2. (8 points) A worker is deciding how long to stay in coo Assume that the only

Question

2. (8 points) A worker is deciding how long to stay in coo Assume that the only cost of schooling is foregone earnings and that the worker lives forever. Let r denote the discount rate per year. Let b denote the increase in earnings with each year of schooling. If a worker attends school for k years, then her annual earnings are 10 +b k. (a) Explain whether the optimal level of schooling is increasing or decreasing in r (b) Explain whether the optimal level of schooling is increasing or decreasing in b

Explanation / Answer

Thanks for the question.
In this problem, an individual has to decide whether to join the job market and earn money or to invest more years in acquiring higher education. The discount rate per annum is r% meaning that if the person works and invests his money in the bank, he will earn r% interest on his income every year. On the other hand, if he prefers to acquire higher education, he forgoes his income and the interest earned on it. However, each year of education leads to an increase in his income by b units.
Here, if the person decides to get k years of education, his annual earnings increase to 10 + b.k from 10 units had he not acquired any education. So, he earns bk additional units of income when he acquires k years of education.
On the other hand, had he worked for these k years and saved the money, he would have,
k(10 + 10r/100) = k(10 + 0.1r) at the end of k years.
The person will decide whether to get higher education based on these two factors i.e. the income forgone during those years k(10 + 0.1r) and the additional income bk earned if he gets k years of education. The greater the value of discount rate r, the larger the income forgone if he acquires more education and lesser is the incentive to get higher education. Also, larger the value of b, the greater is the additional income earned after getting higher education which increases the incentive to get higher education.
Therefore, the optimal level of schooling decreases with increase in r and increases with increase in b.

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