MATH

• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Demand curve shifting right

  Increases the equilibrium price and quantity
• If you add up marginal utility for each unit you get total utility
• Whole (natural) numbers


  Numbers that appear as a result of counting single objects
• Addition


  An operation of finding the sum of some numbers
• Subtraction


  An operation of finding an addend by a sum and another addend
• Multiplication


  An operation of repeating a multiplicand as an addend a certain number of times
• Division


  An operation of finding one of the factors by a product and another factor
• Raising to a power


  Repeating a number as a factor a certain number of times
• Extraction of a root


  Finding the base of a power by the power and its exponent
• Order of operations


  Brackets

  1. Raising to a power and extraction of a root
  2. Multiplication and division
  3. Addition and subtraction
• Commutative law of addition

  • The sum doesn't change when the addends are rearranged
• Commutative law of multiplication


  • The product doesn't change when the factors are rearranged
• Associative law of addition

  • The sum doesn't depend on the grouping of the addends
• Associative law of multiplication


  • The product doesn't depend on the grouping of the factors
• Distributive law of multiplication over addition


  • (m + n) * k = m*k + n*k
• Prime numbers


  Numbers divisible only by 1 and themselves
• Composite numbers


  Numbers with factors other than 1 and themselves
• Factorization


  Expressing a composite number as a product of its prime factors
• Greatest common factor (GCF)


  The largest number that divides each of the given numbers without a remainder
• Finding the GCF


  Express each number as a product of its prime factors

  1. Write the powers of the prime factors
  2. Take the least power of each common factor
  3. Multiply the least powers
• Least common multiple (LCM)


  The smallest positive integer that is divisible by each of the given numbers
• Finding the LCM


  Express each number as a product of its prime factors

  1. Write the powers of the prime factors
  2. Take the greatest power of each factor
  3. Multiply the greatest powers
• 504


  2 · 2 · 2 · 3 · 3 · 7 = 23 · 32 · 71
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• Divisibility by 2


  A number is divisible by 2, if its last digit is 0 or is divisible by 2. Numbers, which are divisible by 2 are called even numbers. Otherwise, numbers are called odd numbers.
• Divisibility by 4


  A number is divisible by 4, if its two last digits are zeros or they make a two-digit number, which is divisible by 4.
• Divisibility by 8


  A number is divisible by 8, if its three last digits are zeros or they make a three-digit number, which is divisible by 8.
• Divisibility by 3 and by 9

  A number is divisible by 3, if a sum of its digits is divisible by 3. A number is divisible by 9, if a sum of its digits is divisible by 9.
• Divisibility by 6


  A number is divisible by 6, if it is divisible by 2 and by 3.
• Divisibility by 5


  A number is divisible by 5, if its last digit is 0 or 5.

  
• Divisibility by 25


  A number is divisible by 25, if its two last digits are zeros or they make a number, which is divisible by 25.
• Divisibility by 10


  A number is divisible by 10, if its last digit is 0.
• Divisibility by 100


  A number is divisible by 100, if its two last digits are zeros.