2. A homothetic taste can be represented by a utility function that is homogeneous of degree k,

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2. A homothetic taste can be represented by a utility function that is homogeneous of degree $k$, i.e., $U(tx_1, tx_2) = t^kU(x_1, x_2)$, for $t \neq 0$. Then the homothetic taste can always be represented by a homogeneous utility function of degree 1.