1. U ( x 1 , x 2 ) = 2 x1 + 3 x 2...

1. U ( x 1 , x 2 ) = 2 x₁ + 3 x ₂

If the price of good 1 is $4/unit, the price of good 2 is $5/unit , and income is $20...

What is this person's optimal consumption level for good 1?

2. U( x 1 , x 2 ) = 5 x₁ + 3 x₂

If the price of good 1 is $2/unit, the price of good 2 is $1/unit , and income is $10...

What is this person's optimal consumption level for good 1?

Solutions

Expert Solution

Ans.1

I = PxX + PyY or 20 = 4X + 5Y or in slope intercept form Y = 4– (1/4)X

To find the consumption bundle that maximizes utility is where the slope of the indifference curve (MUx/MUy) is equal to the slope of the budget line (Px/Py) in absolute value terms.

MUx = Y and MUy = X, so MUx/MUy = Y/X.

Px/Py = 4/5 So, Y/X = 5/4 or X = 4Y/5

Substitute this into the budget line to get Y = 4 – (1/4)(4Y/5) or Y = 2.5. If Y = 2.5, then X = 2

Therefore, The consumption bundle that maximizes utility is thus (x,y) = (2, 2.5).

Ans. 2
I = PxX + PyY or 10 = 2X + 1Y or in slope intercept form Y = 10– (1/2)X

To find the consumption bundle that maximizes utility is where the slope of the indifference curve.

(MUx/MUy) =(Px/Py)

MUx = Y and MUy = X, so MUx/MUy = Y/X.

Px/Py = 2/1 So, Y/X = 1/2 or X = 2Y

Substitute this into the budget line to get Y = 10 – (1/2)(2Y) or Y = 2.5. If Y = 2.5, then X = 5

Therefore, The consumption bundle that maximizes utility is thus (x,y) = (5, 2.5).

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Let X1, X2 ,X3 ∼U[0,1] be independent, and letX(1),X(2),X(3) be the order statistics, i.e., X(1) <...

Let X1, X2 ,X3 ∼U[0,1] be independent, and letX(1),X(2),X(3) be the order statistics, i.e., X(1) < X(2) < X(3) (a) Find f(1)(x), f(2)(y) and f(3)(z). (b) Verify that the joint density of X(1) and X(2) is f(1,2)(x,y)=6(1−y), 0 (c) Find the conditional density of X(1) given X(2). (d) Find E(X(1)+X(3 )/ X(2))

each of the following situations, 3. U(X,Y) = X1/2Y1/2 M = $36; PY = $1; PX...

each of the following situations, 3. U(X,Y) = X1/2Y1/2 M = $36; PY = $1; PX is initially = $1; the price of Good X increases to PX = $9. 4. U(X,Y) = X1/2Y1/2 M = $64; PY = $1; PX is initially = $16; the price of Good X decreases to PX = $1. 1）calculate the change in the quantity demanded of Good X that is due to the Substitution Effect 2）calculate the change in the quantity demanded of...

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price...

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price of good 2 is $4/unit and income is 114.. What is this person's optimal consumption level for good 2?

Solve x(y^2+U)Ux -y(x^2+U)Uy =(x^2-y^2)U, U(x,-x)=1

1. U( x 1 , x 2 ) = min { x 1, x 2 }...

1. U( x 1 , x 2 ) = min { x 1, x 2 } If the price of good 1 is $8/unit, the price of good 2 is $2/unit, and income is $51... What is this person's optimal consumption level for good 2? 2. U( x 1, x 2 ) = min { x1 /2 , x 2} If the price of good 1 is $4/unit, the price of good 2 is $8/unit, and income is $93... What...

a) U = xy b) U = (xy)^1/3 c) U = min(x,y/2) d) U = 2x...

a) U = xy b) U = (xy)^1/3 c) U = min(x,y/2) d) U = 2x + 3y e) U = x^2 y^2 + xy 4. All functions except c) are differentiable. Do these functions exhibit diminishing marginal utility? Are their Marshallian demands downward sloping? What can you infer about the necessity of diminishing marginal utility for downward- sloping demands?

Given the utility function U ( X , Y ) = X 1 3 Y 2...

Given the utility function U ( X , Y ) = X 1 3 Y 2 3, find the absolute value of the MRS when X=10 and Y=24. Round your answer to 4 decimal places.

Consider the utility functions of three individuals: u(x) = x1/2, v(x) = ln x, and h(x)...

Consider the utility functions of three individuals: u(x) = x1/2, v(x) = ln x, and h(x) = x – 0.01 x2, where x represents wealth. Consider also the following lotteries: X = (w0 + x1, w0 + x2, w0 + x3; ¼, ½, ¼ ) = (4, 16, 25; ¼, ½, ¼), where w0 = $2, and lottery Y in which w1 = $10, so that Y = (12, 24, 33; ¼, ½, ¼). Note that Y = X +...

Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation...

Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation for Sara’s indifference curve that goes through the point (2,8). b. Suppose that the price of each good is 1 and that Clara has an income of 11. Draw her budget line. Can Sara achieve a utility of 36 with this budget? Why or why not? c. Evaluate the marginal rate of substitution MRS at (x1, x2) = (1, 5). Provide an economic interpretation...

Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent...

Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent the two goods Sophie consumes. Sophie's income is $3400 and the prices are given as x1 = $2 and x2 = $160 a) derive & represent in two separate diagrams the demand for x1 and x2 ( for any income and prices) b) If Sophie's income is increased to $6600, what is the income effect on x1? Is x2 a normal good? Justify your...

Subjects