Problem Set 5 Answer Key

Problem Set 5 Answer Key - j ⊂ R 2 Y j = x y | x ≤ y...

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CB046/Starr 15.1˙15.3˙ May 5, 2011 11:43 1 15.1 Consider production without P.IV(b), but fulFlling P.I–P.III and P.IV(a). ±ormulate an example of Y 1 and Y 2 in R 2 so that the set of points attainable in Y 1 is not bounded. Suggested Answer: Set r = (10 , 10). Let Y 1 = { ( x, y ) | x 0 , y 0 , x = - 2 y } , let Y 2 = { ( x, y ) | x 0 , y 0 , - 2 x = y } . Then the set of points attainable in Y 1 is arbitrarily large. Starting with 10 units of y, Y 1 can produce 20 units of x from which Y 2 can produce 40 units of y, from which Y 1 can produce 80 units of x, . .. . 15.3 In chapter 15 the supply function for Frm j is deFned as S j ( p ) = b y * j | y * j Y j maximizes p · y for all y Y j B . The artiFcially bounded sup- ply function for Frm j , is deFned using the truncated technology set t Y j Y j ± y | y R N , | y | ≤ c ² . t S j ( p ) = { y * j | y * j ˜ Y j , y * j maximizes p · y for all y t Y j } . To demonstrate that using the artiFcially bounded supply function is useful, show that there are examples of Y j fulFlling P.I – P.V so that S j ( p ) is not well deFned even when t S j ( p ) is well deFned. Suggested Answer: Let Y
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Unformatted text preview: j ⊂ R 2 . Y j = { ( x, y ) | x ≤ , y ≥ , y ≤ [-x + r (-x )]. Then for p = ( 1 2 , 1 2 ), S j ( p ) is undeFned as the proFt maximizing production plan is arbitrarily large. t S j ( p ) is well-deFned (though it may be a bit messy to calculate) as ( x, [-x + r (-x )]) so that | ( x, [-x + r (-x )]) | = c . 15.2. Let Y j = { (-x, y) | for 1000 > x ≥ 0, y ≤ ; for x = 1000, - ∞ < y < ∞ } . 1 1000 − x − 1 1000 Let r = (1100, 0). Then the attainable set in Y j and the attainable set in Y are unbounded. 1 16.1. At p' = (0,1), B i (p') = { (x 1 , x 2 ) | x 1 , x 2 ≥ 0, x 1 + x 2 ≤ 10 }. This set is unbounded and admits values of x 1 arbitrarily large. But u(x 1 , x 2 ) is strictly increasing in x 1 so D i (p') is not well defined. = (c, 10), bounded and well defined. D ∼ i ( p ) 1...
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This note was uploaded on 11/30/2011 for the course ECON 311 taught by Professor Zambrano during the Fall '08 term at Cal Poly.

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Problem Set 5 Answer Key - j ⊂ R 2 Y j = x y | x ≤ y...

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