multiplier

Examples of multiplier in the following topics:

• The Multiplier Effect

  • When the fiscal multiplier exceeds one, the resulting impact on the national income is called the multiplier effect.
  • In economics, the fiscal multiplier is the ratio of change in the national income in relation to the change in government spending that causes it (not to be confused with the monetary multiplier).
  • When the fiscal multiplier exceeds one, the resulting impact on the national income is called the multiplier effect.
  • Although the multiplier effect usually measures values of one, there have been cases where multipliers of less than one are measured.
  • During recessions, the government can use the multiplier effect in order to stimulate the economy.

• Multiplying Vectors by a Scalar

  • Multiplying a vector by a scalar changes the magnitude of the vector but not the direction.
  • A scalar, however, cannot be multiplied by a vector.
  • To multiply a vector by a scalar, simply multiply the similar components, that is, the vector's magnitude by the scalar's magnitude.
  • Multiplying vectors by scalars is very useful in physics.
  • (ii) Multiplying the vector $A$ by 3 triples its length.

• Fiscal Policy and the Multiplier

  • Fiscal policy can have a multiplier effect on the economy.
  • In addition to the spending multiplier, other types of fiscal multipliers can also be calculated, like multipliers that describe the effects of changing taxes.
  • The size of the multiplier effect depends upon the fiscal policy.
  • The multiplier on changes in government purchases, 1/(1 - MPC), is larger than the multiplier on changes in taxes, MPC/(1 - MPC), because part of any change in taxes or transfers is absorbed by savings.
  • Describe the effects of the multiplier beyond its relevance to fiscal policy

• Multiplying Algebraic Expressions

  • Note that, when multiplying two monomials together, unlike terms can be multiplied, which differs from the addition of algebraic expressions.
  • When multiplying monomials, their integers are multiplied.
  • A monomial can be multiplied by a polynomial of any size.
  • The monomial should be multiplied by each term in the polynomial separately.
  • Following the FOIL method, multiply the first, outside, inside, and last terms:

• Sums, Differences, Products, and Quotients

  • In this case, two unlike terms (3 and x) could be multiplied.
  • If the terms both contain the same variables, their exponents are added together and their multipliers are multiplied.
  • Multiplying binomials and trinomials is more complicated, and follows the FOIL method.
  • Dividing equations uses similar theory as multiplying, since division is the equivalent of multiplying by the inverse.
  • The general form of the FOIL method using only variables as the potential multipliers.

• Unit Vectors and Multiplication by a Scalar

  • Multiplying a vector by a scalar is the same as multiplying its magnitude by a number.
  • In addition to adding vectors, vectors can also be multiplied by constants known as scalars.
  • When multiplying a vector by a scalar, the direction of the vector is unchanged and the magnitude is multiplied by the magnitude of the scalar .
  • (i) Multiplying the vector A by 0.5 halves its length.
  • (ii) Multiplying the vector A by 3 triples its length.

• Fiscal Levers: Spending and Taxation

  • However, the tax multiplier is smaller than the spending multiplier.
  • The money that is saved does not contribute to the multiplier effect .
  • The government spending multiplier is always positive.
  • In contrast, the tax multiplier is always negative.
  • The tax multiplier is smaller than the government expenditure multiplier because some of the increase in disposable income that results from lower taxes is not just consumed, but saved.

• Simplifying, Multiplying, and Dividing

  • Rational expressions can be multiplied and divided in a similar manner to fractions.
  • Recall that when two fractions are multiplied together, their numerators are multiplied to yield the numerator of their product, and their denominators are multiplied to yield the denominator of their product.
  • Following the rule for multiplying fractions, simply multiply their respective numerators and denominators:
  • Notice that we multiplied the numerators together and the denominators together, but we did not multiply the numerator by the denominator or vice-versa.
  • We follow the same rules to multiply two rational expressions together.

• Multiplication of Complex Numbers

  • Two complex numbers can be multiplied to give another complex number.
  • Thus, we multiply $a+bi$ and $c+di$ by writing $(a+bi)(c+di)$ and multiplying the First terms $a$ and $c$, and then the Outer terms $a$ and $di$ and then the Inner terms $bi$ and $c$ and then the Last terms $bi$ and $di$.
  • Similarly, a number with an imaginary part of $0$ is easily multiplied as this example shows: $(2+0i)(4-3i)=2(4-3i)=8-6i.$
  • Note that it is possible for two nonreal complex numbers to multiply together to be a real number.

• The Money Multiplier in Theory

  • The money multiplier measures the maximum amount of commercial bank money that can be created by a given unit of central bank money.
  • In order to understand the money multiplier, it's important to understand the difference between commercial bank money and central bank money.
  • The money multiplier measures the maximum amount of commercial bank money that can be created by a given unit of central bank money.
  • We can derive the money multiplier mathematically, writing M for commercial bank money (loans), R for reserves (central bank money), and RR for the reserve ratio.
  • If banks instead lend less than the maximum, accumulating excess reserves, then commercial bank money will be less than central bank money times the theoretical multiplier.