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Jan. 06, 2013

FInancial Modelling and Equity 1 @ IIM- INDORE, PGCFR at mangalayatan university and Candidate of CFA Level 1 at CFA institute, IPCC @ICAI

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- 1. Production Analysis Production is transformation activity that connects factor inputsand outputs. For example, a farmer uses land, labor and seeds as inputsto transform them into corn. An input refers to any good or service thatassists in producing an output. A good or service may be input for onefirm, but may be output for another. For example, steel is an input for anautomobile manufacturer, but output for a steel producer. The process of transformation of inputs to outputs can betransformed in any of following three ways: 1} Change in form: E.g. transformation of raw materials into finishedgoods. 2} Change in place: E.g. transportation 3} Change in Time: E.g. storage
- 2. Production Function Production function deals with the maximum output that can be produced witha limited and given quantity of inputs. For example, the production function of a steel firm takes intoconsideration, various inputs like labor, raw material, power consumption, cost ofland, etc. It also takes into account the quantity of output that is being produced, using allthe above fixed and variable inputs. Thus, production function deals with input as well asoutput. A production function can be expressed as an equation, table, or a graph.If a firm uses inputs like labor (L) and capital (K), then the production function can beformed as Q = f (K, L) Production function has no focus towards the least cost combination or theprofit maximization. If the firm fails to utilize the available resources effectively, it may not be able tosurvive in the long run. Firms using the efficient production processes enjoy minimumcost but earn maximum profits.Example: The production function of a steel company can have inputs like cost ofprocuring the ore, power charges, labor charges, etc. Whereas the production function ofa tour operator can be cost of fuel, vehicle maintenance charges, wages and salaries ofemployees
- 3. Factors Factors that are used for production are called factors ofproduction. There are four important factors of production. They are – Land Labor Capital Entrepreneurship The prices of these factors are rent, wage, interest and profitrespectively. Factor of Production Price Land Rent Labor Wage Capital Interest Entrepreneurship Profits
- 4. Concepts of ProductThere are three types of product concepts that are crucial to theproduction function. Total product Marginal product and Average product.
- 5. Total Product, Average Product and MarginalProductTotal product The amount of output produced using a given quantity of inputs isknown as total output. As the input increases, the total output also increases. Forexample, for a firm producing leather shoes, as the number of labor and the rawmaterial is increased, output also increases. When the firm is using just a singlelabor the firm produces 2,000 units of shoes. On increasing the labor to three, thetotal output rises to 3,000. It can be observed that total product increases with the increase in theoutput, and rate of increase starts decreasing after reaching a point, which it canbe observed in the TP graph as well. It can be seen in the graph that the totalproduct rises by smaller and smaller increments as additional units of labor areadded. TP curve rises initially and starts declining after reaching a point.
- 6. Average product Average product can be defined as the total product per unit of factoremployed in the production process. In the given example, average product is 2000with one labor, every additional labor has resulted in the fall in the average product.Marginal productMarginal product can be defined as the extra product or output added by one extraunit of that input while other inputs are held constant. In the given example, it canbe seen that the first labor can produce 2000 units of shoes alone, i.e. the marginalproduct of the first labor is 2000. On adding one more unit of labor, total productincreases to 3,000, resulting in decline in the marginal product. With addition ofeach labor unit, marginal product keeps declining. When the 6th labor unit is added,marginal product becomes negative.Marginal product helps in determining the wages of the labor. Based on themarginal product, the firm can arrive at the cost and output relationship of eachadditional labor. The concept of marginal product also helps a firm to allocate thescarce resources of the firm. For example, in the given case a firm could haveavoided adding the 6th labor, as it is resulting in the fall of total product itself.
- 7. The Three Stages of ProductionBased on the law of diminishing returns, Prof. Cassels proposed threestages in the production process.Stage I: Stage I offers increasing average returns to the factor ofproduction, i.e. (Q/L)/ðL > 0 or MPL > APL. Thus, in stage I, averageproduct increases and the marginal product is greater than theaverage product. Stage II: In stage II, the average product decreases and so does themarginal product. But marginal product remains positive. This stagemay be called the stage of decreasing returns.Stage III: In stage III, total product decreases and the marginalproduct becomes negative.
- 8. The Three Stages of Production
- 9. Points to Remember When MP = AP, AP will be maximum When MP = 0, TP will be maximumStages of Marginal Returns Increasing marginal returns: From the starting point of MPuntil MP reaches its maximum point. Diminishing marginal returns: From the maximum point ofMP until MP = 0. Negative marginal returns: From the point where MP = 0
- 10. Short Run and Long Run Time period can be classified into short run and longrun based on the nature of factors of production.Short run refers to a period of production where all factors ofproduction are not variable. The period defers from industryto industry, country-to-country, and firm-to-firm, etc.Example: Matchbox industry : 1 day Soap industry : one year Shipbuilding industry : 10 yearsLong run refers to a period of production where all factors ofproduction are variable.
