The processing of payroll for the 10,000 workers in a large firm can either be done using 1 hour of computer time (denoted by K) and no clerks or with 10 hours of clerical time (denoted by L) and no computer time. Computers and clerks are perfect substitutes; for example, the firm could also process its payroll using 1/2 hour of computer time and 5 hours of clerical time. a. Sketch the isoquant that shows all combinations of clerical time and computer time that allows the firm to process the payroll for 10,000 workers. b. Suppose computer time costs $5 per hour and clerical time costs $7.50 per hour. What are the cost-minimizing choices of L and K? What is the minimized total cost of processing the payroll? c. Suppose the price of clerical time remains at $7.50 per hour. How high would the price of an hour of computer time have to be before the firm would find it worthwhile to use only clerks to process the payroll? A firm produces an output with the production function Q = KL, where Q is the number of units of output per hour when the firm uses K machines and hires L workers each hour. The marginal products for this production function are MPg = L and MP;, = K. The factor price of K is 4 and the factor price of L is 2. The firm is currently using K = 16 and just enough L to produce Q = 32. How much could the firm save if it were to adjust K and L to produce 32 units in the least costly way possible? A firm operates with the production function Q = K2L. Q is the number of units of output per day when the firm rents K units of capital and employs L workers each day. The marginal product of capital is 2KL, and the marginal product of labor is K2. The manager has been given a production target: Produce 8,000 units per day. She knows that the daily rental price of capital is $400 per unit. The wage rate paid to each worker is $200 day. a. Currently, the firm employs 80 workers per day. What is the firm's daily total cost if it rents just enough capital to produce at its target? b. Compare the marginal product per dollar spent on K and on L when the firm operates at the input choice in part (a). What does this suggest about the way the firm might change its choice of K and L if it wants to reduce the total cost in meeting its target? c. In the long run, how much K and L should the firm choose if it wants to minimize the cost of producing 8,000 units of output day? What will the total daily cost of production be