A firm produces output using the technology:

Q = 5K^0.33L^0.5

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 W_L = $20, and the hourly rental rate of capital (IN EFFECT CAPITAL COSTS $2 PER MACHINE HOUR) is W_K = 3 and the Price is $10.

(a)Does this production function display increasing returns to scale, constant returns to scale or decreasing returns to scale(hintuse 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 = 1296 machine hours over the course of the year. Determine the equilibrium level of Labor.

(d) If the wage level in China is $4, (given the same MP_L in the US), what is the equilibrium level of Labor demanded in China.

(e)If wages in China fall to $2, what is the new level of demand for labor in China?

(f)How can the workers in the US combat this potential transfer of jobs to China (there are two possible solutions).

(g)At What number of employees would you maximize output but not lose money?