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# Homogeneous degree

A function f(X,Z) homogeneous degree y , we multiply each argument a constant, ?, f(?X,?Z)=?Tf(X,Z). Thus, if a function is homogeneous of degree zero, f(?X,?Z)=f(X,Z) because ?0=1. Show that optimal conditions for Cobb-Douglas utility function U(X,Z)=xaz1-a are homogeneous of degree zero. Explain why that result is consistent with the intuition that if we double all prices and income, the optimal bundle does not change. Let the price of good X be Px, let the price of good Z be Pz, and let income be Y. Solve the optimal value of good X and Z!Boyd has the following utility function: U=100B.C0.5, where B represents books and C represents audio CDs. Bundle A contains 7 units of good B and 36 units of good C. Bundle B contains 10 units of good B and 9 units of good C. Which bundle does he prefer? How much is his total level of utility in this case?

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