This question requires that you use the law of motion of capital, the production function, and the national income accounts identity. Suppose that a nation’s production function is Y_t = F(K_t, L_t) = K_t^{\alpha}L_t^{1-\alpha}
You have the following information:
The share of income paid to owners of capital \alpha = \frac{1}{3}
The rate of depreciation, \delta = 1
The savings rate s=.15
The initial capital stock K_0=1
The labor supply, for all t\geq 0 is L_t=5
Assuming that L_t is the number of workers, What is the long run level of output per worker?
Please give an exact answer. This question will accept any answer within .1 of the exact answer

Required information problem 15-1a production costs computed and recorded; reports prepared lo c2, p1, p2, p3, p4 [the following information applies to the questions displayed below. marcelino co.'s march 31 inventory of raw materials is $84,000. raw materials purchases in april are $540,000, and factory payroll cost in april is $364,000. overhead costs incurred in april are: indirect materials, $59,000; indirect labor, $26,000; factory rent, $38,000; factory utilities, $19,000; and factory equipment depreciation, $58,000. the predetermined overhead rate is 50% of direct labor cost. job 306 is sold for $670,000 cash in april. costs of the three jobs worked on in april follow. job 306 job 307 job 308 balances on march 31 direct materials $30,000 $36,000 direct labor 25,000 14,000 applied overhead 12,500 7,000 costs during april direct materials 133,000 210,000 $100,000 direct labor 105,000 150,000 101,000 applied overhead ? ? ? status on april 30 finished (sold) finished in process (unsold) required: 1. determine the total of each production cost incurred for april (direct labor, direct materials, and applied overhead), and the total cost assigned to each job (including the balances from march 31). a-materials purchases (on credit). b-direct materials used in production. c-direct labor paid and assigned to work in process inventory. d-indirect labor paid and assigned to factory overhead. e-overhead costs applied to work in process inventory. f-actual overhead costs incurred, including indirect materials. (factory rent and utilities are paid in cash.) g-transfer of jobs 306 and 307 to finished goods inventory. h-cost of goods sold for job 306. i-revenue from the sale of job 306. j-assignment of any underapplied or overapplied overhead to the cost of goods sold account. (the amount is not material.) 2. prepare journal entries for the month of april to record the above transactions. 3. prepare a schedule of cost of goods manufactured. 4.1 compute gross profit for april. 4.2 show how to present the inventories on the april 30 balance sheet.