How can I prove that perfect substitutes utility function and perfect complements utility function are homothetic...

How can I prove that perfect substitutes utility function and perfect complements utility function are homothetic functions?

Expert Solution

A function is HOMOTHETIC if it can be represented as a monotonic transformation of a function that is Homogeneous of Degree 1 i.e. HOD(1).

Since utility functions for perfect substitutes and perfect complements are HOD(1), they are automatically homothetic;

-----
Please leave an upvote if this helped!

Rahul Sunny answered 2 years ago

Compute the expenditure function for the perfect complements utility function. Then compute the expenditure function for...

Compute the expenditure function for the perfect complements utility function. Then compute the expenditure function for the perfect substitutes utility function. Do your results make sense?

Suppose chipotle has a perfect substitutes and production function, McDonald's has a near perfect complements production...

Suppose chipotle has a perfect substitutes and production function, McDonald's has a near perfect complements production function, and Pizza Hut has a Cobb-Douglas production function. The town passes a law to increase the minimum wage in the city to $15. Which one of these firms will see a large substitution out of labor (as percent of initial labor)? Explain your answer

Braden views Coke (C) and Pepsi (S) as perfect substitutes. His utility function is: U =...

Braden views Coke (C) and Pepsi (S) as perfect substitutes. His utility function is: U = C + S. The corresponding marginal utility for each good is: MUC = 1 and MUS = 1. The price of a 12-ounce can of Coke is $4 and the price of a 12-ounce can of Pepsi is $3. Also, assume that his income is $60. Find Branden's utility-maximizing bundle of Coke and Pepsi. Make sure to show all your work. Show his optimal...

substitutes, complements, or unrelated

How can two inputs be substitutes in production and yet be classified as gross complements?

An agent considers good 1 and good 2 "perfect substitutes" and thus her preferences can be represented by the utility function u (x,y) = 4x + 2 y.

An agent considers good 1 and good 2 "perfect substitutes" and thus her preferences can be represented by the utility function u (x,y) = 4x + 2 y. The agent starts with $10. Use this information to answer the following questions. (a) What is the slope of this agents indifference curves (i.e. the mrs)? Hint: You do not need to use calculus if you solve for the equation of an indifference in slope-intercept form. (b) What is the maximum price at which...

Cherise considers movies and concerts to be perfect substitutes. When Cherise maximizes her utility, what will...

Cherise considers movies and concerts to be perfect substitutes. When Cherise maximizes her utility, what will the optimal bundle of movies and concerts probably look like? Explain your reasoning by drawing a graph that includes her indifference curves and a hypothetical budget constraint.

Who are the Amazon's closest competitors?and are there any close substitutes or complements?

There are many bizarre examples of complements and substitutes in the real world. For example, in...

There are many bizarre examples of complements and substitutes in the real world. For example, in my home ketchup and Kraft macaroni and cheese are complements (everyone else here puts ketchup on their mac and cheese, which concerns me!). a. Come up with two bizarre/odd real-world examples of a pair of goods that are complements. Explain why they are complements. b. Choose one of those pairs of complements. Draw a consumer’s demand curve for each good (so two graphs). Suppose...

A utility-maximizing consumer believes two goods are Perfect Substitutes u(x, y) = 3x + 4y. She...

A utility-maximizing consumer believes two goods are Perfect Substitutes u(x, y) = 3x + 4y. She pays pY = 2 and pX = 1. Her income is m = 24. Next month the price of good x will rise to pX = 3. Round your final answers to 3 decimal places. What is the EV, CV and Approximate ΔCS?

Question