The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y)?

A consumer can consume three goods, x₁, x2, and x3. In the markets where she buys them, she is a price-taker and faces prices for the three goods equal to P₁, P₂, and p3, respectively. The consumer has m dollars to spend. Her preferences can be represented by the following utility function: U(x₁, x₂, x3) = x₁x²x². X a) Derive the consumption bundle that maximizes the consumer's utility, subject to her budget constraint. b) Show that the optimal consumption bundle found in part a) is a global maximum. IMG_4479-2.png

Beans and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and donuts (K). Utility function of the consumer is the following: U(B,K) = 100∙B^0.25 · K^0.75 The price of beans (can) is ISK 2,000. but the price of a donut (box) is ISK 4,000. Consumption restrictions are placed on the consumer since his income is ISK 400,000. Put on all form donuts on the x-axis and beans on the y-axis. a) Show an equation for the bean's success rate for a single donut in light of the utility function. Draw the equivalence curve on a picture and explain what the equation is performance ratio is stated at each point on the equivalence curve. Explain with the concept of the efficiency ratio of the curvature of the equivalent curve. b) Find the most efficient consumption combination and draw on the diagram. c) The government decides to support the consumption of beans so its price drops to 1,000. Who is the most economical consumption combination based on the changed price…

= 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.

Given the total utility function for a consumer, consuming two goods is U = x+2y + xy+2 the prices of x and y are 4 TL and 6 TL respectively (Px = 4 and Py = 6), and the total budget of the consumer (B) is 130 TL; a) Write the constraint ( budget) function. b) Write the lagrangian function. c) What are the first-order conditions for utility maximization? d) Find the critical values of x, y and \lambda (x*,y*and \lambda *) according to the first order conditions. e) is the second order suficent condition for maximum utility satisfied 2 4 10 [ [:] 8 Write the appropriate commands to create A and d matrixes in R software. A-1. din R language? Given A = 1 3 And d = How can you formulate the equation X =

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.

Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are pa, py, and I. Write out the consumer's budget constraint and the Lagrangian function for the problem.

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!

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

Alice receives an allowance of 500 dollars that she spends on buying snacks (S) and tea (T). The price of each snack is 10 dollars and the price of each tea is 5 dollars. Her utility is given by: U (S, T) = 2S³/4 +T3/4 (a) Find her marginal rate of substitution (MRS) between S and T. (b) Write Alice's budget constraint. (c) Find Alice's optimal consumption and the optimal A. (d) What is her new consumption if the price of tea becomes 10 dollars? Note: numeric solutions for questions (c) and (d) are not integers.