The Firm and Production

A firm is an organization that produces goods or services for consumers (other
firms and households). Since the property, claims, and obligations of a firm are established by laws and regulations, the firm is a legal identity, and can enter into contractual arrangements with natural persons and other legal identities.

There are different types of firms defined by the law, such as sole proprietorship, simple partnership, limited liability company, joint stock company, and government owned company.

The firm transforms raw materials into output(s) by means of machinery and equipment operated by workers. This process
is called “production” and the basic function of a firm is to organize the production process.

The production process has two aspects: technological and social.

The technological aspect of the production process can be defined in terms of physical quantities.

The technological aspect of the pin production process can be represented as follows:
100 kg of wire + 6 workers + 18 tools → 50 boxes of pins

Value added is the increase in the value of a good or service as it goes through the stages of production (from raw materials into the
final good or service).

The neo-classical theory considers the firm as a “black-box” and ignores how the decisions are made within the firm. The firm is
an organization that transforms inputs (“factors of production”) into an output (or outputs), and that transformation is represented by a “well-behaved” production function.

The behavioral theory of the firm criticizes profit maximization assumption as unrealistic and proposes an alternative theory based on empirical observations of actual decision making processes in business firms.

The behavioral theory suggests that the firms, or to be more specific, the managers of the firms, would certainly prefer to earn more profit, but they cannot maximize profits.

The managerial theory of the firm says that managers are interested in their own utility, not the profit of the firm. This is a typical principal-owner problem where the principal is the manager, and the owner is the shareholder. 

The evolutionary theory of the firm combines the behavioral theory with the Schumpterian idea of innovation, and suggests that firms try to be more profitable but they cannot maximize profit because of the lack of perfect information and computational capability. 

The question was first answered by Ronald H. Coase in 1937 who subsequently won the Nobel Prize in Economics in 1991. Coase suggested that both the market and the firm are coordination mechanisms, and there are certain costs involved in using these mechanisms. The main cost of the firm as a coordination mechanism is the cost of management, whereas the “most obvious cost of ‘organising’ production through the price mechanism is that of discovering what the relevant prices are” and the (actual and potential) costs of contracts, i.e., transaction costs. When managerial costs are lower than transaction costs in coordinating two operations, these operations will be performed and coordinated in a firm. The firm exists because of transaction costs, and the boundaries of the firm (the number of operations performed within the firm) will be determined by the difference between transaction and managerial costs. The size of a firm is
bounded because when the firm gets larger, the managerial costs will increase, and the firm will stop growing at the point where managerial costs exceed transaction costs.

Capital goods (or physical capital) used in the production process. Capital goods are outputs of other firms. “Capital” in the production function does not mean financial capital (money capital) invested by the firm.

Output(s) and inputs are flow variables, and measured in flow units like, hours worked per year, machine hours per year, tons of cement produced in a year, etc.

The maximum quantity of output is defined as a function of the quantities of inputs as follows:
q* = f (K, L, M)

where q*, K, L and M are quantities of output, capital, labor and raw materials (including energy and intermediate inputs), respectively, and f is the production function. q* is the maximum amount of output that can be produced given the quantities of K, L, and M.

Production function is the functional relationship between inputs (factors of production) and the maximum amount of output that can be produced with a given technology within a given period of time.

Isoquant is the combinations of factors of production (capital and labor) that can produce a given level of output (say, q1). With two inputs, K and L, an isoquant is the set of K and L that satisfies q1 = f (K, L).

log(q) = a0 + aKlog(K) + aLlog(L) + aKKlog2(K) + aLLlog2(L) + aKLlog(K)log(L)

The concept of (technical) efficiency defines a relationship between actual output and potential output.

Productivity is the relationship between the output and the inputs.

There are a number of different productivity measures:

• Partial productivity
• Total factor productivity
• Marginal productivity, or marginal physical product

Partial productivity is the ratio between the output and one of the inputs. For example, labor productivity is defined as output produced per unit of labor, and is equal to the output/labor (q/L)
ratio. Labor productivity is basically the average productivity of all workers. Capital productivity is defined accordingly.

Total factor productivity is the ratio between output and the weighted average of all inputs: q/(wKK + wLL) where wK and wL are the weights of capital and labor, respectively, and, by definition
wK + wL = 1

Marginal productivity, or marginal physical product, is the productivity of an additional (marginal) input: marginal productivity of labor (MPL) is the change in output produced by employing one more worker while holding the capital input constant. The MPL is defined as:
MPL = ∂q/∂L = fL

where fL is the partial derivative of the production function with respect to labor.

Marginal rate of technical substitution (MRTS) is the rate at which one input can be substituted for another one while holding
output constant along an isoquant.

The TFP growth rate is equal to the difference between the labor productivity growth rate and the growth rate of capital intensity multiplied by a parameter, the elasticity of output with respect to capital.