Question

(a) Determine the socially optimal amount of furniture, x_o, that maximizes the total surplus of these n students.

(b) Determine the total amount x^* that will be donated by n individuals.

(c) Compare x_o with x^*, and provide the intuition.

In this scenario, the Economics Department is collecting money from n graduate students to refurbish a student lounge. Each student donates a certain amount of money to purchase furniture, and their utility depends on the total amount of furniture and the cost of each unit. The goal is to find the socially optimal amount of furniture (x_o) and the total amount that will be donated by all students (x^*). Comparing these two values will reveal whether the students' donations are aligned with the socially optimal level and provide insight into the efficiency of the contribution process.

Answer 1

To determine the socially optimal amount of furniture and the total amount donated by students, compare the marginal utility to the cost of each unit of furniture. If the donations are less than the socially optimal level, it implies inefficiency in the contribution process.

Step-by-step explanation:

The socially optimal amount of furniture, x_o, that maximizes the total surplus of these n students can be determined by comparing the marginal utility of each student with the cost of each unit of furniture. The socially optimal amount occurs where the ratio of marginal utility to price is equal for all students.

The total amount that will be donated by all students, denoted as x^*, can be determined by adding up the individual contributions of each student.

By comparing x_o (the socially optimal amount) with x^* (the total amount donated by all students), we can determine if the students' donations are aligned with the socially optimal level. If x_o is greater than x^*, it means that the students are not donating enough to reach the socially optimal level of furniture.