A firm produces output using the technology:
Q = 5K0.33L0.5
where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and Q denotes the yearly output. The hourly wage rate in the United States WL= $10, and the hourly rental rate of capital (IN EFFECT CAPITAL COSTS $2 PER MACHINE HOUR) is WK= 2 and the Price is $10.
(a) Does this production function display increasing returns to scale, constant returns to scale or decreasing returns to scale (hint—use labor). Please show how you arrived at this conclusion (this requires a mathematical answer that you must show).
(b) Compute the marginal products of labor and capital. Show that there are diminishing, but positive, returns to the labor input.
(c) Suppose that the firm has signed a contract to rent K = 800 machine hours over the course of the year. Determine the equilibrium level of Labor.
(d) If the wage level in Chile is $4, (given the same MPLin the US), what is the equilibrium level of Labor
demanded in Chile. If wages in Chile fall to $2, what is the new level of demand for labor in Chile? (3 Points) How can the workers in the US combate this potential transfer of jobs to Chile (there are two possible solutions).