LMY EC2104 A+ Cheatsheet.docx - EC2104 A Cheatsheet Week 1...

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EC2104 A+ Cheatsheet Week 1: Speaking logically - P is a sufficient condition for Q (if P, then Q) - P is a necessary condition for Q (if Q, then P) - P is a necessary and sufficient condition for Q (P if and only if Q) and Models in economic analysis - The structure of a model is described by equations - The aim is to derive a set of logical conclusions that follow from the assumptions - An equation is a mathematical statement setting 2 algebraic expressions equal to one another o Definitional equations: set up an identity between 2 alternative expressions that have exactly the same meaning: o Behavioural equations: specifies the manner in which a variable behaves in response to changes in other variables C = 75 + 10Q Utility = sleep / homework o Conditional equations: states a requirement to be satisfied. The standard market model requires the equilibrium condition, which describes the pre-requisite for there to be an equilibrium in the market Quantity demanded = quantity supplied Functions of one variable - If y depends on the value of x, we might be able to say that y is a function of x, or y = f(x) - Here, f is the function. The actual symbol for the function is not important, but f and g are commonly used for generic functions. f(x) is the value that the function generates when given input x - x = independent variable, y = dependent variable - Every value of x must generate a unique value of y = f(x) for f to be a valid function. However, there can be multiple values of x that generate the same y Formal definition of a function - The domain of function f is the set of values of the argument for which the function is defined - The range of function f is the set of possible resulting values of f(x) A note on graphing functions - In economics, we generally use Cartesian coordinates, aka xy or xyz coordinates - In most graphs, the independent variables goes on the x-axis and the dependent variable goes on the y-axis - In price quantity graphs in economics, the reverse is true. Price, the independent variable, is always on the y-axis - Demand function: D(p) = 6 – 2p
- Inverse demand function: Common functions: - Polynomial functions o Linear functions o Quadratic function - Power function - Exponential function - Logarithmic function Polynomial function - - Highest power, n, is called the degree of polynomial - Depending on the degree, n, we have the following subclasses o Linear function - - Graph is a straight line with slope/gradient a and y-intercept b Market model - Suppose the market demand and supply are given by the following equations o Demand: q D = 10 – 2p o Supply: q S = -5 + 3p - Market equilibrium requires demand = supply - 10 – 2p = -5 + 3p p = 3 - When p = 3, quantity = 4
- Quadratic functions - Quadratic functions are polynomial functions of degree 2 - - Solution 1: by factoring o - Solution 2: quadratic formula o Power functions - - Three classes o r > 1: function is increasing and convex o 0 < r < 1: function is increasing and concave o r < 0: function is decreasing and convex a = 1, r > 1 increasing and convex, global minimum point
a = 1, 0 < r < 1 increasing and concave, there will be a global