Economics - Law of variable proportions - Notes - Economics, Study notes of Economics

Download Economics - Law of variable proportions - Notes - Economics and more Study notes Economics in PDF only on Docsity! 1.4. 2 Law of variable proportions The production function shows the maximum quantity of the output that can be produced per unit of time for each set of alternative inputs, given the best available production technology available. In the short-run, at least one factor of production remains fixed. For instance, in the case of an agricultural production function, various alternative commodities of labour or capital per unit of time may be used in relation a fixed amount of land. The total product curve increases at an increasing rate first until the point of inflection, after which it starts increasing at a decreasing rate, reaches its maximum and then starts declining. The average product of labour (APL/APK) is then obtained from total product (TP) divided by the number of units of labour/capital used. The marginal product of labour (MPL/ MPK) represents the change in TP per unit change in the quantity of labour/capital used. The shapes of curve determine the shape of the APL and MPL curves. The APL, at any point on the TPL curve is given by the slope of the straight line from the origin to that point on the TP curve. The AP curve usually first rises, reaches a maximum, and then falls, but remains positive as long as the TP is positive. The MPL is equal to the slope of the TP curve, reflecting the change in output due to a unit change in input between the two points. The MP curve also rises first, reaches a maximum (before the AP curve reaches its maximum), and then declines. The MP becomes zero when the TP is maximum. This is the law of diminishing returns. If labour is factor input considered, the relationship between the APL and MPL curves can be used to define the three stages of production. Stage I starts from the origin to the point where the APL is maximum. Stage II starts from the point where the APL is maximum to the point where the MPL is zero. Stage III covers the area over which the MPL is negative. A rational producer will not operate in stage III, even with free labour, because it is possible to increase total output by using less labour on the given land. Likewise, a rational producer will not operate in stage I because it corresponds to the area where full TP is still increasing with an additional unit of labour employed. Therefore, a rational producer would only operate in stage II. In stage I; MP2 > 0, when TP is maximum MPL = 0, and when TP falls MPL<0. This is shown by diagram-5. ∂X/∂ L=0 ∂X/∂ L< 0 ∂X/∂L=0 TP I LABOUR II LABOUR III LABOUR ∂X/∂L APL MPL Land Diagram 4 : Law of Variable Proportions 1.4.3 Returns to scale Law of returns to scale represents the long-term perspective of production analysis, when all factors of production are variable. There are three types of returns to scale. (a) Constant returns to scale: This indicates that if all factors of production are increased in a given proportion then the output produced would also increase in exactly the same proportion. That is, if the quantities of labour or capital or both are increased by 10%, output would also increase by 10%. This is illustrated by diagram-6. P ro du ct K F C IQ 300 B IQ 200 A IQ 100 0 L Diagram 8: Decreasing Returns to Scale The diagram shows that the distance between the successive isoquants along the product line goes on increasing, due to increased input requirements resulting from diseconomies of scale. That is, OA < AB < BC. 1.5 Cost Concepts A cost function expresses the relationship between the cost of production and levels of output. The various cost concepts are:- (1) Social and private costs: Social cost of producing a commodity refers to the opportunities of producing other commodities foregone, given the scarce resources. In simple terms, it is the cost of alternative good sacrificed by a community in producing a certain amount of one good. Private costs, on the other hand, include the costs incurred by an individual firm to obtain the resources used for the production of commodity. The reduction in private cost of a product would result in the reduction in of social cost, due to the emergence of a divergence between the social and private motives. (2) Explicit and implicit costs: Production of a commodity generally requires different kinds of labour and capital in many forms. Modern economists call the direct production expenses as the explicit costs of production. It includes the expenses incurred by a producer on buying the productive services owned by others. Whereas, implicit costs include the evaluation of a producer’s efforts and sacrifices incurred in production process. In other words, it refers to the reward a producer would like to pay self for self-owned and self-employed resources. They include a normal return on own investment, and the opportunity cost (alternative earnings) of own labour. (3) Economic versus accounting costs: Accounting cost includes the expenses incurred on production process, in addition to the wear and tear of machines and equipments, which can be translated into monetary terms. The accountant records all the explicit costs in the account book, so as to compare them with the sale proceeds in order to compute profits. Whereas, economic cost includes all the implicit and explicit costs of production. It involves the estimation of opportunity cost, which is the price a factor of production can receive in any alternative use, including the implicit costs of the factors owned by the entrepreneur. (4) Sunk costs: They are the costs which cannot be recovered, and therefore, are not included in the decision making process. They include the costs of highly specialized resources or inputs, which once installed, cannot be put to any alternative use. For e.g., a big plant or machine installed by a firm which has become obsolete or inoperative due to non-availability of some parts, then the money spent on it is known as a sunk cost. It is sunk because neither can the firm uses it, nor sell it, or put it to any alternative use. Hence, sunk costs have no relevance in decision making. (5) Fixed and variable costs: In production process, some factors are constant in the short run, while others are variable. Fixed costs are costs which do not vary with a