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The existence of firms increases factor market transactions. This conclusion is implied in Stephen Cheung's article The Contractual Nature of the Firm. Before you can tell if this statement is correct, you must understand the theory of the firm on which Cheung based his argument.

The market has Invisible Hand to allocate resources for production, why does the firm exist at all? Why don't the individuals contract with one another, dictated by the market price, to produce the goods. Why instead we have the firms to produce the goods? This is the question answered by Ronald Coase.

Trade between firms are dictated by market forces. But inside a firm, who-do-what is arranged by management, that is, by command and order. Inside a firm, market forces are replaced by managerial functions. Coase explained that there are transaction costs involved in using the market, costs such as search and information cost, bragaining, policing and enforcement costs, etc. when there are no firms. Firms arise when they can internally arrange the production and somehow avoid these costs.

Cheung in his article points out that there are many contracts involved in different stages of production, each guided by price signals. These contractual arrangements exist also inside a firm.

An example is you can buy vegetables in a supermarket. The supermarket is a product market. People who grow vegetables are supplying their labour. They form the factor market (market for factors of production). When you buy vegetables directly in a farm from the person who grows the vegetables, the distinction between a product market and a factor market is blur. Are you buying the product or are you buying the labour, probably both. In this case, the product market and the factor market is one and the same thing. The same thing occurs in a firm when the employer pays the workers by piece rate. It is not clear whether the workers are supplying the product or their labour. This is what Cheung argues as having a market within a firm.

An example to explain the increase in factor market transactions is illustrated by a builder who pays the contractor to build houses. The contractor contracts out the work to different sub-contractors. Some sub-contractors find the workers to do the job. Some are paid to get the materials. It looks as if the builder's firm builds the houses but it involves many contracts to many people. At each stage of subcontracting out the job, factor market transactions are involved. The final product, the houses are sold in the product market but the houses are created with a series of factor market transactions.