In: Economics
The utility function is given as
, and the budget constraint would be as
or
.
(a) The marginal utility of milk would be as
or
or
or
.
(b) The marginal utility of banana would be as
or
or
or
.
(c) The utility would be maximum where
or
. If the agent cosumes 1 unit of both goods, we have
or
or
and
or
or
.
So, if the agent consumes 1 units of both products, we have
, and hence the agent is maximizing utility.
(d) The utility would be maximum where
or
. If the agent cosumes 2 units of milk and 6 units of banana of
both goods, we have
or
or
and
or
or
or
.
As can be seen, we have
.
So, the agent is not maximizing utility when consuming 2 units
of milk and 6 units of banana. In order to maximize utility and
achieve
, the agent must decrease
and/or increase
, ie must decrease
and/or increase
.
Now, for
, and since
or
and
or
,
would decrease if milk consumption increases and/or banana
consumption decreases.
Also, for
, and since
or
and
or
,
would increase if milk consumption increases and/or banana
consumption decreases.
Hence, in order to maximize utility, the agent should increase milk consumption and/or decrease banana consumption.