Question: Consider the Cobb-Douglas function \(U(x, y)=x^{\alpha} y^{\beta}\)

1. Derive the MRS
2. For commodity bundles for which \(y=x\), how does the MRS depend on the values of \(\alpha\) and \(\beta\) ? Develop an intuitive explanation of why if \(\alpha>\beta\), MRS \(>1\).
3. Suppose an individual obtains utility only from amounts of \(x\) and \(y\) that exceed minimal subsistence levels given by \(x_{0}, y_{0}\), so that his utility function is given by \(U(x, y)=\left(x-x_{0}\right)^{\alpha}\left(y-y_{0}\right)^{\beta}\)

Is this function homothetic?

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