Gisela and Lynn Are Friends

question 41

Essay

Gisela and Lynn are friends. New clothing is the only good that gives them utility. Each girl spends a certain amount of money per year on clothing. Let x be the amount that Gisela spends on clothing (in thousands of dollars)and let y be the amount of money (in thousands of dollars)that Lynn spends. Gisela's utility expressed as a function of x and y is given by: UG(x, y)= 12x - x2 - xy and Lynn's utility is given by UL(x, y)= 12y - y2 - xy.
i)Calculate x* and y* that Lynn and Gisela spend on clothing when they maximize their utility functions independent of each other.
ii)Calculate the efficient amount of money to be spent on clothing by each of them.
iii)Do they spend too much or too little on clothing? Explain.

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Definitions:

Proposition

A declarative sentence that can be evaluated as true or false, conveying a statement or assertion.

Standard Form

In logic, the standard form refers to a way of structuring categorical propositions to clearly express their subject, predicate, and quantifier, facilitating easier analysis.

Hypothetical Syllogism

A form of logical reasoning that connects two conditional statements to arrive at a conclusion, typically structured as "If P, then Q; if Q, then R; thus, if P, then R."

Werewolves

Mythical or folkloric creatures said to transform from humans into wolves or hybrid wolf-like creatures, often during a full moon.