Solved by verified expert:Please See Attachment for clarity – All work/steps to solution must be shown Simplify the following expression so that it contains only a single exponent of x [8 points] Differentiate the following function with respect to x [8 points]: Evaluate the derivative ofat x = 2 [8 points]. [8 points] Find Y* (equilibrium output) from the following [Hint: Y=(Y1/2)2]: [8 points] Find the maximum profit and the quantity (Q) that will maximize the profit function below.Show evidence that profit is indeed maximized: [8 points] Find the price elasticity of demand of the following:[8 points total] Find the derivatives of the following by first taking the natural logs:[ points] Given the following matrices:[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? a. b. [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. [8 points] Find the values of x, y and that maximize the following utility function subject to the budget constraint: ; Find, or if it does not exist state that it does not exist: [2 points] AD’[2 points] D’C[2 points] E’D[2 points] FB’[2 points] A-1C[2 points] B-1 [8 points] Consider the following system of equations: Find x1 using Cramer’s rule.
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Instructions: Show all work
1. Simplify the following expression so that it contains only a single exponent of x [8 points].
1
[2 x 2 (3 x 2 ) 2 ]3 (4 x) 2
2. Differentiate the following function with respect to x [8 points]:
(9 x 2 2)(3x 1) 2
f ( x)
2x
3. Evaluate the derivative of
x 1
at x = 2 [8 points].
2×3
4. [8 points] Find Y* (equilibrium output) from the following [Hint: Y=(Y1/2)2]:
Y C I 0 G0
1
C 25 6Y 2
I 0 16
G0 14
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:
(Q) 13 Q 3 3Q 2 5Q 3
6. [8 points] Find the price elasticity of demand of the following:
Qd
10
P2
7. [8 points total] Find the derivatives of the following by first taking the natural logs:
a. y
3x
( x 2) 2
b. y ( x 2 3)e x
2
1
8. [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.
y (5 2x) 4 8
9. [8 points] Find the values of x, y and that maximize the following utility function subject to the
1
budget constraint: U ( 2 x 2 y 2 ) 2 ;
I 100 x 2 y
10. [ points] Given the following matrices:
A
4 0 1
1
B 2 0 0 C
3
0 2 3
2
7
E 3 0 1 F33 0
Find, or if it does not exist state that it does not exist:
1
D 4 0 2
2
a.
b.
c.
d.
e.
f.
[2 points] AD’
[2 points] D’C
[2 points] E’D
[2 points] FB’
[2 points] A-1C
[2 points] B-1
11. [8 points] Consider the following system of equations:
x1 3x 2 2 x3 24
5 x 2 x3 8
x3 6 x1
Find x1 using Cramer’s rule.
12. [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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