Establish that U(x,y)=xy2 is a quasi-concave function.
07. Show that the function u(x, y) In(5x +y) -5(z +y)2 is concave. 07. Show that the function u(x, y) In(5x +y) -5(z +y)2 is concave.
consider a quasi-linear utility function: U(x, y) = lnx + y. Show that the MRS is the same on all indifference curves at a given x. Illustrate your result in a suitable diagram. please show all steps, so I can better understand how you reached your final answer.
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (d) The initial income is $576, initial prices are...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2) (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2) c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2) (d) The initial income is $576,...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2) (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2) (c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2) (d) The initial income is $576,...
Pierce has a concave utility of wealth function, u(x). Pierce prefers prospect X to prospect Y. Which of the following statements is therefore necessarily true for Pierce? CE(X) > CE(Y). U(EV(X)) > U(EV(Y)) EU(X) < EU(Y) Y is a mean preserving spread of X.
Price Changes (16 points) The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2) (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2) (c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2) (d) The...
3. (ICs for Quasi-Linear Preferences) Consider the utility function: u(x, y) = x1/2 + y. a. Find the expression for the MRS (= – dy/dx). b. Draw one IC making sure its shape reflects your expression for MRS above. c. Given your expression for MRS, draw another IC above the one you just drew, and comment on how the slopes of the ICs compare at a given level of x (e.g., at x = 1).
. (a) Show that the function u= 4x2 - 12.xy2 is harmonic and v=12.xy-4v2 is a harmonic conjugate of u. [Consequently, the function f =u+iv is entire, thus it has an antiderivative and that any contour integral of f is path independent.] (b) Find an antiderivative F(-)= F(x+iy)=P(x, y)+i Q(x, y) of the function f; and (c) evaluate ( f (2) ds , where C is any contour from 0 to 1–2i .
A function y = f(x) is defined implicitly by the equation 2x²y - xy2 - 2y = 0 near the point (2, 3). Then f '(2) 3 7 1 - 2 4 3 5 2