Final answer:
To maximize utility with a $25 budget, you need to consider the utility from each movie and concert, costing $2.00 and $5.00 respectively. An ideal combination cannot be identified without knowing the utility values. If income increases to $2,000, preferences and diminishing marginal utility will dictate the new utility-maximizing choice.
Step-by-step explanation:
To determine the optimal combination of movies and concerts to attend to maximize utility given an income of $25, one must consider the budget constraint and the costs of movies and concerts. With movie tickets priced at $2.00 each and concert tickets costing $5.00 each, it's necessary to look at different combinations within the $25 budget.
For example, if you were to only attend movies, you could attend 12 movies (since 12 movies × $2.00 = $24) and have $1 left over. Conversely, if you only wanted to attend concerts, you could attend 5 concerts (since 5 concerts × $5.00 = $25) and use your entire budget.
However, without specific information on the utility derived from each movie or concert, it is impossible to provide a definitive optimal combination. In economic terms, utility refers to the satisfaction or value one receives from consuming goods or services. If attending concerts gives you more utility than movies, you might prioritize attending as many concerts as your budget allows. Alternatively, if movies provide equal or greater utility, you could choose to attend more movies instead.
If the income increases to $2,000, the new budget constraint allows for many more movies and concerts to be attended. The utility-maximizing choice will depend on the marginal utilities of the concerts and movies. If these remain constant, a person might simply consume more of both goods. However, more often, consumption will not increase proportionally due to diminishing marginal utility; as one consumes more of a good, the additional satisfaction tends to decrease. Therefore, the new optimal combination will still require an assessment of utility and personal preferences under the adjusted budget constraint.