Plot the contours of u(x,y)=xy and its harmonic conjugate v(x,y).

Expert Solution

Colby Messinger answered 2 years ago

If the function u (x, y) is a harmonic conjugate of v (x, y) prove that...

If the function u (x, y) is a harmonic conjugate of v (x, y) prove that the curves u (x, y) = st. and v (x, y) = stations. are orthogonal to each other. These curves are called level curves. Now consider the function f (z) = 1 / z defined throughout the complex plane except the beginning of the axes. Draw them level curves for the real and imaginary part of this function and notice that they are two...

For the following u(x, y), show that it is harmonic and then find a corresponding v(x,...

For the following u(x, y), show that it is harmonic and then find a corresponding v(x, y) such that f(z)=u+iv is analytic. u(x, y)=(x^2-y^2) cos(y)e^x-2xysin(y)ex

define U=x+y, V=x-y. find the joint and marginal pdf of U and V

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?

Let u(x, y) be the harmonic function in the unit disk with the boundary values u(x,...

Let u(x, y) be the harmonic function in the unit disk with the boundary values u(x, y) = x^2 on {x^2 + y^2 = 1}. Find its Rayleigh–Ritz approximation of the form x^2 +C1*(1−x^2 −y^2).

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...

Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...

Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3) S = {(x,y): 1 < x2 + y2 < 4}, u(x,y)= 5 (on outer circle) and = 7 (on inner circle) I have these two problems to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!

Find u(x,y) harmonic in the region in the first quadrant bounded by y = 0 and...

Find u(x,y) harmonic in the region in the first quadrant bounded by y = 0 and y = √3 x such that u(x, 0) = 13 for all x and u(x,y) = 7 if y = √3 x . Express your answer in a form appropriate for a real variable problem.

Suppose that U = XY . The prices of good X and good Y are $10...

Suppose that U = XY . The prices of good X and good Y are $10 and $5, respectively. How many units of good X does the consumer buy if she has $1000 of income? a) 10 b) 25 c) 50 d) 41

For a demand function u (x, y) = xy, show the demand functions for good x...

For a demand function u (x, y) = xy, show the demand functions for good x and good y. (Remember that MRS = (du/dx) / (du/dy) = px / py in the point of interest, the tangency point of budget line and indifference curve. The budget condition is given by pxx + pyy = m) for u (x, y) = x1/3 y2/3

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