Let individual i have the utility function Ui(x,y) = x^1/2 * y Suppose the initial endowment is x = 16 and y = 2. a. Determine 4 combinations (x,y) for which Ui=8 ; Ui=16. b. What is the minimum amount of x that i would have to be compensated to introduce him to give up 1 unit of y?
The utility function is given as
.
(a) For utility level be 8, we have
or
or
. For y=1,
. For y=2,
. For y=4,
. For y=8,
.
Hence, the required four combinations of (x,y) for U=8 is
.
For utility level be 16, we have
or
or
. For y=1,
. For y=2,
. For y=4,
. For y=8,
. Additionally, for y=16,
.
Hence, the required four combinations of (x,y) for U=16 is
.
(b) For the given endowment, we have
. From the set of bundles
, we can see that, consumer is endowed at second point. To go to
the first point, thereby reducing the consumption of y by 1 unit,
the consumer must be compensated with 64 minus 16, ie 48 units of
x. Hence, the minimum amount of x is 48 units, which have to be
compensated to induce consumer to give up 1 unit of y.
Let individual i have the utility function Ui(x,y) = x^1/2 * y Suppose the initial endowment...
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