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To determine if preferences are homothetic, you need to check if the utility function can be expressed in a specific form, typically as ( U(x_1, x_2) = f(g(x_1, x_2)) ), where ( f ) is a monotonic function and ( g ) is a homogeneous function of degree one. This means that if you scale all inputs by a positive factor ( t ), the utility changes in a proportional manner, i.e., ( U(tx_1, tx_2) = tU(x_1, x_2) ). If this condition holds, preferences are homothetic, indicating that the consumer's marginal rate of substitution remains consistent across different consumption levels.

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3w ago

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Related Questions

How can one demonstrate that a function is homothetic?

A function is homothetic if it can be transformed into another function by scaling both the input and output variables by the same factor. This can be demonstrated by showing that the function's shape remains the same when both variables are scaled proportionally.


What is the relationship between a homothetic function and its scaling properties?

A homothetic function is a type of function that exhibits scaling properties, meaning that it maintains its shape when scaled up or down by a constant factor. In other words, the function's behavior remains consistent regardless of the scale at which it is observed.


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