经济代写|微观经济学代写Microeconomics代考|ECON2516

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经济代写|微观经济学代写Microeconomics代考|From the Production Function to the Total Cost Curve

The last column of Table $5.1$ is reproduced as a graph in panel (b) of Figure $5.1$ to show Paolo’s cost of producing pizzas. In this example, the cost of operating the factory is $€ 30$ per hour, which remains fixed; we assume labour is the only factor of production which can be varied in the short run, and the cost of a worker is $€ 10$ per hour. If Paolo hires one worker, his total cost is $€ 40$. If he hires two workers, his total cost is $€ 50$ and so on. With this information, the table now shows how the number of workers Paolo hires is related to the quantity of pizzas he produces and to his total cost of production.

An important relationship in Table $5.1$ is between quantity produced (in the second column) and total costs (in the sixth column). Panel (b) of Figure $5.1$ graphs these two columns of data with the quantity produced on the horizontal axis and total cost on the vertical axis. This graph is called the total cost curve.
Now compare the total cost curve in panel (b) of Figure $5.1$ with the production function in panel (a). The total cost of producing the quantity $Q$ is the sum of all production factors where $P_L$ is the price of labour per hour and $P_K$ is the price of hiring capital. $C(Q)=P_L \times L(Q)+P_K \times K(Q)$. Here $L(Q)$ and $K(Q)$ are the labour hours and the amount of capital employed to produce $Q$ units of output.

These two curves are opposite sides of the same coin. The total cost curve gets steeper as the amount produced rises, whereas the production function gets flatter as production rises. These changes in slope occur for the same reason. High production of pizzas means that Paolo’s kitchen is crowded with many workers. Because the kitchen is crowded, each additional worker adds less to production, reflecting diminishing marginal product. Therefore the production function is relatively flat. If we turn this logic around, when the kitchen is crowded, producing an additional pizza has used a lot of additional labour and is thus very costly. Therefore, when the quantity produced is large, the total cost curve is relatively steep.

经济代写|微观经济学代写Microeconomics代考|The Relationship Between Short-Run and Long-Run Average Total Cost

For many firms, the division of total costs between fixed and variable costs depends on the time horizon. Over a period of a few months, for example, Paolo cannot expand the size of his factory. The only way he can produce additional pizzas is to hire more workers at the factory he already has. The cost of Paolo’s factory is, therefore, a fixed cost in the short run. By contrast, over a period of several years, Paolo can expand the size of his factory, build or buy new factories. Thus the cost of Paolo’s factories is a variable cost in the long run.
Because many decisions are fixed in the short run but variable in the long run, a firm’s long-run cost curves differ from its short-run cost curves. Figure $5.5$ shows an example.

The figure presents three short-run average total cost curves representing the cost structures for three factories. It also presents the long-run average total cost curve. As Paolo adjusts the size of his capacity to the quantity of production, he moves along the long-run curve, and he adjusts capacity to the quantity of production.

This graph shows how short-run and long-run costs are related. The long-run average total cost curve is a much flatter U-shape than the short-run average total cost curve. In addition, all the short-run curves lie on or above the long-run curve. These properties arise because firms have greater flexibility in the long run. In essence, in the long run, the firm chooses which short-run curve it wants to use. In the short run, it must use whatever short-run curve it chose in the past.

The figure shows an example of how a change in production alters costs over different time horizons. When Paolo wants to increase production from 150 to 200 pizzas per day, he has no choice in the short run but to hire more workers with only two factories. Because of diminishing marginal product, average total cost rises from $€ 6$ to $€ 10$ per pizza. In the long run, however, Paolo can expand both his capacity and his workforce by building or acquiring a third factory, and average total cost returns to $€ 6$ per pizza.

How long does it take for a firm to get to the long run? The answer depends on the firm. It can take several years for a major manufacturing firm, such as a car company, to build a larger factory. By contrast, Paolo might be able to find new premises and expand sales in a matter of months. There is, therefore, no single answer about how long it takes a firm to adjust its production facilities.

