aps3 301 f06 1_Solutions - Econ 301 F06 PROBLEM SET 3 -...

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p /p x y = 1 PCC y x u=x+y y x PCC u=min{x,y} Econ 301 – F06 PROBLEM SET 3 - ANSWERS Wissink 1. For changes in Px, diagrammatically show what the price offer/consumption curve (POC = PCC) looks like for the following utility functions: u(x,y) = xy; u(x,y) = x + y; u(x,y) = min{x,y}. y x POC/PCC u=xy
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ICC u=xy y x ICC u=min{x,y} y x 2. For changes in I, diagrammatically show what the income consumption/offer curve looks like for the following utility functions: u(x,y) = xy; u(x,y) = x + y; u(x,y) = min{x,y}. 3. For changes in Px, diagrammatically show the income and substitution effects ala’ Hicks for the following utility functions: u(x,y) = xy; u(x,y) = x + y; u(x,y) = min{x,y}. See next page. 2 y x indifference curves budget lines ICC Suppose "x" costs less than "y" u=x+y
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y x u=xy E E E 0 1 H x y indifference curves budget lines u=x+y E E = E 0 H 1 suppose px<py y x u=min{x,y} E 0 H E = E 1 4. Derive the demand functions for x & y for the utility function: u(x,y) = y + bln(x). Assume values so that x>1. u(x,y) = y + bln(x) implies MRS = b/x. The ERS = Px/Py. At the optimal bundle it will be true that MRS = ERS which implies that b/x = Px/Py or, rearranging, that
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aps3 301 f06 1_Solutions - Econ 301 F06 PROBLEM SET 3 -...

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