If the ratio of labor costs to materials costs
is ½ and labor costs are decreasing by 10 percent per year while material costs
are increasing by 10 percent per year, what is the ratio at the end of the
second year? (Note: This means that at the present time labor costs are 50
percent of materials costs.” Does the result seem reasonable?
Assume a labor cost of $10 and a material cost of $20 at the present time. This gives us the labor costs being 50% of materials cost. Next year, labor would decrease by 10%, so would be $9. Materials costs would increase by 10%, so would be $22. This ratio of labor to materials is $9/$22, or 41%. This does not seem unreasonable. There are many reasons why labor costs would decrease, including increased worker efficiencies and hiring more productive workers. At the same time, it is not unreasonable that materials costs could increase by 10%. There could be increased demand in the industry for the material which would drive up prices. The decrease in the ratio form 50% to 41% does not seem unreasonable.