Rubinstein2005-page84

Rubinstein2005-page8 - and w a number Consider the set G = p x ∈ ± K × ± K | x is optimal in B p w(For some price vectors there could be more

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October 21, 2005 12:18 master Sheet number 82 Page number 66 Problem Set 5 Problem 1. ( Easy ) Calculate the demand function for a consumer with the utility function k α k ln ( x k ) . Problem 2. ( Easy ) Verify that when preferences are continuous, the demand function x ( p , w ) is continuous in prices and in wealth (and not only in p ). Problem 3. ( Easy ) Show that if a consumer has a homothetic preference relation, then his demand function is homogeneous of degree one in w . Problem 4. ( Easy ) Consider a consumer in a world with K = 2, who has a preference relation that is quasi-linear in the first commodity. How does the demand for the first commodity change with w ? Problem 5. ( Moderately Difficult ) Let ± be a continuous preference relation (not necessarily strictly convex)
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Unformatted text preview: and w a number. Consider the set G = { ( p , x ) ∈ ± K × ± K | x is optimal in B ( p , w ) } . (For some price vectors there could be more than one ( p , x ) ∈ G .) Calculate G for the case of K = 2 and preferences represented by x 1 + x 2 . Show that (in general) G is a closed set. Problem 6. ( Moderately difficult ) Determine whether the following behavior patterns are consistent with the consumer model (assume K = 2 ) : a. The consumer’s demand function is x ( p , w ) = ( 2 w /( 2 p 1 + p 2 ) , w /( 2 p 1 + p 2 )) . b. He consumes up to the quantity 1 of commodity 1 and spends his excess wealth on commodity 2....
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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