Question

Acme Container Corporation produces egg cartons that are sold to egg distributors. Acme has estimated this production function for its egg carton division:

            Q = 25L0.6K0.4,                    

where Q = output measured in one thousand carton lots, L = labor measured in person hours, and K = capital measured in machine hours. Acme currently pays a wage of $10 per hour and considers the relevant rental price for capital to be $25 per hour.

i) The marginal product of labor and the marginal product of capital are, a) both decreasing. b) both increasing. c) increasing and decreasing, respectively. d) decreasing and increasing, respectively.

ii)This production function exhibits, a) increasing returns to scale. b)decreasing returns to scale. c) constant returns to scale. d) returns to scale that are undefined.

iii) Using calculus, the marginal product of capital, MPk_, is: a) L^0.6/K^0.6 b) 10 L^0.6 c) 10 L^0.6/K^0.6   d) 1/K^0.6

iv) The total cost of producing, if the company uses 10 labor hours and 6 machine hours at the cost-minimization point is: a) 100 b) 150 c) 35 d) 250

v)  Using calculus, the marginal product of labor, MP_L, is: a) 15 K^0.6/L^0.4 b)K^0.6/L^0.4 c) 15 K^0.6 d) 1/L^0.4

Answer 1

25 L 0.6-1 O.y I< 15L MPL - 15 L IK 6 LK 0.6 o-1 s 10 L IK 0.640, у t) D-6 ,,0'4 - 15L

0'6 Laare.ct 25 L 25(0-6) L