Consider a labor surplus economy producing a single output, which can be consumed (as food) or invested (as capital). Labor, once employed, must be paid a fixed wage w which is fully consumed. All surpluses from production are reinvested.
A) Draw a diagram showing how output is distributed between consumption and reinvestment, for some chosen level of employment. Show profit-maximizing employment: level call it L*.
B) Reinvested surplus raises consumption tomorrow. Suppose that a social planner cares about consumption today and consumption tomorrow. Show that she will always wish to choose an employment level not less than: L*
C) Suppose that the planner wishes to employ L units of labor, where L>L*. carefully describe a subsidy scheme to profit maximizing employers that will make them choose this level of employment.