Returns to scale

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In economics, returns to scale and economies of scale are related terms that describe what happens as the scale of production increases. They are different terms and are not to be used interchangeably.

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[edit] Returns to scale

Returns to scale refers to a technical property of production that examines changes in output subsequent to a proportional change in all inputs (where all inputs increase by a constant). If output increases by that same proportional change then there are constant returns to scale (CRTS), sometimes referred to simply as returns to scale. If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportion, there are increasing returns to scale (IRS)

Short example: Where all inputs increase by a factor of 2, new values for output should be:

Twice the previous output given = a constant return to scale (CRTS)

Less than twice the previous output given = a decreased return to scale (DRS)

More than twice previous output given = an increased return to scale (IRS)

[edit] Economies of scale

Economies of scale and diseconomies of scale refer to an economic property of production that affects cost if quantity of all input factors are increased by some amount. If costs increase proportionately, there are no economies of scale; if costs increase by a greater amount, there are diseconomies of scale; if costs increase by a lesser amount, there are positive economies of scale. When combined, economies of scale and diseconomies of scale lead to ideal firm size theory, which states that per-unit costs decrease until they reach a certain minimum, then increase as the firm size increases further.

Economies of scale refers to the decreased per unit cost as output increases. More clearly, the initial investment of capital is diffused (spread) over an increasing number of units of output, and therefore, the marginal cost of producing a good or service decreases as production increases (note that this is only in an industry that is experiencing economies of scale)

An example will clarify. AFC is average fixed cost

If a company is currently in a situation with economies of scale, for instance, electricity, then as their initial investment of $1000 is spread over 100 customers, their AFC is \left ( \frac{1000}{100} \right ) = \$10 .

If that same utility now has 200 customers, their AFC becomes \left ( \frac{1000}{200} \right ) = \$5 ... their fixed cost is now spread over 200 units of output. In economies of scale this results in a lower average total cost.

The advantage is that "buying bulk is cheaper on a per-unit basis." Hence, there is economy (in the sense of "efficiency") to be gained on a larger scale.

Economies of scale tend to occur in industries with high capital costs in which those costs can be distributed across a large number of units of production (both in absolute terms, and, especially, relative to the size of the market). A common example is a factory. An investment in machinery is made, and one worker, or unit of production, begins to work on the machine and produces a certain number of goods. If another worker is added to the machine he or she is able to produce an additional amount of goods without adding significantly to the factory's cost of operation. The amount of goods produced grows significantly faster than the plant's cost of operation. Hence, the cost of producing an additional good is less than the good before it, and an economy of scale emerges. Economies of scale are also derived partially from learning by doing.

The exploitation of economies of scale helps explain why companies grow large in some industries. It is also a justification for free trade policies, since some economies of scale may require a larger market than is possible within a particular country — for example, it would not be efficient for Liechtenstein to have its own car maker, if they would only sell to their local market. A lone car maker may be profitable, however, if they export cars to global markets in addition to selling to the local market. Economies of scale also play a role in a "natural monopoly."

Typically, because there are fixed costs of production, economies of scale are initially increasing, and as volume of production increases, eventually diminishing, which produces the standard U-shaped cost curve of economic theory. In some economic theory (e.g., "perfect competition") there is an assumption of constant returns to scale.

[edit] Network effect

Network externalities resemble economies of scale, but they are not considered such because they are a function of the number of users of a good or service in an industry, not of the production efficiency within a business. Economies of scale external to the firm (or industry wide scale economies) are only considered examples of network externalities if they are driven by demand side economies.

[edit] Formal definitions

Formally, a production function \ F(K,L) is defined to have:

  • constant returns to scale if (for any constant a greater than 1) \ F(aK,aL)=aF(K,L)
  • increasing returns to scale if \ F(aK,aL)>aF(K,L),
  • decreasing returns to scale if \ F(aK,aL)<aF(K,L)

where K and L are factors of production, capital and labor, respectively, and a is some factor > 1.

As an example, the Cobb-Douglas functional form has constant returns to scale when the sum of the exponents adds up to one. The function is:

\ F(K,L)=AK^{b}L^{1-b}

where A > 0 and 0 < b < 1. Thus

\ F(aK,aL)=A(aK)^{b}(aL)^{1-b}=Aa^{b}a^{1-b}K^{b}L^{1-b}=aAK^{b}L^{1-b}=aF(K,L)

[edit] References

  • John Eatwell (1987). "returns to scale," The New Palgrave: A Dictionary of Economics, v. 4, pp. 165-66.
  • Joaquim Silvestre (1987). "economies and diseconomies of scale," The New Palgrave: A Dictionary of Economics, v. 2, pp. 80-84.
  • Spirros Vassilakis (1987). "increasing returns to scale," The New Palgrave: A Dictionary of Economics, v. 2, pp. 761-64.

[edit] See also

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