assume that U(x, y) = xy, Px = 1, Py = 4 and B = 120....

assume that U(x, y) = xy, Px = 1, Py = 4 and B = 120.

Using the Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. Show steps.

Expert Solution

Colby Messinger answered 1 year ago

Let assume that a consumer has a utility function u(x, y) = xy, and px =...

Let assume that a consumer has a utility function u(x, y) = xy, and px = 1 dollar, py = 2 dollars and budget=50. Derive the followings. (3 points each) 1) Marshallian demands of x and y 2) Hicksian demands of x and y 3) Indirect utility function 4) Expenditure function 5) Engel curve

Consider the following utility function U(X,Y) = X^1/4Y^3/4 Initially PX = 2 PY = 4 I...

Consider the following utility function U(X,Y) = X^1/4Y^3/4 Initially PX = 2 PY = 4 I = 120 Suppose the price of X changes to PX = 3. Perform a decomposition and fill in the table X Y Substitution Effect Income Effect Total Effect

Consider the following utility function: u(x, y) = x2/3y1/3. Suppose that Px = 4, Py =...

Consider the following utility function: u(x, y) = x2/3y1/3. Suppose that Px = 4, Py = 2 and the income is I = 30. Derive the optimal choice for both goods.

Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y]. Suppose PX = 1 and PY...

Suppose a consumer has preferences given by U(X,Y) = MIN[2X,Y]. Suppose PX = 1 and PY = 2. Draw the Income Consumption Curve for this consumer for income values • M = 100 • M = 200 • M = 300 To do this, carefully draw the budget constraints associated with each of the prices for good X, and indicate the bundle that the consumer chooses in each case. Also, be sure to label your graph accurately.

One reasonable consumer is choosing to maximize U(X,Y)=XY under a budget constraint of PxX+PyY=M. (Px,Py,M)=(4,2,24). (1)...

One reasonable consumer is choosing to maximize U(X,Y)=XY under a budget constraint of PxX+PyY=M. (Px,Py,M)=(4,2,24). (1) Explain what Px/Py=2 means. (2) Draw a budget line. (3) Draw an indiscriminate curve that conforms to a given utility function. (4) Find the optimal consumption (X*,Y*). (5) Calculate the income elasticity of demand for product X.

One consumer is choosing to maximize U(X,Y)=XY under a budget constraint of PxX+PyY=M. (Px,Py,M)=(4,2,24). (1) What...

One consumer is choosing to maximize U(X,Y)=XY under a budget constraint of PxX+PyY=M. (Px,Py,M)=(4,2,24). (1) What does Px/Py=2. mean in this case? (2) Draw a budget line. (3) Draw an indiscriminate curve that conforms to a given utility function. (4) Find out the optimal consumption (X*,Y*). (5) Calculate the income elasticity of demand for X goods.

Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y, with some Px and Py...

Consider a quasi-linear utility function, U(X, Y) = X1/2 + Y, with some Px and Py a. For an interior solution, solve step-by-step for the demand functions of X* and Y*. b. Under what circumstance would the optimal consumption involve a corner solution for the utility maximization problem? c. (Now, let Py = $1, I = 24, and suppose that Px increases from $0.5 to $2. Find the Compensating Variation (CV) and the Equivalence Variation (EV). In this example, how...

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?

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...

At the equilibrium consumption bundle, which of the following holds? MRSX,Y = PY/PX. MRSX,Y = −PX/PY....

At the equilibrium consumption bundle, which of the following holds? MRSX,Y = PY/PX. MRSX,Y = −PX/PY. MRSX,Y = PX/PY. MRSX,Y = −PY/PX.

Question