The Function of Buses and a Diminishing Return to Scale - Essay Example

WORK ASSIGNMENT 2 In Utoprica, there are two types of vehicle: cars and buses. 6 people repair vehicles (or make a new vehicle, if an old one can’t be repaired): each person works on cars or buses, but not both. In Utropica, 16 machines are used to make/repair cars or buses; a machine cannot be used for both cars & buses. The number of buses in Utropica is given by the production function N buses = 0.4 K1.1 L0.41 where K is the number of machines used to make/repair buses, and L the number of employees who make/repair buses. Task A The function of buses produced implies a diminishing return to scale. This is because the return scale decreases as the production factors are increased. Diminishing returns take place when the labour marginal productivity begins to fall. In the present case, an extra unit of labour is added to a fixed capital when production of buses takes place. It reaches a place where marginal production of extra labour is maximized after which the output for each additional unit of labour falls. Diminishing returns is a law that takes place because production factors like capital labour inputs are imperfect substitutes (Jehle & Philip, 2000). This implies that when producing a product like for this paper, buses and cars, the resources put in use are inefficient when turned for a production of a different service or another good. For instance, workers deployed in the vehicle industry to make buses and cars may be inefficient, if they are re-employed in a cement producing industry. Similarly, quite a number of item involving capital equipment specify to a single type of production. If switched to different uses, there would be inefficiency in production of output. Production factors like capital and labour are said to be immobile occupationally as they can be turned to other functions, although with a resultant productivity loss. An inverted relationship does exist between production factors and the cost of production of a unit in a firm. When there is low productivity, cost per unit of supplying service or a good turns out to be higher (Frank, 2006). Therefore, a firm can get higher returns and be efficient in its labour force leading to higher profits and lower costs. Here, K represents capital employed in the form of machine while L stands for labour employed which in this paper is the number of men who repair or make new vehicles. Using N buses = 0.4 K1.1 L0.41 L=0 L=1 L=2 L=3 L=4 L=5 L=6 K=16 0 8.4 11.0 13.5 15.2 16.0 17.7 K=14 0 7.3 9.5 11.7 13.1 13.9 15.3 K=12 0 6.2 8.0 9.8 11.1 11.7 12.9 K=10 0 5.0 6.5 8.1 9.1 9.6 10.6 K= 8 0 4.0 5.1 6.3 7.1 7.5 8.3 K= 6 0 2.9 3.7 4.6 5.2 5.5 6.0 K= 4 0 1.8 2.4 2.9 3.3 3.5 3.9 K= 2 0 0.9 1.1 1.4 1.5 1.6 1.8 K= 0 0 0.0 0.0 0.0 0.0 0.0 0.0 Task B Edge worth box This box is frequently used in a theory of general equilibrium. It helps represent competitive equilibrium in a range of outcomes, which satisfies economic efficiency. It can also aid in detecting difficulty in reaching efficiency in the presence of a bilateral monopoly. From the table above, it is noted that as the number of men is increased holding machine constant number of buses produced increase but in a decreasing rate. This implies that the output or returns to scale diminishes. Therefore, it means that the ratio of employed labour to the number of machines is not that proportional. This creates inefficient use of resources, and in this case, it is the labour employed. If labour is not used efficiently, the firm incur a lot of costs in the form of salaries and wages that are not effectively used (Mas-Colell et al., 1995). This may lead a firm to diminishing returns to scale. If there is no labour or machine employed, there is no output at all as output is only evident when there is a combination of the two. On the other hand, holding labour constant and adding more machines leads to a steady output as the labour that is available can only use up to a certain no of machines. Task C In the edge box, there are two curves for cars and buses. Whenever these curves touch each other, or they be tangent to each other in this box, two factors of production are identified. These yields both utility level for the producer which couldn’t be made better for one factor by reallocation with no decrease in the other factors utility. This combination of production factors is taken to be at its optimal level. The points that are tangent to each other between pairs of isoquant curves if they all traced out, turn out to form a connection at their origins. The curve that connects the two points, which is not necessarily a straight line, is the locus of efficiency. This is because it is optimal at that point. The most suitable vocabulary that is applicable for contents in the edge worth box do not converge. Contract curve is the name given to all set of edge worth box while some scholars confine the definition to points that make the two curves well off because they still lie in their original endowment. In order to work out the set, isoquant slope for both production factors must be worked out at each point. The gradient is the opposite of technical rate of marginal substitution. Therefore, this set in which both isoquant curves form a tangent, is likewise the set in which factors technical rate of marginal substitution becomes equal. This box shows efficiency when both capitals employed and the people working are equal at fails to be efficient at any other point in the edge worth box. The two factors in this box become inefficient when they fail to produce max number of vehicles using the provided capital and labour. Task D Contract curve is the name given to all set of edge worth box while some scholars confine the definition to points that make the two curves well off because they still lie in their original endowment. In order to work out the set, isoquant slope for both production factors must be worked out at each point. The gradient is the opposite of technical rate of marginal substitution. Therefore, this set in which both isoquant curves form a tangent, is likewise the set in which every factors technical rate of marginal substitution becomes equal (Colander, 2008). Using the curve from part C and part B, there is no any other better combination as these two factors at employment of three people and 8 machines they remain better off in their original endowment. Hence, this makes the aspect of contract curve to be relevant to this particular situation. In case 3, people use 8 machines for the production of cars it is evident that the production is steady this is because the employed labour is proportional to the number of machines. In such a situation, both factors are optimally used and hence efficiency is realized. From this scenario, it can be concluded that using the curve from part C and part B, there is no any other better combination as these two factors at employment of three people and 8 machines they remain better off in their original endowment. In conclusion, from the parts A, B, C and D a production function shows in graphical or mathematical form, the amount of output that can be obtained from a combination of a given set of features. For instance, in our question, labour in the form of people is combined with capital in the form of machines. In particular, maximum possible output is shown by the function given available technology and factor endowments. There are always unique functions of production for different technology of production. The function of production sometimes is always referred to as requirement specification for minimum input to produce a given output quantity with a given a technology. In such a function, physical outputs are related to physical inputs and, therefore, costs and prices should be neglected. It is vital to have it in mind that the function of production describes the technology and not the behaviour of economics. Bibliography Bade, R. & Parkin, M., 2001. Foundations of Microeconomics. 1st ed. Addison Wesley Paperback. Bouman, J., 2011. Principles of Microeconomics - free fully comprehensive Principles of Microeconomics and Macroeconomics texts. Maryland. Colander, D., 2008. Microeconomics. 7th ed. McGraw-Hill. Dunne, T.J., Jensen, B. & Mark, J.R., 2009. Producer Dynamics: New Evidence from Micro Data. University of Chicago Press. Eaton, B.C., Eaton, D.F. & Douglas, W.A., 2002. Microeconomics. 5th ed. Prentice Hall. Frank, R.A., 2006. Microeconomics and Behavior. 6th ed. McGraw-Hill/Irwin. Jehle, G.A. & Philip, J.R., 2000. Advanced Microeconomic Theory. 2nd ed. Addison Wesley. Mas-Colell, A., Whinston, M.D. & Green, J.R., 1995. Microeconomic Theory. New York: Oxford University Press. Osborne, M.J. & Rubinstein, A., 1994. A Course in Game Theory. Cambridge: MIT Press. Read More