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Product code:-Math-QA56

  1. Simplify the following expression so that it contains only a single exponent of x [8 points]
  2. Differentiate the following function with respect to x [8 points]
  3. Evaluate the derivative of    at x = 2 [8 points]
  4. [8 points] Find Y* (equilibrium output) from the following [Hint: Y=(Y1/2)2]           
  5.  [8 points] Find the maximum profit and the quantity (Q) that will maximize the profit function below.  Show evidence that profit is indeed maximized:                 
  6.  [8 points] Find the price elasticity of demand of the following:                
  7.  [8 points total] Find the derivatives of the following by first taking the natural logs:

a.  b.

  1.  [8 points] Find the critical values of the following and use the Nth derivative test to determine if the values determine a maximum, minimum or inflection point.             
  2.  [8 points] Find the values of x, y and that maximize the following utility function subject to the budget constraint:   ;   

10.[ points] Given the following matrices:

Find, or if it does not exist state that it does not exist:

  1. [2 points] AD’
  2. [2 points] D’C
  3. [2 points] E’D
  4. [2 points] FB’
  5. [2 points] A-1C
  6. [2 points] B-1
  1.  [8 points] Consider the following system of equations:

Find x1 using Cramer’s rule.

  1.  [8 points]  Assume a stock price is a positive function of earnings per share[E], a negative function of bond interest rate [i], and a positive function of inflation [π] and GDP [Y].  The function is denoted:  S = S(E, i, π, Y).  To complicate matters GDP is a negative function of bond interest rate.  Write the total differential equation.  What can you say about the total derivative of S with respect to the bond interest rate?







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Simplify the following expression so that it contains only a single exponent of x. Solution (1): The expression can be written as ["2" "x" ^("-" "1" /"2" ) ("3" "x" ^"2" )^"2" ]^"3" /("4x" )^"2" = (729x^(17/2))/2 The simplified expression is(729x^(17/2))/(2 )

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