Das Kapital, or Capital, was published in 1867, during the latter half of the life of Karl Marx, its main author.  This mammoth book of socialist theory was not the only book which Marx wrote, but it is the best known, and that which provides the most insight into the details of the system which he hoped would replace Capitalism.  Marx and Engels, Das Kapital's other author, hoped to make such a solid case for their ideas against those of the capitalist nations, that political reform would take place, resulting in the redemption of the supposedly exploited working class.  Although it is historically evident that they succeeded in making their ideas appetizing enough to be ultimately tried on a major scale, it is equally evident that these ideas failed, and the supposedly grandiose reform never really took place.  Through careful analysis of the book, serious problems become apparent in the basic assumptions and fundamental arguments that are made against Capitalism.
 Marx begins with a discussion of commodities. As in all economic systems, Capitalism's focus is on the wealth of the nation.  The wealth of a Capitalist nation is nothing but a collection of commodities. And because these commodities are the most basic building block of Capitalism, Das Kapital begins with a study of commodities.
 What is a commodity? It is necessary to grasp the meaning of an idea before analyzing its properties. In the first section of chapter one, Marx says, "A commodity is an external object," by which he means one apart from ourselves, "a thing which through its qualities satisfies human needs of whatever kind."  It does not matter whether it is a necessity or not, it matters only if a person perceives it to be necessary, or at least beneficial. It also makes no difference whether it is the human which requires something or his dog which requires something; for if it is important to the human that the dog be fed, he still sees the commodity as beneficial.
 After explaining the definition of a commodity, Marx proceeds to explain the properties of such a commodity: first, that any commodity, or useful thing, has both quantity and quality; and second, that every useful thing has many properties, and therefore many uses.  For example, because wood is both durable and inflammable, it is used both as a building material and for fuel.
 The usefulness of a thing, which derives from its properties, may be called its use value. However, the use value of a thing has no bearing on the amount of labor necessary to produce those useful qualities.  For example, gems have very little use value, but a great amount of labor is needed to make them useful, or at least desirable.  On the other hand, a tree requires little or no labor to raise, but once raised, it is a most useful object.
 These use values may be traded commercially. The proportion in which they are traded may be referred to as the exchange value of the use value.  It is important to note that the proportion, and therefore the exchange value is in constant flux. This is caused by the average difficulty in obtaining different commodities also changing, due to differences in time and place as well as other factors.
 Having set forth these definitions, the book proceeds to set up an argument to prove the basic assumptions on which Marx's ideas are based.
 To begin, Marx states an equation. 1 quarter of corn = x cwt iron; or, in english, one quarter of corn, a quarter being a unit of corn, is equal to an unknown amount of iron in units cwt.  Marx claims that because both sides of the equation are exactly equal, they should be reducible to a third unit or element. Marx claims, however, that this element cannot be any of the properties of the commodity.  What brought him to this conclusion he does not explain.  The properties matter only as they affect the use value of the commodity in question.
 Quality and quantity are wholly separate properties which do not overlap and have no bearing on each other. Use value is nothing but quality, while exchange value is nothing but quantity, says Marx. Thus, use value and exchange value are unrelated.  Next, without any explanation or proof, the author states that totally disregarding the use value of a commodity, all that remains is the product of labor.  Therefore, because all that remains apart from use value is exchange value, and aside from use value is only the product of labor, it follows that exchange value is the manifestation of labor.
 The residue of labor may be characterized as nothing but a sort of crystallized homogeneous human labor power which has been expended toward a certain goal. Therefore, an object is desirable, or has an exchange value because it contains expended labor power.  How then does one measure the amount of labor power spent in producing a commodity? By the number of labor hours necessary to produce it. It might be argued that it would be to the worker's advantage to waste time, thereby making the amount of hours spent greater, causing the exchange value of the commodity produced to rise.  Marx answers this objection by saying that it is not the amount of hours it takes a laborer to produce a commodity, but the number of hours that it is on average necessary to spend, which determines the labor power expended.
 In response to these ideas on exchange value, a very solid idea can be argued.  If a cook with no skill whatsoever attempted to create a gourmet dinner,  he might work for hours, using up a large amount of his time, and when he was finished would have produced something worth absolutely nothing. He would have produced something which nobody would buy.  Therefore he would have spent labor power, and have produced little or no exchange value. How then could exchange value possibly be directly related to labor value alone? It certainly cannot.
  To understand how Marx errs in asserting that all labor results in an exchange value directly proportionate to the amount of labor spent, we must first examine the true contents and origin of exchange value
 A person, seeing himself in need of a commodity, goes to make the purchase not because he realizes that the item was difficult to produce, but because he believes that it will satisfy a need that he feels, whether that need is physical or mental, direct or indirect, true or perceived.  The amount which he is willing to exchange for the commodity is based on the degree to which he feels the commodity is useful.  From this I conclude that use value has at least some bearing on the amount the commodity will exchange for (its exchange value).
 However, the use value cannot be the only factor involved.  This is evident from the example of a diamond.  A diamond has very little use value, yet it sells for large amounts.  I propose that it is a perceived use value, or what we might call a "want value", that causes a diamond to sell for much more than its use value would dictate.  A woman might take it into her head that she simply must have a diamond. She decides this not because there is any absolute objective use value inherent in the diamond, but because the woman perceives it as desirable.  For our purposes, it makes no difference whether she perceives a use value or she perceives that it is beautiful. All that matters is that she decides that she wants the commodity.
