Given the utility function U = 2X + 4Y, what is the indifference function for the bundle where X = 2 and Y = 1?

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Study for the University of Central Florida ECO2023 Principles of Microeconomics Final. Prepare with multiple choice questions, flashcards with helpful hints and explanations. Ace your exam!

To find the indifference function for the utility function ( U = 2X + 4Y ) at the specific bundle ( X = 2 ) and ( Y = 1 ), we first need to determine the utility level associated with that bundle.

Plugging in the values into the utility function:

[ U = 2(2) + 4(1) = 4 + 4 = 8 ]

Now, to find the indifference function, we set ( U = 8 ) and solve the equation for ( Y ):

[ 8 = 2X + 4Y ]

Rearranging this to solve for ( Y ):

[ 4Y = 8 - 2X ] [ Y = 2 - 0.5X ]

Thus, the indifference function shows how utility remains constant as the quantities of ( X ) and ( Y ) change. The derived equation ( Y = 2 - 0.5X ) represents a linear relationship between ( X ) and ( Y ) where the consumer would have the same level of utility given different combinations of goods. This relationship corresponds to the answer