- 11. Products Costs in the Short Run(Law of Diminishing Returns) In the short run, the shape of the total product (TP) curve is determined by the law of diminishing returns. Law of Diminishing Returns (also known as Law of Variable Proportions) states that given the state of technology, if we go on employing more of one factor of production, other things remaining the same, its marginal productivity will diminish after some point.Assumption Law of diminishing returns is based on the following assumptions. State of technology is constant. One factor of production must always be fixed. Thus, this law is not applicable when all the factor inputs are variable. This law is not applicable when the two inputs are used in a fixed proportion. This amounts to say that the law is applicable only to varying ratios between the two inputs.
- 12. Product Costs in Long Run Law of diminishing returns is operational only in short run because of itsassumption of one fixed factor input. But in the long run all the factor inputs arevariable. Law of Returns to Scale: It refers to the long run analysis of production.According to the law, the long run output can be increased by changing all the factorsin the same proportion, or by different proportions. As all factor inputs are variable in the long run, the production function isgiven by Q = f (K, L)The returns to scale may be of three types –Constant returns to scaleDecreasing returns to scaleIncreasing returns to scale
- 13. Types of Returns to Scalea.Constant Returns to Scale: If the proportionate change in outputis same as the proportionate change in input, then we say that thereare constant returns to scale (CRS). Symbolically, CRS: % ΔQ = %ΔIb.Decreasing Returns to Scale: If the proportionate change inoutput is less than the proportionate change in input, then we say thatthere are decreasing returns to scale (DRS). DRS: %ΔQ < %ΔIc.Increasing Returns to Scale: If the proportionate change in outputis more than the proportionate change in input, then we say that thereare increasing returns to scale (IRS). IRS: %ΔQ > %ΔI
- 14. Returns to Scale Returns to scale show the responsiveness of total product when all theinputs are increased proportionately. Returns to scale is a factor that is studiedin the long run. Returns to scale can be constant, increasing or decreasing.Constant returns to scale:In this case, the change in inputs results in proportional change in output.For example, if a firm is using three factors of production, land, labor andcapital, and if it doubles all these inputs, output should also be doubled.
- 15. Increasing returns to scale:When rise in inputs result in more than proportional increase in the output,it is known as increasing returns to scale.For example, if a plant is producing 100 units of the product using 10 unitsof labor and 100 units of capital. If the labor is doubled to 20 units andcapital is also doubled to 200 units, and the output generated is 250 units,then the firm is operating at increasing returns to scale level.Decreasing returns to scale:When increase in all the inputs result in less than proportional increase inoutput, then it is known as decreasing returns to scale.For example, if a firm increases all its inputs by 20 percent and the resultingincrease in the output is just 15 percent, then it is the case of decreasingreturns to scale.
- 16. The Production Isoquant If a firm is having two variable inputs, the approach to determine theoptimal input rates is completely different. In this scenario, the problem of efficientresource allocation can be solved in two ways. Maximize the production, utilizing the available resources. These twoproblems are known as constrained optimization problems. The problem ofresource allocation can also be solved by producing the profit maximizing output.Isoquants also known as production-indifference curves, represent thecombinations of inputs that produce same quantity of output. This can be explainedwith the help of an example, Factor Labor Capital Combinations A 2 24 B 4 16 C 6 10 D 8 6 E 10 4
- 17. Characteristics of an Isoquant CurveThe properties of an isoquant are similar to that of anindifference curve.The following are the important properties of an isoquantcurve. 1) Isoquant curve will be downward sloping: The level ofoutput is same along the isoquant curve. Thus, if a firm usesmore of one input, it must use less of another input to attainthe same level of output. 2) An isoquant curve is convex to the origin: 3) Two isoquant curves cannot intersect each other. Likeindifference curves isoquant curves too do not intersect eachother. 4) Isoquant Map: A higher isoquant curve gives higherlevel of output
- 18. ConvexityThe slope of the isoquant curve measures the marginal rate of technicalsubstitution (MRTS) as it shows the rate at which one input can be substitutedwith another. The slope of isoquant curve diminishes or becomes flatter as wemove from point j to m. This implies that we can substitute lesser and lesseramount of K for L as we move down the curve. This is because of the operation oflaw of diminishing returns.
- 19. Isoquant MapIn the figure, each isoquant curve reflects a difference level of output. As wemove from the original, each successive isoquant curve reflects a higher levelof output. This is because at a higher isoquant curve we use more of both L andK, which means more output.
- 20. Expansion Path We know that a rational firm, to maximize its outputsubject to cost constraint, employs factor inputs in a proportionsuch that marginal rate of technical substitution (MRTS) is equalto factor price ratio. Given the factor prices, we can get a number of parallelisocost lines by varying the cost constraint. Each isocost line istangent to one isoquant curve. The locus of all such points oftangencies between the isoquants and isocost lines forms theexpansion path of the firm. The points on the expansion path arethe most efficient combinations of the two inputs. As all factors of production are variable in the long run,the firm moves along the expansion path to expand its level ofoutput, given the factor prices.

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