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Part B: Answer THREE of the following four questions. Worth 66\frac{2}{3} points.
1. Stutsky decomposition: A consumer has $u = x_1^{\frac{1}{2}}x_2^{\frac{1}{2}}$
(a) Solve for the consumer's demands for good 1 and 2 as a function of income, $M$, and prices $p_1$ and $p_2$ using the MRS and the budget line.
(b) Suppose $M = 60$, $p_1 = 2$ and $p_2 = 1$ but then $p_1$ falls to 1. For good 1 compute the
substitution and income effects of this price change, and show these effects on a clear complete
graph.
(c) Does the substitution effect have to be positive for any Cobb-Douglas utility function?
Explain.