Question

Q. Assume that you are deciding whether to move to Umeå or stay in Stockholm. If you stay you will earn a constant wage wS throughout your career, and if you move you will earn wU throughout your career. Also assume that you live and work forever. Moving costs are equal to M.

a) Derive the condition under which you are indifferent between moving and staying.

b) Explain how changes in moving costs, in the interest rate and in the wage differential (wU–wS) would affect your decision

Answer 1

Part a)

Let the interest rate be constant and equal to r.

If we stay in Stockholm,

the present value of earnings would be:

PV_S = w_S/(1+r) + w_S/(1+r)² + ...

PV_S = w_S/r

If we decide to move to Umea,

the present value of earnings would be:

PV_U = -M + w_U/(1+r) + w_U/(1+r)² + ...

PV_U = (w_U/r) - M

If we are indifferent between staying and moving, both present values need to be equal.

Hence:

PV_S = PV_U

w_S/r = w_U/r - M

Hence:

M = (w_U - w_S)/r ......... This is the condition for being indifferent

Part b)

Let us consider that currently we are indifferent between the two.

If moving cost M increases, PV_S > PV_U and hence staying in Stockholm is preferred, and vice versa for M decreasing.

If interest rate r increases, PV_S > PV_U and hence staying in Stockholm is preferred; and vice versa for r decreasing.

If wage differential (w_U - w_S) increases, PV_S < PV_U and hence moving to Umea is preferred; and vice versa for (w_U - w_S) increasing.