# Cost in the Long Run

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7.3 Cost in the Long Run

To determine cost in the long run, a firm can make flexible selection to expand certain things, like factories, buildings, labor force, as well as design of products, or may add innovative products. Here we reveal how a firm can trim down cost of production and also analyze the relation or interaction among long run costs and output level. Let’s start it with scrutinizing as in how capital gear is utilized and thus influence the productions decision making along with cost of labor.

The user cost of capital

Firms often run capitals that are used in production process, sometimes it is purchased as well, however in economics it is assumed that capitals are rented, the reason behind this assumption can be further explained through an example- let’s take that some xyz airline has planned to purchase a new Boeing 777 airbus for \$ 200 million. But economics is going to allocate the purchase price to its lifespan because this way it would be easier for xyz to evaluate revenue and cost on annual flow basis, let’s say  that the lifespan of the airbus is 40 years, there will be an annual economic depreciation every year for this airbus throughout its life span.

The Cost-Minimizing Input Choice

Now we are going to discuss about the ways firms select the combination of inputs so that it could minimize the value of cost of production of a particular output in terms of wages, user cost of capital etc. followed by elaborate discussion on how long run cost and level of output are related to each other.

Let us take a major issue that every firm faces, and that is the selection of inputs to produce a particular output with minimum cost of production. Here we will use two variables of inputs, first the labor which is measured on the basis of working hours per year and second is capital which is measured usage hours of machinery every year. The amount of utilization of both the categories is solely depends on the price of the inputs. We have to work on the basis of assumption that the market is a competitive market and the prices are not affected by the firm’s operational structure. The price of labor is taken as wage rate here.

The price of capital

The capital of a firm what is utilizes is flexible in long run, in spite of the fact that some capitals might consist of specialized machineries which might have no substitute for it or which cannot be used in any other way, expenditure of this kind of machinery mandatory to be taken into account. Initially large expenditure on capital is necessary for any firm. To make a comparison between capital expenditure and ongoing labor cost of a firm, the capital expenditure is termed as “flow”. We do it by amortizing expenditure; we extend it throughout the lifespan of the capital. Here the forgone interest which is invested elsewhere of a firm must also be taken into consideration, this is the same thing we do for calculating the user cost of capital.

As we learned that we assume capital often be rented not purchased. We can take the example of an office building; in this, the price of office building is rental rate. The cost will be taken as the cost for renting. If it’s a competitive capital market, this rate will be equal of user cost because in this kind of market the firms that own the capital expect a competitive return earning when they rent. This competitive return is termed as user cost of capital. Therefore most of the textbooks indicate that all those capitals which are rented have a rental rate ‘r’. It can be said that it is reasonable but now we have to find out the reason behind it. It is so because the capital purchased treated as rented at a rental rate equals user cost of capital. It is also based on the assumption that firms treat the downcast capital’s cost as fixed cost which is extended over time.

The Isocost Line

The cost of hiring factors inputs of a firm is represented as Isocost lines of a firm. It shows the probable combinations of labor and the firm’s capital which can be purchased based on a given total cost.

It can be said that isocost line has a slope which displays the ratio of wage to the rental of capital. The mentioned slope resemble the slope of budget line that consumer faces in various stages as it is entirely determined by the price of a good whether it is an input or output this theory is applicable to both the aspects. The model can be demonstrated this way – a firm gave up on a unit of labor and let’s say recovered \$ w in cost to buy w/r units of capital at a cost of \$r per unit, the total cost of production will remain the same.

Choosing Inputs

To choose inputs let us now predict that we are planning to produce an output level. We will find the ways to do it in a minimum most cost. Isocost curves show the combination of inputs same as production cost to a firm. An increase of price of labor makes the isocost line steeper in the graph. To find out the procedure through which isocost line relates to a firms production process, we have to read the analysis of production technology.

The effect of effluent fees on input choices

We all know that steel plants are usually developed near rivers, this is because ready easy and inexpensive availability of transportation is possible near river for iron ore which is a raw material for steel factory and used in production process and the also for the finished product steel to distributing it to various places, the drawback here is rivers are also becomes the place for cheap disposal methods of by-products that grows throughout the production process.

The cost-minimizing response to an effluent fee

The waste removal methods or private treatment plants are expensive, for example- the steel plant’s waste taconite particles is no degradable waste which is very harmful to fishes, river animals and vegetation which are also taking part in some other parts of rivers. Therefore the Environmental Protection Agency (EPA) has settled a an effluent fee, a rate per unit basis must be paid by the steel plant in order to restrict what goes on into the river. For the firm and its managers it’s difficult to deal with this imposition of fee to tackle the production cost.

If a steel plant produces 2000 tons of steel per month, with using 2000 machine hours of capital and 10000 gallons of water containing taconite particles when the wastes goes in the river. If the firm estimates that the cost of machine hour is \$40 and each gallon of waste water cost \$10, the total cost of production will be \$180000: \$80000 for capital and \$100000 for waste water, so in this case the question will be how the managers will be handling this EPA-imposed effluent fee rule?

