Gupta, Abhay (2007): Skills Distribution, Migration and Wage Differences in Pure Service-Exchange Economy.
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This paper considers an economy with skilled agents exchanging their services. Using Cobb-Douglas preferences, the paper shows that there exists an optimal (average welfare maximizing) skills' distribution. This optimal distribution is independent of productivity and is welfare equalizing.
If the skill-distribution is not optimal, then some agents are better-off than others. In such a scenario, migration in some sectors is average-welfare improving while inviting skilled-agents in others reduces average welfare.
"Productivity increase of worse-o sector" without changing the overall skills' composition of economy increases the wage gap.