constant returns to scale

Examples of constant 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.
  • 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 .
  • If output changes proportionally with all the inputs, then there are constant returns to scale.
  • This graph shows that as the output (production) increases, long run average total cost curve decreases in economies of scale, constant in constant returns to scale, and increases in diseconomies of scale.

• 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 2Qreturns 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

  • 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.
  • A long-run supply curve connects the points of constant returns to scales of a markets' short-run supply curves. ; the bottom of each short-term supply curve's "u."
  • Eventually the market reaches a state of constant returns to scale.
  • How long this period of constant returns is varies by industry.
  • Agriculture has a longer period of constant returns while technology has shorter.

• Marginal Product of Labor (Physical)

  • 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.
  • The key factor is that the variable input is being changed while all other factors of production are being held constant.
  • Under such circumstances diminishing marginal returns are inevitable at some level of production.
  • This table shows hypothetical returns and marginal product of labor.

• 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, decreasing returns are said to exist.
  • In Figure V.9 economies of scale are said to exist up to output QLC.

• 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.
  • The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant ("ceteris paribus"), will at some point yield lower per-unit returns .
  • 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.

• 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.
  • Most industries exhibit different types of returns to scale in different ranges of output.
  • 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

• Production

  • Alternatively, a firm may build a series of plants to achieve constant or even increasing returns.
  • In this simplified version, each production function or process is limited to increasing, constant or decreasing returns to scale over the range of production.
  • In more complex production processes, "economies of scale" (increasing returns) may initially occur.
  • Eventually, decreasing returns or "diseconomies of scale" may be expected when the plant size (fixed input) becomes "too large."
  • This more complex production function is characterized by a long run average cost (cost per unit of output) that at first declines (increasing returns), then is horizontal (constant returns) and then rises (decreasing returns).

• 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.

• Solving Problems with Logarithmic Graphs

  • 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.
  • That means that if we want to graph a function that is unwieldy on a linear scale we can use a logarithmic scale on each axis and retain the properties of the graph while at the same time making it easier to graph.
  • The primary difference between the logarithmic and linear scales is that, while the difference in value between linear points of equal distance remains constant (that is, if the space from $0$ to $1$ on the scale is $1$ cm on the page, the distance from $1$ to $2$, $2$ to $3$, etc., will be the same), the difference in value between points on a logarithmic scale will change exponentially.
  • 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.
  • A key point about using logarithmic graphs to solve problems is that they expand scales to the point at which large ranges of data make more sense.