(1) Interpret each argument in each term, and each term in equation (8.1) in Quiet Revolution in Welfare Economics. What does the equation say? What are the implications for efficiency?
(2) According to the H&A model of the conflict school, what would be the effect of higher turnover rates on the efficiency of the economy? Briefly explain.
(3) A firm’s output in time t is a positive function of the amount of two different kinds of labor done: x(t) = x(LD1(t),LD2(t)) for t = 1,2. Both first partial derivatives of x(t) are positive.
The amount of each kind of labor done is a function of the number of hours of that kind of labor and of the employee’s effort level: LD1(t) = LD1(h1(t),e(t)); LD2(t) = LD2(h2(t),e(t)) for t = 1,2. Both first partials of all LDs are positive.
Effort is a positive function of employer bargaining power:
e(t) = e(BP(t)) for t = 1,2. The first derivative of e w.r.t. BP(t) is positive.
Empoyer bargaining power in period 2 is negatively affected the more of characteristic C employees have in period 2: BP(2) = BP(2)(C(2)). The first derivative of BP(2) w.r.t. C(2) is negative.
Performing hours of type 1 labor in period 1 has no effect on characteristic C in period 2. However, performing hours of type 2 labor in period 1 increases characteristic C in period 2: C(2) = C(2)(h2(1)). The derivative of C(2) w.r.t. h2(1) is positive.
Assume both society and the employer have a 10% rate of time discount. Assume the price of x is 1 in both time periods. Assume the retention rate for employees from period 1 to period 2 is 80%. Finally, assume the hourly wage rate for each kind of labor is set exogenously in its labor market, and does not change from period 1 to period 2, i.e: W1(1) = W1(2) = W(1) and W2(1) = W2(2) = W(2).
(a) Formuate the profit function for the firm.
(b) Write out two first order conditions, FOCs, for maximizing profits: the first order condition for profit maximization regarding the amount of type 1 labor to hire in period 1, and the first order condition for profit maximization regarding the amount of type 2 labor to hire in period 1.
(c) Interpret all the terms in each FOC: Specifically state if a term refers to an effect in period 1 or 2; if the term is a part of traditional analysis or only appears in a conflict theory of the firm analysis; if the term is positive or negative, if the term is a private benefit or private cost to the employer; and if the term is a social benefit or social cost to society.
(d) Explain what the FOC for each type of labor implies about how many hours of each type of labor a profit maximizing employer will hire compared to what traditional analysis predicts.
(e) Explain what the FOC for each type of labor implies about how many hours of each type of labor a profit maximizing employer will hire compared to the amount that is socially efficient.
(f) How would an increase in the employer’s rate of time discount affect any inefficiency in the use of either type of labor? Briefly explain.
(g) How would an increase in the retention rate of employees affect any inefficiency in the use of either type of labor? Briefly explain.
(h) Give a real-world example of a kind of labor activity that would be like type 2 labor.