Question

Gerald grew up in Michigan, and recently graduated from the University of Michigan. He has two job offers, one from an employer in Detroit, another from an employer in San Francisco. If he works in Detroit, he can live in his family's house at no cost. The Detroit job pays $55,000 per year. If he moves to San Francisco, he must also pay moving costs. Housing is expensive in San Francisco, costing $24,000 per year. But the San Francisco job pays well, $86,000 per year. Suppose all other costs - food, gas, etc, are the same in both locations. a. Ignoring moving costs, what is the opportunity cost of working in Detroit? b. Suppose Gerald will only work one year. What is the most he'd be willing to pay in moving costs? Moving costs aren't just the price of paying for people to move your stuff. You also leave friends and family, and support networks. You need to spend time and effort learning new directions, making new friends, and so on. Suppose the total moving cost is $20,000. How many years would Gerald need to spend in San Francisco, to make moving worthwhile? c.

Answer 1

a. Solution: $62,000

Explanation: The opportunity cost of working in Detroit will be the benefit of working in San Fransisco, minus the (additional) cost of living there. Thus it will equal $62,000 (=86,000 - 24,000)

b. Solution: $7,000

Explanation: The net benefit to moving to San Francisco for one year will equal $7,000 (= 62,000 - 55,000). When the moving costs equal $7,000, Gerald will be indifferent to moving and not moving. At any cost less than that, Gerald would prefer moving to San Francisco.

c. Solution: 3 Years

Explanation: As calculated in Part-b, the net benefit per year (ignoring moving costs) to living in San Francisco equals $7,000. If Gerald lived there only or a year, moving would lead to a net loss of $13,000 (=7,000-20,000). Two years would also equal a net loss of $6,000. However after 3 years, the total benefit to moving equals $21,000 (= 3*7,000), which compensates for the $20,000 cost in previous years. If Gerald stays there 3 years or more, he should move, else should stay in Michigan and continue working in Detroit.