It is known to managers that production process has some flexibility as well, if the firm uses expensive effluent treatment equipment to reduce waste water generation, same output can be achieved with less waste water. From this we can learn that factors can be substituted in the process of production and the degree of substitution if higher the firm has to pay less.

We previously discussed the paths cost minimizing firms follow to select combination of input and output, for further analysis we will see the procedure through which a firms cost is dependent on the output level. We need to determine the firms cost minimizing factors in terms of quantities of input for each level and then will go for the calculation for final cost.

The Expansion Path and Long-Run costs

According to economic models, long run of total cost curve gives a straight line, it assumed such way because constant returns take place in the production scale, as inputs and outputs are proportionate to each other.

7.4 Long-Run versus Short-Run Cost Curves

To protect and preserve the natural resources policymakers all over the world is under continuous research, so that energy consumption or utilization can be reduced. In today’s fast growing problem of global warming, preservation of nature and its resources is a very important factor to keep in mind because most of the energy uses fossil fuels which is majorly releases greenhouse gases which is a vital cause of global warming. Energies in any forms such as oil, gas, coal, nuclear etc. are costly, so by reducing the use of energy in production can actually reduce their production cost and save the environment simultaneously.

There are two ways to put this into application, firstly by substituting other production factor in place of energy, like buying energy- efficient machineries which can be a little costly but can actually save energy and thus saving the capital as well, because the firm has to pay less for energy was tee mission. These days actually firms are installing more energy-efficient machineries like heating and cooling systems, processing equipment, cars, trucks, energy-efficient other vehicles etc. to save their cost of production and indirectly protecting the environment from global warming.

Secondly the energy use can be reduced by bringing technological change, in modern world there are continuous researches are going on for innovation in technology, as a result by engaging fewer inputs like less capital, less labor, less energy, it’s possible to get same amount of output which we used to get by using more inputs, for example- there are major advancement taken place in robotics in the past two years due to which trucks, cars etc are produced using less inputs. In economics there is a model showing how firms are combining capital and energy in production process.

In the time of short run, a firms production cost may not possibly can be reduced due to inflexibility in inputs utilization.

Long-Run Average Cost

In the long run there is flexibility in changing the capital amount. In economics we can view it through the long-run average cost curve and marginal cost curve. The most important determining factor in this regard is the relation between the firm’s operational scale and the required inputs to minimize costs. It can be explained this way, if a firm’s production shows continuous returns in terms of scale for all the levels of inputs, this can be handled by making the input double followed by double output, as the cost of inputs are same but output increases, therefore the overall production cost remain same for every output level.

With the same judgment, during the time when returns to scale is decreased, the overall average production cost must increase along with output.

The LMC (Long-Run marginal cost) curve in economics can be established by examining the long-run average cost curve; the LMC calculates the changes of output’s long-run total cost.

Economies and Diseconomies of scale

If output increases of a firm, then average production cost of that particular output will decrease to a certain point. This is possible because if the firm has large operational range then they can train or specialize the workers in their activities; as a result they can be even more productive. Another reason is if the scale of a firm is higher it provides flexibility, so the managers can vary the combination of inputs versus outputs and thus can organize and run the process much effectively. Firm can also buy some inputs at a lower price by increasing the quantities of those inputs, because while buying large quantities, better price can be negotiated.

There is another angle of this entire aspect, the average production cost might increase in some point with increase of output levels, here is why? In case of short run the workers may not work as effectively due to factory space and machineries may make it difficult for them. For the managers who manage, a larger firm could be difficult as the activities or tasks increases, the complexity increases which decrease the efficiency. Also buying in bulk or huge quantities can make them scarce at some point of time, which can result into limitation of supply of key inputs and thus increasing their price.

In the same way, there are Diseconomies of scale as well, it comes into scenario when the doubling of output needs more than double cost. The scale consists of returns to scale, but here, it is quite more generalizing because it demonstrates the change in proportion of inputs when a firm’s production level changes. To see the change let’s take a poultry firm, suppose production of eggs needs land, equipment, hens, and feeds, a poultry firm which has 50 hens will function with mix weighted input towards labor not equipment, if all the inputs are doubled , farm with 100 hens can double its eggs also.

It will be similar with 200 hens and so on; here there will be constant return to scale. However bigger poultry farms will have the choice of using machines, likewise when a farm increases from 50 to 100 hens, it will change its technology or process so that it can reduce cost of production of the firm.

The relationship between Short-run and Long-run Cost

If we imagine that any firm is not sure about future demand or not estimated demand for product, therefore it is considering three options in the size of plants. This is a vital decision as the firm might not change the size of the plant for a while, if once put up. In long run, the value of average cost curve in economics the firm is flexible to change its plant size, for this the firm is always going to select that plant which minimizes average production cost. If we pretend that the firm has many choices in selecting plant sizes , with each plant having different short run average cost curve, here the average long run cost curve will be the envelop of short run cost curves.

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