Question
In: Economics
If the Utility function for the consumption of milk and bananas is given by U =qm0.6qb0.4...
- If the Utility function for the consumption of milk and bananas
is given by U
=qm0.6qb0.4
and the price of milk is $12 and price of banana is $8, find
- Marginal Utility from consuming milk
- Marginal Utility from consuming banana
- Will the consumer be maximizing satisfaction when he/she consumes one unit each of milk and bananas? If not, what should he/she consume next to increase satisfaction?
- Will the consumer be maximizing satisfaction when he/she consumes two units of milk and six units of bananas? If not, what should he/she consume next to increase satisfaction?
Solutions
Expert Solution
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.
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