Assume a consumer with the utility function U = U (X, Y) = X2 Y2 and the typical budget constraint M = PxX + PyY a. Set up the constrained maximization problem and derive the first-order conditions. b. Derive the consumer’s demand for X and Y in terms of the parameters.
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- A consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is the quantity of good 2 that is bought. The price of good 1 is $10 and the price for good 2 is $2. If the consumer's income is $100 what will the consumer's optimal utility level be? b. Using Lagrange multilplier method. optimise the utility function x0.25 y0.25 subject to the budget constraint 24=x/10+yA consumer is maximising her utility function: U(x, y) = (x¹/³+y¹/³)³, subject to the budget constraint x + 3y = 100. (a) Set up the Lagrangian function of this utility maximisation problem and derive the first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the Lagrange multiplier. (c) What are the utility maximising amounts of x and y if the budget constraint changes to x + 3y = 50? Also, calculate the Lagrange multiplier.
- A utility maximizing consumer purchases two commodities, Q1 & Q2. The consumer’s utility function is described by the following expression: U = Q1 Q2 + Q1 + 2Q2. The prices of the commodities are P1 = $2 and P2 = $5. Suppose the income of the consumer is $51 (a)Form the Lagrangian function that defines the combination of both commodities the consumer could buy subject to the budget constraint imposed by the prices of the commodities and the income of the consumer. (b)Find the combination of both commodities that maximizes the utility of the consumer. (c)Write and evaluate the Bordered Hessian for this utility maximization problem.Suppose a consumer’s preferences can be represented by the utility function U(X,Y) = Min (2X,Y). Also, suppose the consumer has $300 to spend and the price of Good X is PX = $2 and the price of Good Y is PY = $5. If the consumer maximizes their utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase? X* = Y* =.For a consumer with a utility function u=3x^2y^2 when px=3 and py=4, find the consumption levels that maximize his utility under the $120 budget constraint. What is the maximum benefit?
- Utility Function: U(X,Y)=X1/2Y1/2 Budget Constraint: 2X+2Y=16 If the price of good X changes to Px=3, what is the Equivalent variation?Individuals in a market each have a total budget y to spend on two goods q1 and q2 at the prices p1and p2 respectively. Their preferences are described by the utility function below. I need help with question b) Find the expenditure function corresponding to these preferences.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!
- Consider the utility function U(x,y)=5x +2y. An agent with a budget constraint of 10x + 5y = 20 will choose which of the following bundles in order to maximize his/her utility? 1 unit of x and 2 units of y 10 units of x 2 units of y 2 units of x 4 units of yIndividuals in a market each have a total budget y to spend on two goods q1 and q2 at the prices p1and p2 respectively. Their preferences are described by the utility function below. As in part (a), how can I show the demand of good 2?A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.