Governments often impose costs on businesses in direct relation to how much labor they hire. They may, for instance, require that businesses provide certain benefits like health insurance or retirement plans.
A: Suppose we model such government regulations as a cost c per worker in addition to the wage w that is paid directly to the worker. Assume that you face a production technology that has the typical property of initially increasing marginal product of labor that eventually diminishes.
(a) Illustrate the isoprofits for this firm and include both the explicit labor cost w as well as the implicit cost c of the regulation.
(b) Illustrate the profit maximizing production plan.
(c) Assuming that it continues to be optimal for your firm to produce, how does your optimal production plan change as c increases?
(d) Illustrate a case where an increase in c is sufficiently large to cause your firm to stop producing.
(e) True or False: For firms that make close to zero profit, additional labor regulations might cause large changes in behavior.
B: Suppose that your production technology can be represented by the production function x = 100/ (1+e− (ℓ−5)) where e ≈ 2.7183 is the base of the natural logarithm.
(a) Suppose w = 10 and p = 1. Set up your profit maximization problem and explicitly include the cost of regulation.