This Question Has You Determine the Effect of a Tax

Essay

This question has you determine the effect of a tax on labor on the long-run cost function.Consider a firm with the production function f(L,K)= LK.The wage rate and rental rate on capital are w and r,respectively.
a.Using the Lagrangian,derive the long-run cost function for this firm.
b.Suppose the government taxes labor at by an amount t per unit of labor.Rewrite the long-run cost function including the tax.Hint: the effective wage rate is now w + t.
c.Compute the marginal effect of the tax on the long-run cost function.To do so,compute the partial derivative of the cost function with respect to t.Does an increase in the tax increase the cost linearly?