Application of laplace transforms on first order equations: Mathematical model for developing and analyzing stability of the wage function

In this paper a first order wage equation is developed and solved by Laplace Transforms. The subsequent wage function is then analyzed and interpreted for stability. The function could initially stand off the equilibrium wage rate but in the long run, it asymptotically stabilizes in inter temporal sense. At times, the free market forces are known to cause uncertainties when volatility in wage rate is experienced and this may affect both investments and employment if not controlled. We therefore propose creating a middle path in which wage rate is allowed to oscillate freely within a narrow band managed by employers in consultation with the workers under the watch of the government.