diminishing returns

Examples of diminishing returns in the following topics:

• The Law of Diminishing Returns

  • The law of diminishing returns states that adding more of one factor of production will at some point yield lower per-unit 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 .
  • The law of diminishing returns does not imply that adding more of a factor will decrease the total production, a condition known as negative returns, though in fact this is common.
  • Both marginal cost and average cost are U-shaped due to first increasing, and then diminishing, returns.

• 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 .
  • 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.
  • Identify the three types of returns to scale and describe how they occur

• 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 2Qdiminishing 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.

• 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.
  • Under such circumstances diminishing marginal returns are inevitable at some level of production.
  • This table shows hypothetical returns and marginal product of labor.

• Setting the Right Goals

  • This is also supported by the idea of diminishing returns, which posits that for each unit of investment (be it a minute of time or a dollar) into a given process, less output will be produced.
  • Therefore, combining a series of small objectives (processes) will be more motivating, causing less output to be lost to diminishing returns over time.
  • TMT (which draws from these two theories of time perspective and diminishing returns) and SMART goal setting together therefore tell us that to maximize motivation and therefore output, managers should divide projects into several more immediate, specific, and realistic sub-goals.

• Optimal Quantity of a Public Good

  • Due to the law of diminishing marginal utility, the demand curve is downward sloping.
  • Because of the law of diminishing returns, the marginal cost increases as the quantity of the good produced increases.

• Commercial Banks

  • Credit Risk – Risk that a borrower may not return the entirety of the payment owed.
  • Operational Risk – Risk that an operational issue will diminish returns.

• Implications for Variance

  • A fundamental justification for asset allocation (or Modern Portfolio Theory) is the notion that different asset classes offer returns that are not perfectly correlated, hence diversification reduces the overall risk in terms of the variability of returns for a given level of expected return.
  • Expectations for return are often derived in the same way.
  • This is why it's possible to reduce variance without compromising expected return by diversifying.
  • Diversifying asset classes can reduce portfolio variance without diminishing expected return

• Return on Common Equity

  • Return on equity (ROE) measures how effective a company is at using its equity to generate income and is calculated by dividing net profit by total equity.
  • Return on equity (ROE) is a financial ratio that measures how good a company is at generating profit.
  • Also note that the product of net margin and asset turnover is return on assets, so ROE is ROA times financial leverage.
  • Financial leverage benefits diminish as the risk of defaulting on interest payments increases.
  • The return on equity is a ratio of net income to equity.

• Solutions to Chapter 5 Exercises

  • Notice that a half-diminished seventh can be (and sometimes is) written as it is here, as a minor seventh with flat five.
  • The supertonic (ii) is diminished.
  • If the seventh scale note is raised, the III chord becomes augmented, and and the vii chord becomes a diminished chord (based on the sharp vii rather than the vii).
  • The augmented III chord would not be particularly useful in the key, but, as mentioned above, a diminished seventh chord based on the leading tone (here, the sharp vii) is sometimes used in cadences.
  • In this very common progression, the dominant seventh of the dominant (which requires an accidental) makes the dominant feel like a very strong resting point, and the piece will continue on in the dominant key for a while, before returning to the tonic key.