# 经济代写|微观经济学代写Microeconomics代考|ECON2516

## 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.

# 微观经济学代考

## 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

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