rate of change

Examples of rate of change in the following topics:

• Differentiation and Rates of Change in the Natural and Social Sciences

  • This rate of change is called the derivative of $y$ with respect to $x$.
  • Rates of change occur in all sciences and across all disciplines.
  • Economists study the rate of change of gross domestic product and social scientists the rate in which populations vote in a specific area.
  • Accountants study the rate of change of production and supplies, and how any change can affect cost and profit.
  • Give examples of differentiation, or rates of change, being used in a variety of academic disciplines

• Related Rates

  • Related rates problems involve finding a rate by relating that quantity to other quantities whose rates of change are known.
  • In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.
  • The rate of change is usually with respect to time.
  • The volume is changing at a rate of 2 cubic feet per minute.
  • The relevant formulas and pieces of information are the volume of the balloon, the rate of change of the volume, and the radius.

• The Equilibrium Interest Rate

  • Consumption: the level of consumption (and changes in that level) affect the demand for money.
  • Changes in expectations will therefore affect the equilibrium interest rate.
  • Taxes: changes in the tax code affect the willingness of actors to invest or consume, which can therefore change the demand for money.
  • Interest rates fluctuate over time as the result of numerous factors.
  • Use the concept of market equilibrium to explain changes in the interest rate and money supply

• Comparing Marginal and Average Tax Rates

  • An average tax rate is the ratio of the total amount of taxes paid, T, to the total tax base, P, (taxable income or spending), expressed as a percentage.
  • The marginal tax rate is sometimes defined as the tax rate that applies to the last (or next) unit of the tax base (taxable income or spending), it is in effect, the tax percentage on the highest dollar earned.
  • Broadly, the marginal tax rate equals the change in taxes, divided by the change in tax base, expressed as a percentage.
  • A proportional tax is a tax imposed so that the tax rate is fixed, with no change as the taxable base amount increases or decreases.
  • "Proportional" describes a distribution effect on income or expenditure, referring to the way the rate remains consistent (does not progress from "low to high" or "high to low" as income or consumption changes), where the marginal tax rate is equal to the average tax rate.

• Rate

  • Rate is the speed of speaking in words per minute from slow to fast, with normal rate averaging about 125 words per minute.
  • Rate is part of the paralanguage of speech along with loudness and pitch.
  • You can vary the rate depending on the emotions you are feeling or the type of message you are communicating.
  • When speaking you want to speak at a varied rate so that you can emphasize important parts of your message.
  • You also want to change the rate for the mood or emotion of the message and the occasion.

• NPV Profiles

  • Thus, when discount rates are large, cash flows further in the future affect NPV less than when the rates are small.
  • When the value of the outflows is greater than the inflows, the NPV is negative.
  • A special discount rate is highlighted in the IRR, which stands for Internal Rate of Return.
  • And it is the discount rate at which the value of the cash inflows equals the value of the cash outflows.
  • The NPV Profile graphs how NPV changes as the discount rate used changes.

• The Interest Rate Risk

  • Banks experience an interest-rate risk, when changes in the interest rates cause the banks' profit to fluctuate.
  • We show an example of a bank's balance sheet below:
  • When the interest rate varies, these items change almost immediately.
  • On the other hand, the fixed-rate assets and liabilities are not sensitive to interest rate changes.
  • Third, the high volatility of interest rates during the 1980s contributed to the creation of new financial instrument, such as the floating-rate debt.

• Tax Rate

  • The tax rate is the amount of tax expressed as a percentage.
  • An average tax rate is the ratio of the amount of taxes paid to the tax base (taxable income or spending).
  • A marginal tax rate is the tax rate that applies to the last dollar of the tax base (taxable income or spending) and is often applied to the change in one's tax obligation as income rises.
  • For an individual, this rate can be determined by increasing or decreasing the income earned or spent and calculating the change in taxes payable.
  • It may be calculated by noting how tax changes with changes in pre-tax income, rather than with taxable income.

• Macroeconomic Factors Influencing the Interest Rate

  • Taylor explained the rule of determining interest rates using three variables: inflation rate, GDP growth, and the real interest rate.
  • An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender in the market.
  • In economics, a Taylor rule is a monetary-policy rule that stipulates how much the Central Bank should change the nominal interest rate in response to changes in inflation, output, or other economic conditions.
  • According to Taylor's original version of the rule, the nominal interest rate should respond to divergences of actual inflation rates from target inflation rates and of actual Gross Domestic Product (GDP) from potential GDP:
  • In this equation, it is the target short-term nominal interest rate (e.g., the federal fund rates in the United States), πt is the rate of inflation as measured by the GDP deflator, π*t is the desired rate of inflation, r*t is the assumed equilibrium real interest rate, yt is the logarithm of real GDP, and y*t is the logarithm of potential output, as determined by a linear trend.

• The Discount Rate

  • The Fed makes loans to depository institutions and charges different discount rates for each of discount windows.
  • The discount rate charged for primary credit (the primary credit rate) is set above the usual level of short-term market interest rates.
  • The discount rate for seasonal credit is an average of selected market rates.
  • Discount rates are established by each reserve bank's board of directors, subject to the review and determination of the Federal Reserve System's Board of Governors.
  • The discount rates for the three lending programs are the same across all reserve banks except on days around a change in the rate.