Question

Jane has assigned a budget of $50 for books and CD purchases. Her utility function for these activities depends on the number of books she buys (B) and the number of CDs she purchases (C). The price of a book is $15, the price of a CD is $10. She tells you that she has solved her consumer choice problem. By asking her some questions, you determine that:

* Her solution indeed uses up all of her budget.

* The marginal utility of a book in her solution is 45 units of utility.

* The marginal utility of a CD is 40 units of utility.

(A) Using this information, determine whether Jane has achieved the highest possible utility she can achieve. If she has, explain how you know. If she hasn’t, explain how she could do better. (Draw CD’s on the horizontal axis)

(B) How would your answer change if the price of CDs were to double?

Illustrate both (a) and (b) with a diagram.

Answer 1

Jane has not achieved the highest possible utility because the marginal utility per dollar spent on books is not equal to that of CDs, as it should be according to the equal marginal principle. If the price of CDs doubles, Jane's utility-maximizing choice would alter, as this change would affect the marginal utility per dollar ratio.

Step-by-step explanation:

When assessing whether Jane has achieved the highest possible utility, we should consider the principle of maximizing utility whereby the ratio of the marginal utility of each good to its price should be equal across the goods. This is known as the equal marginal principle. In Jane's case, we need to check if her marginal utility per dollar spent on books is equal to the marginal utility per dollar spent on CDs.

The marginal utility per dollar for books is 45 units of utility per $15, which simplifies to 3 units of utility per dollar. For CDs, it's 40 units of utility per $10, simplifying to 4 units of utility per dollar. Since these ratios are not equal, Jane has not achieved the highest possible utility. She can achieve a higher utility by purchasing more CDs and fewer books until the marginal utilities per dollar are equalized.

If the price of CDs were to double to $20, the marginal utility per dollar for CDs would drop to 2 units (40 units of utility per $20). This would change the equal marginal principle calculation, potentially leading to a different combination of books and CDs being the utility maximizing choice. Without redistributing her spending, Jane would not be on her highest indifference curve after the price change. A new consumer equilibrium would need to be found where the new marginal utility per dollar for CDs equals the marginal utility per dollar for books.