Consider an individual whose labor supply function is given by ln H = ln [(1 t)W], where H is the number of hours of work, W is the hourly wage rate, and t is the tax rate at which labor earnings is taxed. (1 t)W is the effective wage rate (s), as for every dollar earned, government takes away t dollars and the individual is left with only 1 t dollars to take home. Assume that > 0. The government tax revenue (R) is thus, R = tW H(s).

1. Calculate the elasticity of labor supply with respect to effective wage rate?
2. Is it possible for the government to increase their tax revenue by lowering the tax rate, i.e. is dR/dt < 0 possible? If so, derive a condition on elasticity in part (a) such that it guarantees dR/dt < 0? (This condition should be expressed as a function of t.)