X y 6step 1 the lagrangian function is set asstep 2 take

Reference no: EM13354721

x +y = 6

Step 1: The Lagrangian function is set as:

Step 2: Take the first order partial derivatives of the Lagrangian and set them to 0 (corresponding to the maximum point)

What does the value of A* tell you?

2. Let's generalize the problem and solve again.

Max z = xy

s.t. x +y = Q

Step 1: The Lagrangian function is set as:

Step 2: Take the first order partial derivatives of the Lagrangian and set them to 0 (corresponding to the maximum point)

What does the value of A* tell you?

2 Consumer Demand

Gilbert Grape gets enjoyment only from consuming Bordeaux wines and organic yogurt.

Gilbert's preference are represented by the following utility function

U(x, y) = x^2/3/y^1/³

Where x is the consumption of Bordeaux and y is the consumption of yogurt.

a) Use the power function rule for taking a derivative (i.e. finding a slope!) to confirm that Gilbert's income M = $300. The prices of x and yare as follows:

Gilbert's income M = $300. The prices of x and yare as follows:

Px = $20/bottle

Py = $4/ container

c) What is the slope of the budget line? Does the slope of the budget line depend on consumer preferences? Why or why not'?

d) Using your expression for the marginal rate of substitution, find the combination of x and y for which

• the slope of the indifference curve equals the slope of budget line and • Gilbert spends his entire budget on x and y, that is 20x +4y = 300

HINT: Answering this sub-question involves solving two equations for two unknowns.

Make sure that you have Esteban Clavell's consumer theory handout, posted to the website. Find the pair of demand functions at the bottom of page 2:

e) For the income and prices given above, use in 3 and 4 to solve for the optimum values of x* and y*.

f) Compare your answer from part (d) and part (e). Explain why they are the same or different.

g) Provide the Gilbert's choices of both Bordeaux and yogurt under the following circumstances (Consider each separately):

1. Gilbert's income increases to $600.

11. The price of Bordeaux increases to $40.

Ill. Gilbert finds a new brand of yogurt that he absolutely loves. As a result, his preferences change, and are now represented by the following utility function

U(x, y) = x^1/⁴y^1/4

Reference no: EM13354721

Questions Cloud

Q1 a 20 kg piece of wood slides on the surface the curved : q1. a 2.0 kg piece of wood slides on the surface. the curved lateral sides are perfectly smooth no resistance but the

Q1 in a gas at standard temperature and pressure what is : q1. in a gas at standard temperature and pressure what is the length of the side of a cube that contains a number of

Q1 a race car has a mass of 718 kg it starts from rest and : q1. a race car has a mass of 718 kg. it starts from rest and travels 45.0 m in 3.0 s. the car is uniformly accelerated

Q1 an electron with a speed of 612 times 108 cms in the : q1. an electron with a speed of 6.12 times 108 cms in the positive direction of an x axis enters the electric field of

X y 6step 1 the lagrangian function is set asstep 2 take : x y 6step 1 the lagrangian function is set asstep 2 take the first order partial derivatives of the lagrangian and set

Q1 what are the highest and lowest payments from the writer : q1. what are the highest and lowest payments from the writer that the bookkeeper farmer team will accept for the 6th

Q1 a 0850 kg block is attached to a spring with spring : q1. a 0.850 kg block is attached to a spring with spring constant 16.0 nm. while the block is sitting at rest a student

Q1 what is an acceleration of two falling sky divers mass : q1. what is an acceleration of two falling sky divers mass 120.0 kg including parachute while the upward force of air

Q1 a car carrying a 77-kg test dummy crashed into a wall at : q1. a car carrying a 77-kg test dummy crashed into a wall at 27ms and is brought to rest in 0.1 s. demonstrate that the

User Account

All Pages