marginal Cost (MC) is the cost of expanding output by one unit => MC = dTC/dQ Average Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC) => ATC = TC/Q = TFC/Q + TVC/Q = AFC + AVC The relationship between the production function and cost can be exemplified by: – Increasing returns With increasing returns, output is increasing relative to input and variable cost and total cost will fall relative to output. – Decreasing returns With decreasing returns, output is decreasing relative to input and variable cost and total cost will rise relative to output.

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Cost Curves for a Firm The line drawn from the origin to the tangent of the variable cost curve: – Its slope equals AVC – The slope of a point on VC equals MC – Therefore, MC = AVC at 7 units of output (point A) Output P FC VC A TC

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Cost Curves for a Firm Unit Costs – AFC falls continuously – When MC < AVC or MC < ATC, AVC & ATC decrease – When MC > AVC or MC > ATC, AVC & ATC increase – When MC = AVC = ATC then AVC and ATC are at minimum Output (units/yr.) Cost ($ per unit) MC ATC AVC AFC

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PRODUCING A GIVEN OUTPUT AT MINIMUM COST Labor per year Capital per year Isocost C 2 shows quantity Q 1 can be produced with combination K 2 L 2 or K 3 L 3. However, both of these are higher cost combinations than K 1 L 1. Q1Q1 Q 1 is an isoquant for output Q 1. Isocost curve C 0 shows all combinations of K and L that cost C 0. C0C0 C1C1 C2C2 C O C 1 C 2 are three isocost lines A K1K1 L1L1 K3K3 L3L3 K2K2 L2L2

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Long-Run Expansion Path The long-run expansion path is drawn as before.. THE INFLEXIBILITY OF SHORT- RUN PRODUCTION Labor per year Capital per year L2L2 Q2Q2 K2K2 D C F E Q1Q1 A B L1L1 K1K1 L3L3 P Short-Run Expansion Path

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– Constant Returns to Scale If input is doubled, output will double and average cost is constant at all levels of output. – Increasing Returns to Scale If input is doubled, output will more than double and average cost decreases at all levels of output. – Decreasing Returns to Scale If input is doubled, the increase in output is less than twice as large and average cost increases with output. RETURNS TO SCALE

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LONG-RUN AVERAGE AND MARGINAL COST Output Cost ($ per unit of output LAC LMC A

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Measuring Economies of Scale Therefore, the following is true: – E C < 1: MC < AC economies of scale – E C = 1: MC = AC constant economies of scale – E C > 1: MC > AC diseconomies of scale ECONOMIES AND DISECONOMIES OF SCALE

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LONG-RUN COST WITH CONSTANT RETURNS TO SCALE Output Cost ($ per unit of output) Q3Q3 SAC 3 SMC 3 Q2Q2 SAC 2 SMC 2 Q1Q1 SAC 1 SMC 1 LAC = LMC With many plant sizes with minimum SAC = $10 the LAC = LMC and is a straight line $10

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LONG-RUN COST WITH ECONOMIES AND DISECONOMIES OF SCALE Output Cost ($ per unit of output SMC 1 SAC 1 SAC 2 SMC 2 LMC If the output is Q 1 a manager would chose the small plant SAC 1 and SAC $8. Point B is on the LAC because it is a least cost plant for a given output. $10 Q1Q1 $8 B A LAC SAC 3 SMC 3 The long-run average cost curve is the envelope of the firms short-run average cost curves, assuming continually variable plant size. The long-run cost curve is the dark blue portion of the SAC curve which represents the minimum cost for any level of output, assuming only three discrete plant sizes.

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Economies of scope exist when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single output. – Firms must choose how much of each to produce. – The alternative combinations can be illustrated using product transformation curves. ECONOMIES OF SCOPE

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PRODUCT TRANSFORMATION CURVE Number of cars Number of tractors O2O2 O 1 illustrates a low level of output. O 2 illustrates a higher level of output with two times as much labor and capital. O1O1 Each curve shows combinations of output with a given combination of L & K.

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The degree of economies of scope measures the savings in cost and can be written: – C(Q 1 ) is the cost of producing Q 1 – C(Q 2 ) is the cost of producing Q 2 – C(Q 1 Q 2 ) is the joint cost of producing both products – If SC > 0 -- Economies of scope – If SC < 0 -- Diseconomies of scope ECONOMIES OF SCOPE

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DYNAMIC CHANGES IN COSTS – THE LEARNING CURVE (optional) The learning curve measures the impact of workers experience on the costs of production. It describes the relationship between a firms cumulative output and amount of inputs needed to produce a unit of output.

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The learning curve in the figure is based on the relationship: DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)

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– L equals A + B and this measures labor input to produce the first unit of output – Labor input remains constant as the cumulative level of output increases, so there is no learning DYNAMIC CHANGES IN COSTS –THE LEARNING CURVE (optional)

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– L approaches A, and A represent minimum labor input/unit of output after all learning has taken place. – The more important the learning effect. DYNAMIC CHANGES IN COSTS – THE LEARNING CURVE (optional)

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Cumulative number of machine lots produced Hours of labor per machine lot The chart shows a sharp drop in lots to a cumulative amount of 20, then small savings at higher levels. Doubling cumulative output causes a 20% reduction in the difference between the input required and minimum attainable input requirement.

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ECONOMIES OF SCALE VERSUS LEARNING (optional) Output Cost ($ per unit of output) LAC 1 B Economies of Scale A LAC 2 Learning C

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