For the following utility function calculate the marginal utility of each asset, the marginal rate of substitution and for each function graph three indifference curves assuming the first represents a profit of 5, the second of 10 and the third of 15.
? (?1, ?2) = min {5?1,10?2}



Marginal rate of substitution (MRS):
Vertical part of IC - MRS tends to ∞
Horizontal part of IC - MRS = 0
At kink - MRS is not defined.
For the following utility function calculate the marginal utility of each asset, the marginal rate of...
Let say the utility function as U(X,Y) = lnX + Y. Show that the marginal rate of substitution (MRS) is the same on all of the indifference curves at a given X. Explain and include graph. (5 Marks)
Question 1 For the following utility functions (3 pts each for a, b, and c): • Find the marginal utility of each good at the point (5, 5) and at the point (5, 15) • Determine whether the marginal utility decreases as consumption of each good increases (i.e., does the utility function exhibit diminishing marginal utility in each good?) • Find the marginal rate of substitution at the point (5, 5) and at the point (5, 15) • Discuss how...
Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that describes Moe’spreferences. For the following, think of q1 as the variable you would graph on the horizontal axis. a. Derive an expression for his marginal utility (U1) from a small increase in q1 holding q2 fixed. Also, find U2. b. What is Moe’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. c. Given your answer...
Question 2. For each of the following utility functions: (i) u1(x1,T2) = 2x2. (a) Graph the indifference curves for utility levels u -1 and u 2 (b) Find the marginal rate of substitution function MRS. (c) For u and us, graph the locus of points for which the MRS of good 2 for good 1 is equal to 1, and the locus of points for which the MRS is equal to 2.
Treat Bob and Joe as having the same utility function as
provided at the beginning of the question
Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding q2 fixed. Also, find b. What is Joe's marginal rate of substitution (MRS)?...
Treat Bob and Joe as the same individual and having the same
utility function as provided at the beginning of the question.
Looking for the solutions to part e and f.
Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding...
1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c)...
Question: Suppose your utility function from a given bundle of goods, (x.y), isWex.y) (y) (a) Suppose y 1. Make a table showing your utility for x 1, x-2x-3' and x (b) Is utility increasing from more units of x? (c) Is marginal utility increasing from more units of x? (d) Derive the equation describing the marginal utility for x, Mu (e) Plot a representative indifference curve that includes 3 bundles of goods of your choosing. Include on your graph the...
Phil’s quasi-linear utility function U (q1q2)= ln q1 + q2. Show that tis marginal rate of substitution (MRS) is the same in all of his indifference curves at given q1.
For each of the following utility functions: Calculate MUx, MUy, MRSx,y; determine whether or not the property of “more is better” is satisfied for both goods; determine whether or not the marginal utility of x diminishes, remains constant, or increases as the consumer buys more x; determine whether or not the marginal rate of substitution diminishes, remains constant, or increases as the consumer substitutes x for y along an indifference curve; and sketch the graph of a typical indifference curve....