Abottling company uses two inputs to produce bottles of the soft drink sludge: bottling machines (k) and workers (l). the isoquants have the usual smooth shape. the machines cost $1,000 per day to run (r), and the workers earn $200 per day (w). at the current level of production, the marginal product of machines (mp subscript upper k) is an additional 316 bottles per day, and the marginal product of labor (mp subscript upper l) is 39 more bottles per day. is this firm producing at minimum cost? if it is minimizing cost, explain why. if it is not minimizing cost, explain how the firm should change the ratio of inputs it uses to lower its cost.

Acompany that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. prior to buying the new equipment, the company used 6 workers, who produced an average of 79 carts per hour. workers receive $16 per hour, and machine coast was $49 per hour. with the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $11 per hour while output increased by four carts per hour. a) compute the multifactor productivity (mfp) (labor plus equipment) under the prior to buying the new equipment. the mfp (carts/$) = (round to 4 decimal places). b) compute the productivity changes between the prior to and after buying the new equipment. the productivity growth = % (round to 2 decimal places)