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Econ 5201 HW 2

Econ 5201 HW 2 - Econ/ARE 5201 Fall 2010 Subhash Ray...

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Econ/ARE 5201 Subhash Ray Fall 2010 Homework Problem Set #2 1. John consumes two goods: good 1 and good 2 and has the utility function 2 1 2 1 4 x x x x U + = where x 1 and x 2 are the quantities of the two goods consumed. The prices of the two goods are p 1 and p 2 , respectively. He spends his entire income on these two goods. (a) Obtain his Marshallian demand functions and ) , , ( 2 1 1 1 m p p x x d = ). , , ( 2 1 2 2 m p p x x d = (b) Obtain his indirect utility function U * = V (p 1 , p 2 , m). (c) For ) 60 , find his optimal consumption bundle. 1 , 4 ( 2 1 = = = m p p (d) Now consider a new situation with ). 64 , 4 , 1 ( 2 1 = = = m p p Is John better or worse off in the new situation? (e) Obtain his optimal consumption bundle directly from V(p 1 , p 2 , m) for the new prices and income. 2. Bill derives utility from the consumption of apples and bananas. He has an endowment of 8 apples and 12 bananas. His utility function is b a x x U + = ) ln( 4 where x a and x b are, respectively, the quantities of apples and bananas consumed by

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Econ 5201 HW 2 - Econ/ARE 5201 Fall 2010 Subhash Ray...

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