Question

Refer to the data. If the consumer has money income of $52 and the prices of J and K are $8 and $4 respectively, the consumer will maximize her utility by purchasing:

a. 2 units of J and 7 units of K.
b. 5 units of J and 5 units of K.
c. 4 units of J and 5 units of K.
d. 6 units of J and 3 units of K.

Answer 1

The correct answer is c. 4 units of J and 5 units of K.

Explanation:

To maximize the utility income we have to try to use most of the $52 buying J and K.

The equation is Utility= J *$8 + K * $4

a. 2 units of J and 7 units of K.

Utility= 2 *$8 + 7 * $4= 44 We have more money to spend.

b. 5 units of J and 5 units of K.

Utility= 5 *$8 + 5 * $4= 60 We don´t have enough money.

c. 4 units of J and 5 units of K.

Utility= 4 *$8 + 5 * $4= 52 maximize.

d. 6 units of J and 3 units of K.

Utility= 6 *$8 + 3 * $4= 60 We don´t have enough money.

Answer 2

Answer: Option C ( 4 units of J and 5 units of K)

Explanation:

First of all to maximize utility means to get the most value from the available money, and in this case it means to buy the maximum amount of items J and K with 52 dollars.

• Option C is for 4 units of J and 5 units of K

• 1 unit of J costs 8 dollars, therefore 4 units of J would cost 4×8=32 dollars.

• 1 unit of K costs 4 dollars, therefore 5 units of J would cost 5×4= 20 dollars.

• The total cost of 4 units of J and 5 units of K would be equal to 32+20= 52 dollars.

• From the calculations above we are able to but 4 units of J and 5 units of K with the 52 dollars and without having and change left or being in debt. This would mean we have maximized our utility.

• If we were to buy 2 units of J and 7 units of K as I option A, we would have a total of 44 dollars which leaves us with a change of 8 dollars. We could still have bought one more of item J or 2 more of item K with the change. Therefore we would not have maximized our utility (the money) if we had done chosen A. The same applies if we go with options B and D, but in this case we would be spending more than what we have.