# Lecture 20 NPTEL - 20 Theory of Production and Cost 1 Recap...

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120 : Theory of Production and Cost
Prof. Trupti Mishra, School of Management, IIT BombayRecap from last Session Contribution AnalysisLearning Curve
Session OutlineProf. Trupti Mishra, School of Management, IIT BombayApplication of Cost AnalysisCost Function: Empirical DeterminationEconomies of Scale
Application of Cost Analysis: Optimum output levelOptimum output has reference to that level of (size) of output which minimizes the average cost of Production, or for which the average cost is equal to marginal cost.Example:Prof. Trupti Mishra, School of Management, IIT Bombay
Application of Cost Analysis: Optimum Inventory levelAll productions are not immediately sold – InventoryOptimum inventory level is defined as that size of stock for which the average cost of inventory held is at minimum.Prof. Trupti Mishra, School of Management, IIT Bombay
Application of Cost Analysis: Optimum Inventory levelTwo types cost are involved: Carrying Cost: includes storage cost, interest cost on borrowed capital to finance stock etc.Prof. Trupti Mishra, School of Management, IIT Bombay
Application of Cost Analysis: Optimum Inventory levelTwo types cost are involved: Reorder cost: includes book keeping costs, telephone charges and some variable costProf. Trupti Mishra, School of Management, IIT Bombay
Application of Cost Analysis: Optimum Inventory levelAverage cost of inventory AC =( K.d/2)+ (F,V,D)S/DCarrying Cost + Reorder CostS = Expected Sale, D –Order Quantity to be Delivered/D = Number of Orders delivered, F = Average Fixed cost of delivery, V = Coefficient of AVC of reorder, K = Average Carrying Cost, D/2 = average inventory held between initial and terminal periods and it is assumed that the demand is spread evenly Prof. Trupti Mishra, School of Management, IIT Bombay
Application of Cost Analysis: Optimum Inventory levelFor deciding an optimum inventory held,= d(AC)/dD = (K/2 – FS/D2) = 0= D = √ 2FS/K → Optimum size of stock/ Economic Order QuantityProf. Trupti Mishra, School of Management, IIT Bombay
Application of Cost Analysis: Optimum ScaleThe optimum scale is given by that value of K(Plant Size) at which the total cost is the least.Necessary Condition = dC/dK = 0Sufficient Condition = d2C/dK2> 0ExampleProf. Trupti Mishra, School of Management, IIT Bombay
Economies of ScaleThe advantages of large scale production that result in lower unit (average) costs (cost per unit)AC = TC / QEconomies of scale – spreads total costs over a greater range of outputProf. Trupti Mishra, School of Management, IIT Bombay
Types Pecuniary Economies: Economies realized from paying lower prices for the factor used in production and distribution of the product, due to bulk buying by the firm as its size increases.