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The long run is defined as a period in which all INPUTS are variable. Because of that all costs are variable too.
You're right that in the short run your rent and the cost of the machines you've already bought are fixed costs. But in the long term they aren't.
In the long term, you can buy or rent a larger building (as you expand your company). Then that cost would go up compared to now. You can buy more machinery and the same thing would happen. You can change anything because ALL inputs are variable.
So even those things that are fixed in the short run become variable in the long term.
"Fixed costs" are only "fixed" to a certain degree. Investments in land, buildings, equipment, and people -- and this latter category, people, is subject to numerous variables -- represent fixed costs to the extent that they constitute productive components, but productivity declines with aging equipment, buildings need to be maintained (and old buildings with equally old heating and cooling systems and plumbing and electrical systems are all expensive to maintain and/or replace), and the retirement of senior-level (i.e., experienced) employees necessitates the hiring and training of replacement personnel. In short, "fixed costs" are "fixed" only for a limited period of time. Property taxes alone can change "fixed" costs associated with real estate. Recapitalization of a factory represents an enormous long-term expense that will, for a certain period of time, establish new sunken or fixed costs. Rent, the question suggests, represents a "fixed cost," but rent is anything but fixed, as rents are generically increased at a minimum to reflect the rate of inflation lest the land or property's owner begin to suffer financial losses from rent levels that represent diminished value due to inflation. Investments in physical plant, in short, represent fixed costs only to the degree that the buildings and equipment remain adequate to the task and, as importantly, remain consistent with environmental and other regulations imposed over time by state and federal governments. Imposition of new regulations pertaining to factory emissions, for example, can translate to new financial investments in equipment and processes necessary to be in compliance with those regulations.
There are, as others pointed out, numerous variables involved in determining "fixed costs" at specific points in time. Suffice to say, it is a fluid situation, termination notwithstanding.
In the longer run there are no fixed costs because businesses or organizations keep on making changes to suit the changing economic conditions. For example, in the short-term premises and equipment may be on rent and they become fixed costs. However, in the longer run, businesses may decide to buy the premises and machines. In such a scenario, the fixed cost will no longer be fixed and it would be a one-time expense. Similarly, the business may decide to outsource part of their operations, as is common for customer support for many companies, to a cheaper country. In that case the fixed cost may become less. Organizations may scale the operations up or down or may venture into an altogether different direction depending on the needs and hence fixed costs may change or vanish altogether. For example, Microsoft is moving from a software only company to a software-hardware company with the purchase of Nokia.
Hope this helps.
In the long run of an organization, there are no constraints that can inhibit changes in output by changing the input. This follows that during the same period all factors of production can be varied (increased or decreased) depending on the business objectives. This basically means the cost associated with these factors also becomes variable which is opposite to the short run period where some costs are fixed while others are variable.
During the long run companies change their output levels with regard to the economy and the profits and or losses they expect. The business may choose to leave or enter an industry; this results in either increase or decrease of the factors of production (land, labor, capital, and entrepreneurship) in response to the prevailing economy.
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