Question

Consider a consumer with preferences represented by the utility function: U(x,y) = 3x + 6 √...

Consider a consumer with preferences represented by the utility function:

U(x,y) = 3x + 6 y  

  1. Are these preferences strictly convex?
  2. Derive the marginal rate of substitution
  3. Suppose, the utility function is:

U(x,y) = -x +2 y  

  1. Are there any similarities or differences between the two utility functions?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a consumer with preferences represented by the utility function u(x,y)=3x+6 sqrt(y) (a) Are these preferences...
Consider a consumer with preferences represented by the utility function u(x,y)=3x+6 sqrt(y) (a) Are these preferences strictly convex? (b) Derive the marginal rate of substitution. (c) Suppose instead, the utility function is: u(x,y)=x+2 sqrt(y) Are these preferences strictly convex? Derive the marginal rate of substitution. (d) Are there any similarities or differences between the two utility functions?
2. Consider a consumer with preferences represented by the utility function: u(x,y)=3x+6sqrt(y) (a) Are these preferences...
2. Consider a consumer with preferences represented by the utility function: u(x,y)=3x+6sqrt(y) (a) Are these preferences strictly convex? (b) Derive the marginal rate of substitution. (c) Suppose instead, the utility function is: u(x,y)=x+2sqrt(y) Are these preferences strictly convex? Derive the marginal rate of sbustitution. (d) Are there any similarities or differences between the two utility functions?
Consider a consumer whose preferences over the goods are represented by the utility function U(x,y) =...
Consider a consumer whose preferences over the goods are represented by the utility function U(x,y) = xy^2. Recall that for this function the marginal utilities are given by MUx(x, y) = y^2 and MUy(x, y) = 2xy. (a) What are the formulas for the indifference curves corresponding to utility levels of u ̄ = 1, u ̄ = 4, and u ̄ = 9? Draw these three indifference curves in one graph. (b) What is the marginal rate of substitution...
A consumer’s preferences are represented by the following utility function: u(x, y) = lnx + 1/2...
A consumer’s preferences are represented by the following utility function: u(x, y) = lnx + 1/2 lny 1. Recall that for any two bundles A and B the following equivalence then holds A ≽ B ⇔ u(A) ≥ u (B) Which of the two bundles (xA,yA) = (1,9) or (xB,yB) = (9,1) does the consumer prefer? Take as given for now that this utility function represents a consumer with convex preferences. Also remember that preferences ≽ are convex when for...
Consider a consumer with the following utility function: U(X, Y ) = XY. (a) Derive this...
Consider a consumer with the following utility function: U(X, Y ) = XY. (a) Derive this consumer’s marginal rate of substitution, MUX/MUY (b) Derive this consumer’s demand functions X∗ and Y∗. (c) Suppose that the market for good X is composed of 3000 identical consumers, each with income of $100. Derive the market demand function for good X. Denote the market quantity demanded as QX. (d) Use calculus to show that the market demand function satisfies the law-of-demand.
A consumer has preferences represented by the utility function u(x, y) = x^(1/2)*y^(1/2). (This means that...
A consumer has preferences represented by the utility function u(x, y) = x^(1/2)*y^(1/2). (This means that MUx=(1/2)x^(−1/2)*y^(1/2) and MUy =1/2x^(1/2)*y^(−1/2) 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 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 price of good y and...
Suppose a consumer has the utility function u(x, y) = x + y. a) In a...
Suppose a consumer has the utility function u(x, y) = x + y. a) In a well-labeled diagram, illustrate the indifference curve which yields a utility level of 1. (b) If the consumer has income M and faces the prices px and py for x and y, respectively, derive the demand functions for the two goods. (c) What types of preferences are associated with such a utility function?
3. Suppose that a consumer has a utility function given by U(X,Y) = X^.5Y^.5 . Consider...
3. Suppose that a consumer has a utility function given by U(X,Y) = X^.5Y^.5 . Consider the following bundles of goods: A = (9, 4), B = (16, 16), C = (1, 36). a. Calculate the consumer’s utility level for each bundle of goods. b. Specify the preference ordering for the bundles using the “strictly preferred to” symbol and the “indifferent to” symbol. c. Now, take the natural log of the utility function. Calculate the new utility level provided by...
Consider a consumer with the following utility function: U(X, Y ) = X1/2Y 1/2 (a) Derive...
Consider a consumer with the following utility function: U(X, Y ) = X1/2Y 1/2 (a) Derive the consumer’s marginal rate of substitution (b) Calculate the derivative of the MRS with respect to X. (c) Is the utility function homogenous in X? (d) Re-write the regular budget constraint as a function of PX , X, PY , &I. In other words, solve the equation for Y . (e) State the optimality condition that relates the marginal rate of substi- tution to...
George has preferences of goods 1 (denoted by x) and 2 (denoted by y) represented by...
George has preferences of goods 1 (denoted by x) and 2 (denoted by y) represented by the utility function u(x,y)= (x^2)+y: a. Write an expression for marginal utility for good 1. Does he like good 1 and why? b. Write an expression for George’s marginal rate of substitution at any point. Do his preferences exhibit a diminishing marginal rate of substitution? c. Suppose George was at the point (10,10) and Pete offered to give him 2 units of good 2...