Prove that if u is a reasonable utility function, then u(w) — u(w − h) > u(w+h)- u(w) for any w > 0 and h € (0, w).

The total utility from two products is maximized at the optimal consumption bundle.   True or False?

Ann's utility function is U = q1q2/(q1 + q2). Solve for her optimal values of q1 and q2 as a function of p1, p2 and Y.

= x 2 y. This Consider a consumer with the utility function U (x, y) = Vxy 글3글2-iy and MU, Vx = x? They have 1 function gives MU Va a budget of $60, and pr 1 and Py 2. Find optimal consumption of x and y.

Assume that a person’s utility depends on two products, x and y. The utility function is given by U(x, y) = (x + 2)^2(y + 3)^3. Find the marginal utility of x and marginal utility of y.

Suppose that a consumer has the utility function U(X,Y)= 2X 1/2 y 1/2 for X>0 and Y> 0. Which of the following utility functions would not represent the same preferences? U(X,Y)= 2(X + Y) 1/2 U(X,Y)=2x1/2y 1/2 - 100 O U(X,Y)= In 2 + InX+ In Y O U(X,Y)= X 1/2 y 1/2 O U(X, Y) = 4XY

Two students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi , xi) = φi(fi) + xi , where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi . EVALUATE THIS CLAIM: Both students eat too much!

Anne is going to the grocery store to buy some fruit. She can buy either apples or oranges. Let a be the quantity of apples she buys, and let zo be the quantity of oranges she buys. Her utility function is: u(xa, xo) = ln xa + 3 ln xo Anne has y pounds to spend. The price of apples is pa and the price of oranges is po (a) (b) Write down Anne's budget constraint and utility maximization problem, and the Lagrangian associated with this utility maximization problem. Find Anne's Marshallian demand functions for apples and oranges. Find Anne's indirect utility function.

Which of the following statement is TRUE based on this question : A utility function with 2 goods (X,Y) is given by U = X^1/2Y. If there’s 3 bundles, bundle A = (9,3); bundle B = (4,1); bundle C = (16, 4)

Anthony seeks to maximize the following utility function u(x, y) = x'/3y2/3 subject to the budget constraint Pæa + PyY = I 1 where pr, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and Pu. Are these shares a function of prices? Pyy* Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pr on Anthony's utility?