Final answer:
The present value of the worker's lifetime earnings in San Juan, with an annual earning of 25 and a discount rate of 10%, is 250. The calculation is based on the present value of perpetuity since the worker lives forever. For her potential earnings in New York, the present value would similarly be calculated, but migration costs would need to be subtracted.
Step-by-step explanation:
The worker's decision to migrate from San Juan to New York involves calculating the present value of her future earnings in both locations. To find the present value (PV) of her lifetime earnings if she stays in San Juan with an annual earning of 25 and a discount rate of r = 0.10 (or 10%), we can use the formula for the present value of a perpetuity:
PV = Annual Earning / Discount Rate
Thus, PV = 25 / 0.10 = 250.
This is because the worker lives forever, so the earnings stream resembles a perpetuity. In New York, the situation is similar, but she would incur a migration cost M at year 0. If we were to include the cost of migration, it would simply be deducted from the present value of earnings in New York.
It's important to note that making such a decision also involves considering other factors that could affect her choice, such as cost of living differences, quality of life, and personal preferences, which are not included in the calculation here.