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MECON PS6 sol

# MECON PS6 sol - Microeconomics Problem Set 6 Questions Due...

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Microeconomics Problem Set 6 Questions Due February 24th, 2010 Winter 2010 ECON 100A 1. Rene also consumes kangaroo burgers and vegemite but she is picky about the ratio in which she eats them. Her preferences can be represented by the utility function U = min(V,B). Rene receives fixed money income Y. a. Compute her Marshallian demand functions x B * (p B , p V , Y) and x V * (p B , p V , Y). Find her indirect utility function v(p B , p V , Y) and show Roy’s identity holds. V B V B p p Y x x + = = * * V B V B p p Y Y p p V + = ) , , ( Roy’s identity: V B p p dY dV + = 1 / 2 ) ( / / V B V B p p Y dp dV dp dV + = = ) ( / / * V B V B p p Y dY dV dp dV x + = - = b. Compute her Hicksian demand functions x B h (p B , p V , U) and x V h (p B , p V , U). (Hint: think about it before plunging in: take a specific indifference curve, what is the cheapest combo of B and V that will get Rene on it.) Find her expenditure function E(p B , p V , U) = p B x B h + p V x V h and show that E/ pi = x i h for each i. U x x h V h B = = U p p U p p E V B V B ) ( ) , , ( + = Shepard’s Lemma ( E/ pi = x i h ) falls out of this easily. c. Imagine a change in the price of kangaroo burgers. Show the Slutsky equation holds in this case. (Hint: remember to differentiate each piece first, plug in for U after.)

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x B / p B = -Y/(p B + p V ) 2 x B h / p B = 0 x B / E * x B = 1/(p B + p V ) * Y/(p B + p V ) = Y/(p B + p V ) 2 . The first is equal to the second plus the negative of the third. Note: the SE is zero! Makes sense, though. Rene does not substitute in any way when prices change…only bundles on the kink are possible. 2.
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MECON PS6 sol - Microeconomics Problem Set 6 Questions Due...

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