. Suppose you moved to another place where the cost of living was higher, but your job paid more there. If a new job at a different place doubled your income per year but also doubled your cost of living per year, then assuming your income per year-standard of living > 0, would you have more money, less money, or the same amount of money left over than before? Prove your answer.
let this be the original place
Income-Expenses=residue savings
let this be the new place
2*income-2*expenses= 2(Income-expenses)=2*residue
so your savings is twice as much.
To determine whether you would have more money, less money, or the same amount of money left over after moving to a place with a higher cost of living and a higher-paying job, let's break down the scenario step by step.
1. Consider your income and standard of living in the original place.
- Let's assume your income per year is represented by I1, and your standard of living per year is represented by S1.
2. Calculate the money left over in the original place.
- The money left over is calculated by subtracting your cost of living from your income per year: Leftover1 = I1 - S1.
3. Evaluate the income and standard of living in the new place.
- If you move to a place where your income doubles, it becomes 2*I1.
- Similarly, if your cost of living also doubles, it becomes 2*S1.
4. Calculate the money left over in the new place.
- The money left over now is: Leftover2 = 2*I1 - 2*S1 = 2*(I1-S1).
Now, let's analyze the comparison between the two scenarios:
- If I1-S1 > 0 (income per year minus standard of living is positive), it means you had money left over in the original place.
- Comparing Leftover2 and Leftover1, we can observe that Leftover2 is double the value of Leftover1.
- Since Leftover1 was positive (as I1-S1 > 0), doubling it will yield a positive value as well.
Therefore, based on these calculations, you would have more money left over after moving to a place with a higher cost of living and a higher-paying job.