 The same principle can be shown through another analogy.  Two men have an amount of money.  The first man has ten one-dollar bills, while the second man has one ten-dollar bill.  These two amounts both add up to ten dollars, an exactly equal amount, from the market's perspective.  The first man wishes to conserve space in his wallet, while the second needs a small bill in order to make a certain inexpensive purchase. Therefore, it is in both their interests to trade what is to the market identical.  Were the items in reality exactly alike in value, the men would have no reason to trade. However, because they each perceive a slightly greater value in what the other man owns, they see that it is to their advantage to trade.  It is important to note, for future purposes, that both men are happy with their trade, and both men are satisfied that they have come away from the trade with the more valuable possession.
 A final analogy is also necessary for future purposes. Two families each own a piece of farm land, each of which produces a large amount of some commodity. The first family therefore, finds that they have an excess of wheat, while the second family finds that they have an excess of corn.  They each perceive that they have no use for the excess they own, while they have much use for the excess their neighbor owns.  They therefore have cause to trade, each finishing happy, because they have traded something with a lesser value for something with a greater value.
 In a trade, the main factor which determines the approximate level at which the price is set, is the price the merchant paid to acquire the commodity.  This price may be traced to how much it cost to produce, or the amount of labor expended in the production.  The second factor is how much he thinks he will obtain for the item, or the perceived use value, which determines how much a buyer will pay, as I have shown.  Thus, the two factors of an exchange value are its labor value and its perceived use value. The equation therefore, is |V|=p.u.v * l.v.
 This new equation can be effectively used to describe any situation.  Recall the analogy of the cook. The lack of skill with which he approached the job at hand produced something which contained little desirability. A possible buyer would see that the meal was not good, and the perceived use value would be nothing. This would cancel all of the cook's labors, and the exchange value would be zero.
 In the analogy of the two men, they each perceived a greater value in what the other man had, and therefore the exchange value rose slightly, causing them to trade.
 Having shown the weakness of Marx's foundation, I shall now show the resulting weakness in his main complaint against capitalism.
 The capitalist's entire wealth is built upon one thing, and that is labor. However, the capitalist himself does not do the entirety of the labor, and indeed could not. Therefore, it is necessary that he obtain workers to build his wealth for him.  In exchange for this service, the laborers are paid wages, or in effect, a part of the commodity produced.  They cannot however, keep all they have produced, for then the capitalist would be left with no gain.  Thus, having worked a day, they receive only a fraction of a day's work in pay.  This, Marx implies, is immoral. It amounts to an exploitation of the workers for the benefit of the upper class capitalists.  Whether in a capitalist system or in a communist system, men will always be depraved, and thus will always attempt to exploit their fellow men. This  exploitation, however, is not inherent in capitalism, as Marx argues.
 The idea that exchange value is equal to labor value is critical to Marx's reasoning.  It is so because if the amount of labor power the worker expended did not result directly in an exchange value being produced, and were it not the only factor involved in the production of that exchange value, it might be argued that the workman only deserved part of the exchange value of the produce as he had only caused part of it. Thus the worker would not be exploited, and capitalism would not be inherently immoral. Very good point- you need to repeat it a number of times though, before it will sink into the average listener.  Think of some ways you can rephrase it.
 This conclusion may also be reached through the assumption that exchange value is equal to labor value times perceived use value.  Assuming labor to be a commodity, one may say that hiring a worker is just another sort of trade.  The laborer trades his power for money, which he may trade for personal necessities.  Thus, his labor has an exchange value, as does the money which he is given.  Thus, both his labor and the money he is given contain the same factors as any other commodity, namely, labor power and perceived use value.  The worker has in his possession an excess of labor power, for which he has no need.  Therefore, he sees that the money which the capitalist owns and wishes to invest is more valuable than the excess of labor power he possesses, and is willing to trade, at what might be considered, from the market's absolute point of view, a slight loss.  The trade then is not unfair.
 The objection might be made to this arguement, however, that although it works initially, what happens after a few months?  The worker has been doing the same job for a year, and now has a wife and a young child to support.  He requires more money to live, and therefore it is necessary that he receive a raise in wages.
 His increase in needs however, is not the only change in his life which effects the exchange of work for pay.  In the year he worked, he has accumulated skill and knowledge of his job, causing him to become more efficient and produce more for his employer.  Thus it is quite rational for him to wish to keep a larger amount of his produce.  The percentage which he keeps need not change, and indeed will most likely be constant.
 Yet if the employer cannot or does not want to raise the wages of worker, all is not lost.  For it is likely that another capitalist will be glad to hire a man with experience.  The original capitalist probably would be pushed out of the market because he could not pay the wages necessary in order to retain experienced labor.
 The strength of the free market lies in this very principle.  The market dictates an equilibrium. All who do not conform do not continue to succeed, perpetuating the equilibrium.  Thus hard work is encouraged and all those who do not work are cast aside before the forces of the market.
 It is apparent then, that Marx's disputes with Capitalism lack a logical soundness which would make them legitimate.  The seemingly common notions which he states, and then builds upon, are as fallacious as the communist ideals which he promotes.