Econ 2000 - Problem Set 5

Econ 2000 Problem Set 5 31 Oct 2022 3. The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as: Q = 0 . 25 K 0 . 25 L 0 . 75 , where Q represents memo pads (boxes per hour), K denotes capital input (units per hour), and L denotes labor input (units of worker time per hour). The marginal products of labor and capital are as follows: MPL = (0 . 75)(0 . 25) K 0 . 25 L − 0 . 25 MPK = (0 . 25)(0 . 25) K − 0 . 75 L 0 . 75 (a) Construct the isocost equation. (b) Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute the level of output. (c) Explain what would happen in the short run (keeping capital fixed) to the appropriate input mix if production were changed to 1,500 units per hour. Would the input combination be different in the long run? If so, how would it change? Explain. 4. Cogswell Cogs short-run cost function is: C ( q, k ) = 12 q 3 K 3 / 2 + 15 K where q is the number of cogs produced and K is the amount of robot hours used. Currently, Cogs uses 16 robot hours to produce 300 cogs. What happens to the average total cost of producing 300 cogs if Cogswell increases robot hours to 25? Econ 2000 Problem Set 5 2 / 2