# Suppose that you know the utility function for an individual is given by the equation U = XY...

## Question:

Suppose that you know the utility function for an individual is given by the equation {eq}U = XY {/eq} where {eq}U {/eq} is the total amount of utility the individual gets when they consume good {eq}X {/eq} and good {eq}Y {/eq}. You are also told that this individual's income is $100 and that the price of good {eq}X {/eq} is$2 and the price of good {eq}Y {/eq} is $4. From this information answer the following set of questions. a) What is the consumption bundle of good {eq}X {/eq} and good {eq}Y {/eq} that maximizes this individual's utility given their income, prices of the two goods, and their tastes and preferences as measured by their utility function? Support your answer with a well-labeled diagram. b) What is the level of utility this individual gets when they maximize their utility given the above information? c) Suppose that the price of good {eq}X {/eq} increases to {eq}$4 {/eq} and nothing else changes. What is the new consumption bundle that maximizes the individual's utility now that the price of good {eq}X {/eq} has increased? What has happened to his utility? Determine the {eq}SE {/eq} and {eq}IE {/eq}.

## Utility function

Utility function is the function which show the satisfaction derived from the consumption of the commodity concerned with the constrained budget. This function shows a negative value when the consumption is more than the optimum level.

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a)

The utility function is:

{eq}\begin{align*} U &= XY\\ M{U_X} &= Y\\ M{U_Y} &= X \end{align*} {/eq}

The budget constraint is {eq}100 = 2X +...