The University of Sydney Page 1 ECON1003 Lecture review slides Weeks 1-7 The University of Sydney Page 2 Slope: Equation of a straight line: The University of Sydney Page 3 Function notation: Inverse functions: Demand: The University of Sydney Page 4 Cost e.g. revenue = price × quantity profit = revenue – cost Revenue and profit: The University of Sydney Page 5 Elasticity of demand: Definition of elastic demand: For a linear demand function P = a – bQ, elasticity of demand is: ! = 1 Demand is elastic if: ! < 1 Demand is unit-elastic if: ! = 1 Demand is inelastic if: ! > 1 The University of Sydney Page 6 Elasticity of supply: Definition of elastic supply: For a linear supply function P = c + dQ, elasticity of supply is: ” = 1 Supply is elastic if: ” > 1 Supply is unit-elastic if: ” = 1 Supply is inelastic if: ” < 1 The University of Sydney Page 7 Quadratic equations: Sketching quadratic functions: Vertical translation (moves the parabola up & down): = # ± Horizontal translation (moves the parabola left & right): = ( ± )# The number of solutions depends on the sign of b2 – 4ac The University of Sydney Page 8 Exponential functions: When you multiply two exponentials with the same base, you add the powers: $× % = $&% When you divide two exponentials with the same base, you subtract the powers: '!'" = $(% When you have an exponential to the power of another, you multiply the powers: $ ) = $) Exponential rules: The University of Sydney Pa
ge 9 Logarithmic functions: (product rule) (quotient rule) (power rule) (change of base rule) The University of Sydney Page 10 Series: The University of Sydney Page 11 Simple interest: The University of Sydney Page 12 Compound interest: The University of Sydney Page 13 Interest compounded several times per year: Continuous compounding: The University of Sydney Page 14 Reducing balance depreciation Net present value The University of Sydney Page 15 Annuities The University of Sydney Page 16 Debt repayments The University of Sydney Page 17 Power rule: Special derivatives: = *→ + = * = ln → + = 1 The University of Sydney Page 18 General differentiation rules: The University of Sydney Page 19 Chain rule: Consider the example: = 2 + 4 # → = 2 × 2 = 4(2 + 4) Product rule: And the derivative as: !”!# = $ + $Note: this is equivalent to thinking of y as: = The University of Sydney Page 20 Quotient rule: Higher derivatives: And the derivative as: !”!# = %&!’&%!%”Note: this is equivalent to thinking of y as: = &% The University of Sydney Page 21 Sketching functions: The University of Sydney Page 22 Turning points: Points of inflection: The University of Sydney Page 23 Optimisation: Finding the global maximum: global maximum local maximum The University of Sydney Page 24 Marginal and average revenue: The University of Sydney Page 25 Marginal and average cost: = = + The University of Sydney Page 26 Elasticity of demand: Constant elasticity of demand: