2) Suppose that the price of good X is $2 and the price of good Y is $3. You have $90 to spend and your preferences over X and Y are defined as:
U(x,y) = x2/3y1/3
Keep in mind that we review this concept because consumer choice is based on their preferences. People demand items that fulfill their Utility (perhaps happiness). As a result, we need to visualize how an individual’s budget is allocated to create the highest level of Utility.
£(X,Y) = x2/3y1/3 + λ(90 – 2X – 3Y)
Note that we would not change the utility function (only the income constraint changed)
2) Suppose that the price of good X is $2 and the price of good Y...
John consumes two goods, X and Y and has an income of $25. Price of good X is S3 per unit and price of good Y is $2 per unit. John's utility function is given by U (X, Y) = 0.5 XY. The marginal utility of X, MUx 0.5Y and the marginal utility of Y, MUy 0.5X. (a) Determine the optimal values of X and Y that will maximize John's utility. (7 marks) (b) Calculate the total utility at the...
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a Budget Constraint = Marginal Utility of good x/Price of good x = Marginal Utility of good y/Price of y Calculate Consumption Bundle using the following information: Price of Good x = $5, Price of Good y = $16 and Income = $100 / 0 Quantity Consumed Total Utility Quantity Consumed Total Utility Calculate: a.) Price Elasticity of Demand =% Change in Quantity Demanded/%Change in...
6. Suppose that the price of good X is $1 and the price of good Y is $1, and that income is $7. The following tables show the marginal utility schedules for X and Y: Good X: Good Y: Qx MUx Qy MUy 1 15 1 12 2 11 2 9 3 9 3 6 4 6 4 5 5 4 5 3 6 3 6 2 7 1 7 1 How much of good X and how much of good Y should the individual purchase to maximize utility? Explain how you know. (Hint: There are 2 conditions that must be satisfied.)
3. A consumer's preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individual's income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumer's preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumer's MRS at...
Q5. Suppose that marginal utility of Good X = 100, the price X is $10 per unit, and the price of Y is $5 per unit. Assuming that the consumer is in equilibrium and is consuming both X and Y, what must the marginal utility of Y be? P12. The following tables illustrate Eileen’s utilities from watching first-run movies in a theater and from renting movies from a video store. Suppose that she has a monthly movie budget of $36,...
Price of x is 12 and price of y is 8. income is $600 U(x, y)=x^0.4 y^0.6 set up lagurangian, write down first order conditions, solve the system of equation in first order condition to find the optimal x and y and . explain how you interpret the value of . and then, find the marginal utility of good x when the consumer chooses the optimal bundle. please solve this step by step. We were unable to transcribe this imageWe were...
Question 2 Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income wWhat is the optimal quantity is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The...
Suppose the price of Good X is $4 and the price of Good Y is $3. If a consumer has a Marginal Rate of Substitution (MRSxy) of 2 for the bundle they are considering, then given their budget constraint, the consumer... Select one O a. Cannot reach a higher level of utility given their budget constraint. Ob. Would have a higher utility if they bought more of Good X. c. Would have a higher utility if they bought less of...
Assume that an individual’s preferences is represented by the following utility function: ?(?, ?) = (?^1/3)*(y^2/3) a. What could you tell about the type of x and y? (“good” , “bad” or a “neuter”) b. Derive the equation for his/her indifference curve for utility level of 100? c. Derive marginal utility of x and marginal utility of y as a function of x,y. d. Does goods x and y exhibit diminishing marginal utility, constant marginal utility, or increasing marginal utility?...
A social planner is considering two items for the state budget: good 1 - education, X, and good 2 - health care, xz. Her preferences over the two items are given by the following function: U(x1,x2) = 3x2 + x2 The prices of education and healthcare are pz = $2 and P2 = $1; the state's budget I = $50. a) Solve for the marginal rate of substitution between the two goods (provide number). b) Find optimal consumption of X1...