1 A firm that makes shopping shelfs for supermarkets and oth

1. A firm that makes shopping shelfs for supermarkets and other stores recently purchased some new equipment that reduces the labour requirements (hours) of the jobs needed to produce the shopping shelfs. Prior to buying the new equipment, the company used four workers, who produced an average of 80 shelfs per hour. Labour cost was $10 per hour and machine cost was $40 per hour. With the new equipment, it was possible to transfer one of the workers to another department. Machine cost increased by $10 per hour while output increased by 5% (or by four shelfs per hour).

a. Calculate the total cost of labour per hour before and after the new equipment. Calculate the total cost of machine per hour before and after the new equipment.

b. Calculate labour productivity before and after the new equipment. Use shelfs per worker per hour as the measure of labour productivity.

c. Calculate the multifactor productivity before and after the new equipment. Use shelfs per dollar cost (labour plus machine) as the measure of multifactor productivity.

d. Calculate the percentage changes in labour productivity and multifactor productivity.

e. Management\'s expectation for the firm is multifactor productivity increase of 10% once the new equipment is installed. Based in your answer to question (1.c), did the firm reach this goal? if it did not, by what percentage must output (shelfs per hour) be increased to achieve a 10% improvement in multivactor productivity (relative to before the new equipmengt is installed)?

Solution

Case 1-

Total worker = 4

Production = 80 per hour

Labor cost = 10

Machine cost = 40

Case 2-

Total worker = 3

Production = 80+4 = 84 per hour

Labor cost = 10

Machine cost = 40+10= 50

a.

Cost of labor per hour before the new equipment = 10*4 = 40

Cost of labor per hour after the new equipment = 10*3 = 30

Total cost of machine before the new equipment = 40

Total cost of machine after the new equipment = 50

b.

Labor productivity before new equipment = total production / number of labor

                                                                    = 80/4 = 20 unit/labor

Labor productivity before new equipment = total production / number of labor

                                                                    = 84/3 = 28 unit/labor

c.

Multifactor productivity before the new equipment = total production/ (total cost)

                                                                                    = 80/ (10*4+40) = 1

Multifactor productivity after the new equipment = total production/ (total cost)

                                                                                = 84/ (10*3+50) = 1.05

d.

Percentage changes in labor productivity = (28-20)/20 = 0.4 or 40%

Percentage changes multifactor productivity = (1.05 – 1)/1 = 0.05 or 5%