change in output. The examples are interest on capital, rent on building, salaries to the staff, etc., which must be incurred, regardless of the level of output. On the other hand, variable costs change with the variations in the level of output. They include the payments made to the variable factors, such as wages paid to workers, raw materials, electricity, transportation cost, etc., Total cost is the sum total of fixed and variable costs. Total Cost = Fixed Costs + Variable Costs or TC = FC + VC TC FC VC ATC or Average Total Cost = = + Q Q Q where, Q = quantity of output produced. Thus, average cost of production is the sum total of average fixed cost and average variable cost. In ordinary accounting statements generally only explicit or money costs incurred in production process are considered. However, for a realistic computation of costs, two additional variables must be included, viz., normal profit and implicit costs or opportunity costs (already seen). Normal profit refers to the returns which the owners expect to receive from the business done by the firm, in the absence of which they would prefer to quit.When total revenue (TR) is equal to total cost (TC), the firm earns only the expected minimum return on the capital invested, i.e. normal profit. Hence, normal profit is a part of the cost of production. When TR exceeds TC, the firm gets super normal profit, which is more than what a firm needs to remain in business. But when TR = TC, the firm earns only normal profit. Equation (2) indicates that TVC will increase as the level of input use increases from X0 to X1, which in turn results in an increase in output from Q to Q1, thus affecting TVC (Barla , 2000). Average and marginal cost: Unit cost and the incremental cost of production can also be computed. It has been seen that total cost of production is the sum total of total fixed cost and total variable cost, i.e., TC = TFC + TVC ----- (3) Dividing both sides of equation (3) by the quantity of output (Q) would give average cost or unit cost of production. Therefore, average cost is the sum total of average fixed cost and average variable cost. i.e., TC TFC TFC = + Q Q Q or AC = AFC + AVC ------ (4) As output increases, average fixed cost registers a decline. Average variable cost, average total cost and marginal cost, decline initially and then show an upward trend. Total fixed cost divided by the quantity of output (Q) is average fixed cost (AFC). Section A of diagram - 10 shows that, the average fixed cost has an inverse relationship with the quantity of output, such that as the output increases, AFC decreases. This makes AFC a rectangular hyperbola, because total fixed cost is divided by different levels of output. Thus, Q.AFC = C, a constant. That is, the area under AFC is always equal to TFC = C, The AFC curve is a rectangular hyperbola (Q.AFC = C), which never touches the axes even if extended indefinitely upward or downward to the right. It only approaches the axes asymptotically. That is, as output increases AFC curve will approach closer to the X axis, but will never touch it because the numerator is still a positive constant. The two axes in section A of diagram - 10 represent the asymptotes of the AFC function. Section B of diagram-10 shows the derivation of AFC from in section A. Choice of certain points on TFC and dividing the vertical distance by the corresponding quantity of output would give the slopes of different rays starting from origin and extending to the TFC. The slopes of OA1, OA2, OA3, OA4 and OA5 indicate average fixed cost at different output levels. Thus: A1X1 TFC OA1 = = OQ1 OQ1 A B Y Y 0 Quantity of Output AFC X XQ1 Q2 Q3 Q4 Q5 Quantity of Output Diagram–10: Derivation of Average Fixed Cost A ve ra ge f ix ed c o st ( R u pe e s) A1 A2 A3 A4 A5 TFC C os t ( R up ee s) It clearly shows that as OQ1 increases, the slope of OA1 declines. This illustrates the inverse relationship between AFC and the level of output (Barla 2000). It is also possible to derive average variable cost (AVC) by measuring the slopes of different rays from the origin to the corresponding points on the TVC curve. However, analyzing the pattern of variation in AVC is more complicated as compared to the AFC, because both of these elements determine its change. Since AVC = TVC, both the numerator (TVC) and the denominator (output) increase together, but not necessarily in the same proportion. The traditional AVC curve is ‘U’ shaped due to the operation of law of variable proportions. Decreasing costs arise due to economies of scale reaped by a firm, whereas increasing costs occur due to diseconomies of scale. Section B in diagram-11 shows TVC at different levels of output. The change in slope indicates that TVC increases at different rates at different quantities of output. For instance, for producing OQ1 units of output, the AVC is OC1, which is nothing but the slope of the ray OC at A on the TVC curve. SMC1 c3 c1 c2 SAC1 SMC2 SAC2 SMC3 LMC SAC3 SAC4 SMC4 SAC5 SAC6 SAC7 LAC 0 Q1 Q2 Q3 Output Diagram-13: Long Run Cost Curves At the initial short-run average cost SAC1, the firm produces OQ1 units of output at per unit cost OC1. When the manager plans to increase output to OQ2 units, the average cost would be OC3 on the rising part of the SAC1 cost curve if the same plant is used. On the other hand, if an additional plant is installed, the cost would fall to OC2 (OC2 < OC1). Thus, the installation of a new plant decreases the cost per unit of output. The diagram shows that average cost will successively fall till the installation of the fourth plant. The lowest AC level is reached at output level OQ3. This level is known as the optimum level of output, at which the long run average cost (LAC) is minimum and the LMC cuts it from below. Here, the long run equilibrium condition of LAC = LMC and LMC cutting LAC from below have been reached. If output increases beyond OQ3, the LAC would rise for every additional plants installed. No rational manager would install new plant beyond it, as they wish to make atleast normal profits in the long run. The long run average cost curve (LAC) is also known as A ve ra ge c os t ( R s. ) envelope curve as it envelopes several average cost curves corresponding to different plant size. Further, it is also known as a planning curve, as it guides the manager in planning the future expansion of plant and output.