Think of the following linear attributes model. There are three goods, x, y and z, available...

Think of the following linear attributes model. There are three goods, x, y and z, available at prices px=3, py=2 and pz=4.A consumer cares about attributes a1 and a2 and one unit of good x has a1x=3 units of a1 and a2x=2 units of a2. For good y and z, suppose a1y=6, a2y=1 and a1z=4, a2z=3. Suppose the consumer has the initial wealth (income)w=12. We assume the consumer will spend all her wealth.

(a)If the consumer wants to consume (a1,a2)=(16,8), how many units of x,y and z should she purchase?

(b)Suppose the consumer has utility function u(a1,a2)=min{a1,a2}. How many units of goods x,y and z will the consumer choose to consume (at optimum)?

Expert Solution

Rahul Sunny answered 2 years ago

Joseph Company operates three divisions, X, Y, and Z. The following information is available for the...

Joseph Company operates three divisions, X, Y, and Z. The following information is available for the most recent month: Joseph Company: Sales revenue .............. $700,000 Segment margin ............. $239,000 Net income ................. $125,000 Division X: Sales revenue .............. $200,000 Contribution margin ........ $140,000 Segment margin ............. $109,000 Division Y: Variable costs ............. 70% of sales Division Z: Variable costs ............. $118,000 Traceable fixed costs ...... $ 56,000 Contribution margin ........ 60% of sales Calculate the total fixed costs incurred by...

ABC Company operates three divisions, X, Y, and Z. The following information is available for the...

ABC Company operates three divisions, X, Y, and Z. The following information is available for the most recent month: ABC Company: Segment margin ............. $200,000 Contribution margin ........ 40% of sales Division X: Sales revenue .............. $732,000 Contribution margin ........ $260,000 Segment margin ............. $ 30,000 Division Y: Sales revenue .............. $276,000 Contribution margin ........ 25% of sales Division Z: Sales revenue .............. $200,000 Traceable fixed costs ...... $ 33,000 Calculate the segment margin reported by Division Z during the...

If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z)...

If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z) b. X×(Y×Z) = (X.Z)Y – (X.Y)Z c. X.(Y×Z) = -Y.(X×Z)

Solve for x,y,z if there if a solution to the given system of linear equations: x...

Solve for x,y,z if there if a solution to the given system of linear equations: x - 3y - 2z = -3 3x + 2y - z = 12 -x - y + 4z = 3

Springer Products manufactures three different product lines, Model X, Model Y, and Model Z. Considerable market...

Springer Products manufactures three different product lines, Model X, Model Y, and Model Z. Considerable market demand exists for all models. The following per unit data apply: Model X Model Y Model Z Selling price $57 $70 $76 Direct materials 6 6 6 Direct labor ($ 12$12 per hour) 12 12 24 Variable support costs ($ 8$8 per machineminus−hour) 8 16 16 Fixed support costs 12 12 12 If there is excess capacity, which model is the most profitable to...

Assume the following preference order for four goods, w, x, y, and z, of a total...

Assume the following preference order for four goods, w, x, y, and z, of a total of 26 people: # of people 9 6 2 4 5 W X Y Y Z Z Y X Z X X Z Z X Y Y W W W W You want to extract the will of the group and employ different rules. What is the group's preference order when you employ: A) Plurality Vote B) Condorcet Vote C) Borda Count D) "Vote...

Solve the following system : z” + y ′ = cos x, y” − z =...

Solve the following system : z” + y ′ = cos x, y” − z = sin x, z(0) = −1, z′ (0) = −1, y(0) = 1, y′ (0) = 0.

Which of the following are correct for P(x,y,z)= xyz + x(yz)' + x'(y + z) +...

Which of the following are correct for P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)' ? 1) P(0, 0, 1) = 0 2) P(0, 1, 0) = 1 3) P(0, 0, 0) = 1 4) P(1, 1, 1) = 1 5) P(1, 0, 0) = 0

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by...

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by row reduction. x+3y-2z=5 3x+5y+6z=7 2x+4y+3z=8

Consider a consumer who derives utility from three consumption goods: x and y and z, which...

Consider a consumer who derives utility from three consumption goods: x and y and z, which prices are given, respectively, by px , py and pz . We let z denote the numeraire good and normalize its prices to unity. The consumer possesses an initial endowment of Z>0 units of z. The utility function of the consumer is given by: (1) U(x,y,z)=v(x)+u(y⋅py)+z. Thus, the consumer is deriving utility from the amount she spends on y and not from the number...

Question