经济代写|微观经济学代写Microeconomics代考|ECON2516

微观经济学代考

经济代写|微观经济学代写Microeconomics代考|From the Production Function to the Total Cost Curve

表的最后一列5.1在图的面板 (b) 中再现为图表5.1来显示 Paolo 生产比萨饼的成本。在这个例子中,工厂的运营成本是€€30每小时,保持不变;我们假设劳动力是唯一可以在短期内变化的生产要素,并且工人的成本是€€10每小时。如果保罗雇用一名工人,他的总成本是€€40. 如果他雇佣两个工人,他的总成本是€€50等等。有了这些信息,表格现在显示了保罗雇用的工人数量与他生产的比萨饼的数量以及他的总生产成本之间的关系。

表中的一个重要关系5.1介于生产数量(第二列)和总成本(第六列)之间。图 (b)5.1将这两列数据绘制成图表,横轴为生产数量,纵轴为总成本。该图称为总成本曲线。
现在比较图 (b) 中的总成本曲线5.1面板 (a) 中的生产函数。生产数量的总成本问是所有生产要素的总和,其中P大号是每小时的劳动力价格,并且P钾是雇佣资本的价格。C(问)=P大号×大号(问)+P钾×钾(问). 这里大号(问)和钾(问)是劳动时间和用于生产的资本量问输出单位。

这两条曲线是同一枚硬币的相反两面。总成本曲线随着产量的增加而变得更陡峭,而生产函数随着产量的增加而变得平坦。这些斜率的变化出于同样的原因而发生。比萨饼的高产量意味着保罗的厨房里挤满了很多工人。因为厨房很拥挤,每增加一个工人就减少了生产,反映了边际产量递减。因此生产函数比较平坦。如果我们把这个逻辑反过来,当厨房很拥挤时,多生产一个比萨饼会消耗大量额外的劳动力,因此成本非常高。因此,当生产量大时,总成本曲线相对陡峭。

经济代写|微观经济学代写Microeconomics代考|The Relationship Between Short-Run and Long-Run Average Total Cost

对于许多公司来说,总成本在固定成本和可变成本之间的分配取决于时间范围。例如,在几个月的时间里,Paolo 无法扩大他的工厂规模。他要生产更多比萨饼的唯一方法是在他已有的工厂雇用更多工人。因此,Paolo 工厂的成本在短期内是固定成本。相比之下,在几年的时间里,Paolo 可以扩大他的工厂规模,建造或购买新工厂。因此,从长远来看,保罗工厂的成本是可变成本。
由于许多决策在短期内是固定的,但在长期内是可变的,因此公司的长期成本曲线不同于其短期成本曲线。数字5.5显示一个例子。

该图显示了三个短期平均总成本曲线,代表三个工厂的成本结构。它还显示了长期平均总成本曲线。当保罗根据生产量调整产能规模时,他沿着长期曲线移动,并根据生产量调整产能。

该图显示了短期成本和长期成本之间的关系。长期平均总成本曲线是比短期平均总成本曲线更平坦的 U 形。此外,所有短期曲线都位于或高于长期曲线。这些特性的产生是因为从长远来看,公司具有更大的灵活性。从本质上讲,从长远来看,企业选择它想要使用的短期曲线。在短期内,它必须使用过去选择的任何短期曲线。

该图显示了生产变化如何在不同时间范围内改变成本的示例。当 Paolo 想将每天的产量从 150 个比萨饼增加到 200 个时,他在短期内别无选择,只能在只有两个工厂的情况下雇用更多工人。由于边际产量递减,平均总成本从€€6至€€10每个披萨。然而,从长远来看,Paolo 可以通过建设或收购第三家工厂来扩大产能和劳动力,平均总成本回报为€€6比萨饼。

一家公司需要多长时间才能达到长期目标?答案取决于公司。大型制造公司(例如汽车公司)可能需要数年时间才能建造更大的工厂。相比之下,Paolo 可能会在几个月内找到新的经营场所并扩大销售。因此,关于一家公司调整其生产设施需要多长时间,没有单一的答案。

经济代写|微观经济学代写Microeconomics代考

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