Question

Consider an individual who lives for two time periods. we will call these period 0 and period 1. in period 0, the individual can choose to attend school or work. in period 1, the individual works. if he does not attend school in period 0, he earns wl ("l" for "low") in both time periods. if he attends school, he pays the cost c in period 0 and earns wh ("h" for "high") in period 1. the individual discounts period 1 earnings using the discount rate, r. assume the individual’s goal is to maximize the present-discounted value (n p v ) of his earnings over these two periods.

Answer 1

The individual should attend school if the present-discounted value (NPV) of the high earnings (wh) in period 1, discounted at the rate r, minus the cost of schooling (c) in period 0, is greater than the earnings without schooling (wl) in both periods.

Step-by-step explanation:

In order to maximize the present-discounted value of earnings, the individual needs to compare the NPV of attending school with the NPV of not attending school. The NPV of attending school is given by:

`\[ NPV_{\text{school}} = wh - c + (wh)/((1+r)) \]`

Here,
`\(wh - c\)` represents the earnings in period 1 after deducting the cost of schooling, and
`\((wh)/((1+r))\)` represents the discounted value of those earnings in period 1. The NPV of not attending school is simply
`\(2 * wl\)`, as the individual earns the low amount (wl) in both periods. Therefore, the decision rule is:

`\[ NPV_{\text{school}} > 2 * wl \]`

Solving this inequality will provide the conditions under which attending school is optimal.

In conclusion, the individual should attend school if the NPV of the high earnings in period 1, discounted at rate r, minus the cost of schooling, is greater than the NPV of earnings without schooling. This decision is based on maximizing the present value of earnings over the two periods while accounting for the discounting factor.