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ECON1003 Lecture review slides
Weeks 1-7
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Slope:
Equation of a straight line:
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Function notation:
Inverse functions:
Demand:
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Cost
e.g.
revenue = price × quantity
profit = revenue – cost
Revenue and profit:
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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
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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
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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
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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:
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Logarithmic functions:
(product rule)
(quotient rule)
(power rule)
(change of base rule)
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Series:
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Simple interest:
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Compound interest:
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Interest compounded several times per year:
Continuous compounding:
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Reducing balance depreciation
Net present value
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Annuities
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Debt repayments
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Power rule:
Special derivatives:
= *→ + = * = ln → + = 1
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General differentiation rules:
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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: =
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Quotient rule:
Higher derivatives:
And the derivative as: !"!# = %&!'&%!%"Note: this is equivalent to thinking of y as: =
&%
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Sketching functions:
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Turning points:
Points of inflection:
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Optimisation:
Finding the global maximum:
global
maximum
local
maximum
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Marginal and average revenue:
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Marginal and average cost:
=
= +
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Elasticity of demand:
Constant elasticity of demand: