Suppose that the price of good X is $2 and good Y is $3. I have $90 to spend and my preferences over X and Y are U(x,y) = (x^2/3)(y^1/3).
How can you calculate the marginal utility of both X and Y using calculus (show the steps/work)?
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...
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...
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.)
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...
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,...
3) Suppose that you have the following utility function: U(x,y)=x04 0:6. The price of x is $6 and the price of y is $3. You have $100 to spend. a. Find the utility maximizing quantity of x and y. b. Plot the budget constraint and show the optimal x and y on their indifference curve on the graph.
Suppose you have the following preferences u(x,y) = xayb. Calculate the optimal demand functions. Is good y a normal or inferior good? Please show work.
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...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
Consider the following 3 utility functions with good x and good y: ? ?(?, ?) = (?^2)*sqrt(?), ? ?(?, ?) = 2? − (1/2)?, ? ? (?, ?) = 4 ln ? + ln ? a. Find Marginal Utility (MUx and MUy) for each these utility functions. b. Is assumption that more is better satisfied for both goods in all of these utility functions? If not, specify for which function(s) and for which good(s) it is not satisfied. c. Does...