In the short run, a firm cannot vary its capital, K = 2, but can vary its labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the short run if its production function is
a. q = 10L + K
b. q = L^0.5K^0.5

White company has two departments, cutting and finishing. the company uses a job-order costing system and computes a predetermined overhead rate in each department. the cutting department bases its rate on machine-hours, and the finishing department bases its rate on direct labor-hours. at the beginning of the year, the company made the following estimates: department cutting finishing direct labor-hours 6,000 30,000 machine-hours 48,000 5,000 total fixed manufacturing overhead cost $ 264,000 $ 366,000 variable manufacturing overhead per machine-hour $ 2.00 " variable manufacturing overhead per direct labor-hour " $ 4.00 required: 1. compute the predetermined overhead rate for each department. 2. the job cost sheet for job 203, which was started and completed during the year, showed the following: department cutting finishing direct labor-hours 6 20 machine-hours 80 4 direct materials $ 500 $ 310 direct labor cost $ 108 $ 360 using the predetermined overhead rates that you computed in requirement (1), compute the total manufacturing cost assigned to job 203. 3. would you expect substantially different amounts of overhead cost to be assigned to some jobs if the company used a plantwide predetermined overhead rate based on direct labor-hours, rather than using departmental rates?

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(30 total points) suppose a firm’s production function is given by q = l1/2*k1/2. the marginal product of labor and the marginal product of capital are given by: mpl = 1/ 2 1/ 2 2l k , and mpk = 1/ 2 1/ 2 2k l . a) (12 points) if the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output q = 18?