Question

Bordered Hessian element

The Lagrangian is L=ln(x+y^2) -z^3/(3*y) -x*y +λ*(x*z +3*x^2*y -r), where r is a parameter (a known real number). Here, ln denotes the natural logarithm, ^ power, * multiplication, / division, + addition, - subtraction. The border is at the top and left of the Hessian. The variables are ordered λ,x,y,z.

Find the last element in the second row of the bordered Hessian at the point (λ,x,y,z) =(0.11, 0, 2440, 0.01167). This point need not be stationary and you do not have to solve first order conditions to calculate the bordered Hessian. Write the element as a number in decimal notation with at least two digits after the decimal point. No fractions, spaces or other symbols.

Answer #1

Maximise the utility u=5*ln(x-1)+ln(y-1) by
choosing the consumption bundle (x,y) subject to the budget
constraint x+y=10. Here, ln denotes the natural logarithm, *
multiplication, / division, + addition, - subtraction. Ignore the
nonnegativity constraints x,y>=0.
Write the quantity x in the utility-maximising
consumption bundle (x,y). Write the answer as a number in decimal
notation with at least two digits after the decimal point. No
fractions, spaces or other symbols.

Implicit derivative 1
Find y’(x) from F(x,y) =2^(-x -y) *ln(3*x +3*y) -x
-y +(x+y)^3 =20 at (x,y)=(1, 1.824). Write y’(1) at this point as a
number in decimal notation with at least two digits after the
decimal point. No fractions, spaces or other symbols. Hint: the
simple solution does not even require taking derivatives.

The problem is to maximise utility u(x, y) =2*x +y
s.t. x,y ≥ 0 and p*x + q*y ≤ w, where p=13.4 and q=3.9 and w=1.
Here, * denotes multiplication, / division, + addition, -
subtraction. The solution to this problem is denoted (x_0, y_0)
=(x(p, q, w), y(p, q, w)). The solution is the global max.
Find ∂u(x_0,y_0)/∂p evaluated at the parameters
(p, q, w) =(13.4, 3.9, 1). Write the answer as a number in decimal
notation with at...

The profit of a monopolist from producing
quantities x,y and selling these in two markets with linear demand
curves is x*(9-x)+y*(1-y)-(x+y)^2. Here, ^ denotes power, *
multiplication, / division, + addition, - subtraction. The
monopolist chooses nonnegative quantities to maximise profit. Now
one of these constraints binds.
Find the quantity x that the monopolist sells in
the first market. Write the answer as a number in decimal notation
with at least two digits after the decimal point. No fractions,
spaces...

The profit of a monopolist from producing
quantities x,y and selling these in two markets with linear demand
curves is x*(10-x)+y*(9-y)-(x+y)^2. Here, ^ denotes power, *
multiplication, / division, + addition, - subtraction. The
monopolist chooses nonnegative quantities to maximise profit.
Assume the nonnegativity constraints do not bind.
Find the quantity x that the monopolist sells in
the first market. Write the answer as a number in decimal notation
with at least two digits after the decimal point. No fractions,...

The profit of a monopolist from producing
quantities x,y and selling these in two markets with linear demand
curves is x*(10-x)+y*(9-y)-(x+y)^2. Here, ^ denotes power, *
multiplication, / division, + addition, - subtraction. The
monopolist chooses nonnegative quantities to maximise profit.
Assume the nonnegativity constraints do not bind.
Find the quantity x that the monopolist sells in
the first market. Write the answer as a number in decimal notation
with at least two digits after the decimal point. No fractions,...

Social planner’s problem, two constraints 2
Five units of good 1 and five units of good 2 are
available. Consumption of good 1 is denoted x_1 and consumption of
good 2 by x_2. There are two agents: A and B. Their utility
functions are u_A(x_1, x_2) = ln(x_1) +a*ln(x_2) and u_B(x_1, x_2)
= x_1 +b*x_2, where a=1.35 and b=0.86. Here, ln denotes the natural
logarithm, * multiplication, + addition.
Maximize u_A subject to the constraints u_B=1 and
that each agent’s...

Social planner’s problem, two constraints 2
Five units of good 1 and five units of good 2 are
available. Consumption of good 1 is denoted x_1 and consumption of
good 2 by x_2. There are two agents: A and B. Their utility
functions are u_A(x_1, x_2) = ln(x_1) +a*ln(x_2) and u_B(x_1, x_2)
= x_1 +b*x_2, where a=1.35 and b=0.86. Here, ln denotes the natural
logarithm, * multiplication, + addition.
Maximize u_A subject to the constraints u_B=1 and
that each agent’s...

Show the vectors [x y z] where xyz=0 is a subspace V of R^3. is it
closed under additon? is it closed under scalar
multiplication?

For f(x,y)=ln(x^2−y+3). -> Find the domain
and the range of the function z=f(x,y).
-> Sketch the domain, then
separately sketch three distinct level curves.
-> Find the linearization of
f(x,y) at the point
(x,y)=(4,18).
-> Use this linearization to determine the
approximate value of the function at the point (3.7,17.7).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 13 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago