Arlo is offered a job in Des Moines, where the CPI is 60, and a job in New York, where the CPI is 125. Arlo's job offer in Des Moines is for $48,000. How much does the New York job have to pay in order for the two salaries to represent the same purchasing power?

a.

$23,040

b.

$52,000

c.

$79,200

d.

$100,000

Question

Arlo is offered a job in Des Moines, where the CPI is 60, and a job in New York, where the CPI is 125. Arlo's job offer in Des Moines is for $48,000. How much does the New York job have to pay in order for the two salaries to represent the same purchasing power?

a.

$23,040

b.

$52,000

c.

$79,200

d.

$100,000

BlackTom AI · Accepted Answer

Let's restate the problem to be clear: Arlo has a job in Des Moines with a CPI of 60 and a salary of $48,000. A different job in New York has a CPI of 125, and we want to find the New York salary that gives the same purchasing power as the Des Moines salary.

First, convert the Des Moines salary into a purchasing power equivalent using real wage = nominal salary / CPI. For Des Moines: 48,000 ÷ 60 = 800. This 800 represents the purchasing power level we want to match in New York.

Now evaluate each option by computing its purchasing power in New York: real wage in New York = NewYorkSalary ÷ 125.

Option a: $23,040. Real wage = 23,040 ÷ 125 = 184.32. This is far below 800, so it does not match the Des Moines purchasing power.

Option b: $52,000. Real wage = 52,000 ÷ 125 = 416. This is still below 800, so it does not match the Des Moines purchasing power.

Option c: $79,200. Real wage = 79,200 ÷ 125 = 633.6. Closer, but still below 800; therefore it does not match the Des Moines purchasing power.

Option d: $100,000. Real wage = 100,000 ÷ 125 = 800. This exactly matches the Des Moines real wage, meaning equal purchasing power between the two locations.

To confirm the general approach, remember the core idea: to compare purchasing power across contexts with different price levels (CPI), you adjust by dividing the nominal salary by the CPI. The goal is to have the same real wage on both sides, i.e., salary1/CPI1 = salary2/CPI2. Applying this rule shows option d achieves equality, while options a, b, and c fall short because their resulting real wages are less than 800.

In summary, the evaluation shows that only the option with $100,000 in New York yields the same purchasing power as $48,000 in Des Moines given the CPI values 60 and 125, respectively.

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