a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?
a. A consumer is willing to trade 3 units of x for 1 unit
of y when she has 6 units of x and 5 units of y. She is
also willing to trade in 6 units of x for 2 units of y when
she has 12 units of x and 3 units of y. She is indifferent
between bundle (6, 5) and bundle (12, 3). What is the
utility function for goods x and y? Hint: What is the
shape of the indifference curve?
b. A consumer is willing to trade 4 units of x for 1 unit
of y when she is consuming bundle (8, 1). She is also
willing to trade in 1 unit of x for 2 units of y when she
is consuming bundle (4, 4). She is indifferent between
these two bundles. Assuming that the utility function is
Cobb–Douglas of the form U (x, y) = xα y β
, where α and
β are positive constants, what is the utility function for
this consumer?
c. Was there a redundancy of information in part (b)? If
yes, how much is the minimum amount of information
required in that question to derive the utility function?
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