increasing returns to scale

Examples of increasing returns to scale in the following topics:

• Economies and Diseconomies of Scale

  • Increasing, constant, and diminishing returns to scale describe how quickly output rises as inputs increase.
  • Returns to scale explains how the rate of increase in production is related to the increase in inputs in the long run.
  • There are three stages in the returns to scale: increasing returns to scale (IRS), constant returns to scale (CRS), and diminishing returns to scale (DRS).
  • Returns to scale vary between industries, but typically a firm will have increasing returns to scale at low levels of production, decreasing returns to scale at high levels of production, and constant returns to scale at some point in the middle .
  • The final stage, diminishing returns to scale (DRS) refers to production for which the average costs of output increase as the level of production increases.

• Few Sellers

  • An oligopoly - a market dominated by a few sellers - is often able to maintain market power through increasing returns to scale.
  • One source of this power is increasing returns to scale.
  • Increasing returns to scale is a term that describes an industry in which the rate of increase in output is higher than the rate of increase in inputs.
  • Cell phone companies have increasing returns to scale, which leads to a market dominated by only a few firms.
  • Explain how increasing returns to scale will cause a higher prevalence of oligopolies

• Defining the Production Function

  • This is also known as diminishing returns to scale - increasing the quantity of inputs creates a less-than-proportional increase in the quantity of output.
  • If it weren't for diminishing returns to scale, supply could expand without limits without increasing the price of a good.
  • If a firm has a production function Q=F(K,L) (that is, the quantity of output (Q) is some function of capital (K) and labor (L)), then if 2Qincreasing marginal costs and diminishing returns to scale.
  • Similarly, if 2Q>F(2K,2L), there are increasing returns to scale, and if 2Q=F(2K,2L), there are constant returns to scale.
  • From this production function we can see that this industry has constant returns to scale - that is, the amount of output will increase proportionally to any increase in the amount of inputs.

• Long Run Supply Decisions

  • This period of supply is known as "increasing returns to scale," because a proportional increase in resources yields a greater proportional increase in output.
  • This period of supply is known as "decreasing returns to scale," because a proportional increase in resources yields a smaller proportional increase in its amount in output.
  • Between these two periods is the "constant returns to scale," where a proportion increase in resources yields an equal proportional increase in the amount of output.
  • In the early stages of the market, where only one or a few firms are producing goods, the market experiences increasing returns to scale, similar to what an individual firm would experience.
  • Eventually the market reaches a state of constant returns to scale.

• The Law of Diminishing Returns

  • In economics, diminishing returns (also called diminishing marginal returns) is the decrease in the marginal output of a production process as the amount of a single factor of production is increased, while the amounts of all other factors of production stay constant.
  • However, as marginal costs increase due to the law of diminishing returns, the marginal cost of production will eventually be higher than the average total cost and the average cost will begin to increase.
  • The typical LRAC curve is also U-shaped but for different reasons: it reflects increasing returns to scale where negatively-sloped, constant returns to scale where horizontal, and decreasing returns (due to increases in factor prices) where positively sloped.
  • Both marginal cost and average cost are U-shaped due to first increasing, and then diminishing, returns.
  • Average cost begins to increase where it intersects the marginal cost curve.

• Production and Cost in the Long-run

  • The terms "economies of scale," "increasing returns to scale," "constant returns to scale," "decreasing returns to scale" and "diseconomies of scale" are frequently used.
  • Conceptually, returns to scale implies that all inputs are variable.
  • When α+β = 1, the production process demonstrates "constant returns to scale. " If L and K both increased by 10%, output (Q) would also increase by 10%.
  • When α+β > 1, production has increasing returns.
  • When α+β < 1, decreasing returns are said to exist.

• Marginal Product of Labor (Physical)

  • The second column shows total production with different quantities of labor, while the third column shows the increase (or decrease) as labor is added to the production process.
  • The law of diminishing marginal returns ensures that in most industries, the MPL will eventually be decreasing.
  • The law states that "as units of one input are added (with all other inputs held constant) a point will be reached where the resulting additions to output will begin to decrease; that is marginal product will decline. " The law of diminishing marginal returns applies regardless of whether the production function exhibits increasing, decreasing or constant returns to scale.
  • Under such circumstances diminishing marginal returns are inevitable at some level of production.
  • This table shows hypothetical returns and marginal product of labor.

• Harmonic and Melodic Minor Scales

  • All of the scales above are natural minor scales.
  • Harmonies in minor keys often use this raised seventh tone in order to make the music feel more strongly centered on the tonic.
  • (Please see Beginning Harmonic Analysis for more about this. ) In the melodic minor scale, the sixth and seventh notes of the scale are each raised by one half step when going up the scale, but return to the natural minor when going down the scale.
  • Melodies in minor keys often use this particular pattern of accidentals, so instrumentalists find it useful to practice melodic minor scales.
  • Listen to the differences between the natural minor (http://cnx.org/content/m10856/latest/tonminnatural.mp3), harmonic minor (http://cnx.org/content/m10856/latest/tonminharmonic.mp3), and melodic minor (http://cnx.org/content/m10856/latest/tonminmelodic.mp3) scales.

• Production Orientation

  • Industrial firms focused on production orientation models that exploited economies of scale to reach maximum efficiency at the lowest cost.
  • For example, companies that focus on increasing economies of scale will see reductions in unit cost as the size of facilities and the usage levels of other inputs increase.
  • In theory, such organizations can ramp up production until the minimum efficient scale is reached.
  • Some common sources of economies of scale include:
  • Technological - taking advantage of returns to scale in the production function

• Solving Problems with Logarithmic Graphs

  • Some functions with rapidly changing shape are best plotted on a scale that increases exponentially such as a logarithmic graph.
  • The fact that the rate is ever-increasing (and steeply so) means that changing scale (scaling the axes by 5, 10 or even 100) is of little help in making the graph easier to interpret.
  • A logarithmic scale will start at a certain power of 10, and with every unit will increase by a power of 10.
  • Thus, if one wanted to convert a linear scale (with values $0-5$ to a logarithmic scale, one option would be to replace $1,2,3,4$ and 5 with $0.001,0.01,0.1,1,10$ and $100$, respectively.
  • Between each major value on the logarithmic scale, the hashmarks become increasingly closer together with increasing value.