How do you find if preferences are homothetic?

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.