For each of the following utility functions, compute the marginal utility of good X (MUx) and the marginal utility of good Y (MUy). a. U(X,Y) = 3X1/2 + 5Y1/2 %3D b. U(X,Y) = X0.5y0.4

Imagine Billy eats brownies (B) and cookies (C) and considers them to be perfect substitutes. Brownies yield him four times more utility than cookies. Which of the following equations could describe his utility function? U= 0.25B + C O U=B+ 0.25C U = B'C OU = BC4 %3D

Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.

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.

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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

1. Sam is going to Baltimore for the day to watch his favorite baseball team (Orioles). Sam loves his Orioles, but he is addicted to drinking beer (B) and eating hotdogs (D) while watching his team. His utility function is: U = (B*D)1/2 a. Suppose Sam has $50 to spend on beer and hotdogs. Beer costs $5 a mug and a hotdog costs $4. Draw Sam's budget constraint. b. Suppose Sam spends all of his income on beer. How many mugs of beer can he buy? What is his utility? c. Will Sam's income allow him to reach a U = 5? d. If Sam buys 4 hotdogs, how many mugs of bear can he buy? What is his utility? e. What is the combination of beer and hotdogs that yield the highest utility? 2. Firm A's Price $20 $15 $20 $40 profit $35 profit Firm B's Price $37 profit $39 profit $15 $49 profit $38 profit $30 profit $35 profit a. Firms A and B are member of an oligopoly. Which solution will Firm A and B select? b. Is there a Nash equilibrium? If so, what is it? c. Which solution will Firm A and B select if Firm…

For the utility function U = Qx^0.84Qy^(1-0.84) rate between good X and good Y at Qx= 7 and Qy=19 find the trade-off

2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂

Consider Gary's utility function: U(X,Y) = 5 XY, where X and Y are two goods. If the individual consumed 10 units of X and received 250 units of utility, how many units of Y must the individual consume? 5 25 0 10