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 of 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 the 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 units of labor, where > L*. Carefully describe a subsidy scheme to profit maximizing employers that will make them choose this level of employment.

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