2. [8 Points) Michael has I dollars to spend on goods 3: and y. Commodity 1' msts p: per unit and commodity 1: costs pg. His utility function is
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# Michael has I dollars to

spend on goods x and y. Commodity x costs px per unit and commodity y costs py. His utility function is U(x, y) = x(y + 1).

2. [8 Points) Michael has I dollars to spend on goods 3: and y. Commodity 1' msts p: per unit and
commodity 1: costs pg. His utility function is U{;r:,y) = 3(y+ 1).
{a} (2 Points} What is the optimal (Marshallian) demand ﬁmction for good I and y?
(b) (2 Points} Calculate Michael‘s indirect utility function and expenditure function.
{c} (2 Points) What is the optimal Hicksisn demand function for commodity :1: and 3:? Suppose now that p, = pi, = 5 and I = 145. {d} (2 Points} Find the substitution and income eﬂ'ects (according to Slutsky decomposition} when the
price of good 1' increases to 10.

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