equation_sheet

equation_sheet - = ax n dF x dx = nax n& 1 F x = a ln x...

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Equation sheet Marginal rate of substitution: MRS x;y = MU x MU y Budget constraint: p x Q x + p y Q y = I Expected value and expected utility: Suppose that a lottery X can take values of X 1 ; X 2 ; :::; X n with associated probabilities p 1 ; p 2 ; :::; p n : Then the expected value of X is given by E ( X ) = p 1 X 1 + p 2 X 2 + ::: + p n X n ; while the expected utility from the lottery X is given by E ( u ( X )) = p 1 u ( X 1 ) + p 2 u ( X 2 ) + ::: + p n u ( X n ) : Marginal rate of technical substitution: MRTS L;K = MP L MP K Isocost line: C = rK + wL + F Total revenue = Total consumer expenditure: P ( Q ) Q Derivatives F ( x ) = a + bx ! dF ( x ) dx = b F ( x ) = a + bx + cx 2 ! dF ( x ) dx = b + 2 cx F ( x
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Unformatted text preview: ) = ax n ! dF ( x ) dx = nax n & 1 F ( x ) = a ln x ! dF ( x ) dx = a x Basic manipulations & x y ± a b = ² y x ³ & a b = 1 ( y x ) a b x a x b = x a + b x a x b = x a & b x a b = y , x = y b a ln x + ln y = ln( xy ) ln x & ln y = ln( x=y ) a ln x = ln x a Roots of a quadratic equation Suppose you want to solve all x for which ax 2 + bx + c = 0 : The solution is given by & b ± p b 2 & 4 ac 2 a 1...
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