Quiz 6: The Theory and Estimation of Production

a. True. The law of diminishing returns takes place when a firm's average product will start to decrease. Law of diminishing returns states that, as the number of new employee's increases, the marginal product of an additional employee will at some point be less than the marginal product of the previous employee. b. False. Decreasing returns to scale occurs when all factors of production are increased in a given proportion, the output increases in a smaller proportion. The main cause of this scenario is that diseconomies outweigh economies of scale. c. True. A linear short run production function implies that the law of diminishing returns does not take place over the range of output being considered. A linear production function has constant marginal product. d. True. Stage-I of the production process ends at the point where the law of diminishing returns occurs. In stage I, the average returns to the variable input are increasing but the fixed factor is being underutilized. In order to achieve maximum profit, purely competitive firm will be to operate in stage II.

The basic difference between the short-run and long-run Production Function is that in short-run at least one of the inputs of production remains fixed, while, in the long- run, all inputs of production becomes variable. The Short-run Production Function is of the form Where, Q represents Short-run Quantity Produced L represents Labor units K represents Capital units The bar over K in the short run Production Function explains that the capital remains fixed in the short run. On the other hand, the long-run Production Function is of the form: For example, there is toy-making company. The company needs the following to manufacture sticks: • Raw materials such as plastic • Labor • A factory Suppose the demand for toys has increased. The company orders more raw materials and hires more labor. Therefore, these are variable inputs. Factory may not be a variable input. It may be time consuming to established new factory. Thus, this is the fixed input. In the short run, the company cannot add another factory, but in the long run all of our inputs are variable, including our factory space.

(a) Law of diminishing returns states that as more and more variable factor is combined with fixed factor a stage must ultimately come where the marginal product of the variable factor starts declining. In this case as the number of new employees' increases, the marginal product of an additional employee will at some point be less than the marginal product of the previous employee. Diminishing returns occurs at 4 th number of Fishermen as the MP of him is 150 while the MP of the third fisherman is 190. (b) The short-run production function can be divided into three separate stages of production. First, increasing returns to factor where the marginal product of the variable factor increases. Second, diminishing returns to factor where the marginal product of variable factor starts decreasing. Third, negative returns to factor where the marginal product of the variable factor is negative. Stage I runs from zero to four units of Fisherman as the average product reaches to maximum. Stage II begins from this point to eight units of Fisherman. Stage III continues from that point. (c) The firm should employ a particular input up to the point at which the revenue contribution of the additional input is equal to the cost incurred by the firm to employ this particular input. Seven fishermen should be employed because adding additional fisherman will give loss because at this point the marginal revenue product is less than the wage rate. (d) The firm should employ a particular input up to the point at which the revenue contribution of the additional input is equal to the cost incurred by the firm to employ this particular input. Six fishermen should be employed because adding additional fisherman will give loss because at this point the marginal revenue product is less than the wage rate. If price is $5/pound then new table is as follows: Eight fishermen should be employed because adding additional fisherman will give loss because at this point the marginal revenue product is less than the wage rate. (e) In short-run, maximum catch of the boat is 725 pounds. If the company wants to increase the catch at least 1,000 pound then firm would have the change the boat with high technique boat, give the training program to fisherman and buy radar to catch fish etc. This is a long run phenomenon.