Question

1. 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
   1. Marginal Utility from consuming milk
   2. Marginal Utility from consuming banana
   3. 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?
   4. 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?

Answer 1

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.