final - You must answer#1 and#2 1(5 points Please nd the...

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You must answer #1 and #2. 1. (5 points) Please °nd the pro°t maximizing bundle of inputs for the fol- lowing °rm. (a) f ( x ) = p x p = 6 ; w = 2 2. (5 points) If a production function is q = p K 2 + L 2 ; and w = r = $1 ; how much does it cost to produce 100 units of this good? Please answer 8 of the following questions. 1. (10 points) Please °nd the IR and PO allocations (in a diagram) for the following economy: u A ( x 1 ; x 2 ) = 2 x 1 x 2 ; ! A = (6 ; 4) u B ( x 1 ; x 2 ) = min f x 1 ; 1 3 x 2 g ; ! B = (4 ; 6) 2. (10 points) Please °nd the IR and PO allocations (in a diagram) for the following economy: u A ( x 1 ; x 2 ) = min f x 1 ; 4 x 2 g ; ! A = (4 ; 0) u B ( x 1 ; x 2 ) = min f x 1 ; 2 x 2 g ; ! B = (0 ; 2) 3. (10 points) Find the WE for the economy in #4. Remember, you need allocations x ° A = ( x ° 1 A ; x ° 2 A ) ; x ° B = ( x ° 1 B ; x ° 2 B ) and prices p 1 ; p 2 for a WE. 4. (10 points) Is the WE you found for #5 stable? Illustrate this in a diagram. 5. (5 points) What do the abreviations IR, PO and WE stand for? 6. (20 points) Please °nd the IR, PO and WE for the following economy: u A ( x 1 ; x 2 ) = x 2 1 + x 2 2 ; !
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