Question

We want to find the optimal affordable bundle for each of the following utility functions (with prices and wealth). In Problem Set \#2, you completed this task for only the problems where the three "regularity conditions" were satisfied; in this assignment, you will find the optimal bundle for the other problems, for which some condition failed. For each problem: (a) If the optimal bundle was found in PS\#2, do nothing- the problem is already solved! (b) If not, briefly discuss the shape of the indifference curves for this problem, and what strategy should be used to find the optimal bundle rather than the tangency method. (c) Find the optimal bundle using the strategy you described in (b)

Answer 1

To find an optimal bundle when tangency methods fail, alternative methods such as comparing total utility or marginal utility to price ratios are used. These approaches help in identifying the highest utility choice within the budget constraint when facing atypical indifference curves or corner solutions.

Step-by-step explanation:

In the context of economics, specifically in consumer theory, we approach identifying the optimal affordable bundle for various utility functions through different strategies. When the traditional method of finding a tangency point between the budget line and indifference curves is not applicable due to the violation of certain regularity conditions, alternative methods need to be employed. One such method involves comparing the total utility of each bundle on the budget constraint and selecting the one with the highest total utility. Another strategy is to start with a random bundle and progressively move towards the bundle with a higher utility by comparing the marginal utility gains and losses of possible moves.

Additionally, one may consider the ratio of marginal utility to the price for each good and find the optimal bundle by ensuring that these ratios are equal for all goods at the point of maximization. An indifference curve represents combinations of goods that provide the same level of utility. Indifference curves further from the origin represent higher levels of utility. The most preferred combination within the budget constraint is the point of tangency between the highest indifference curve and the budget line. However, when a tangency cannot be reached or does not exist, individuals will choose the point that offers them the highest utility that is still within their budget constraints.