Question

Assume that total output is determined by this formula: TOTAL OUTPUT = NUMBER OF WORKERS X PRODUCTIVITY assume there are 100 workers and each worker produces $100 of output. QUESTION: If the workforce is growing by 1% a year but productivity does not improve, how fast can output increase? Remember, the number of workers grows by 1%. Productivity does not change. Also remember the percentage change formula which is: [(new value - original value) / original value] x 100

a1%

b 3%

c2.3

d % $10,500

e $62.50

Answer 1

Given formulas - Total Output = Number of Worker * Productivity.

Total number of workers = 100

Each worker produces $100 of output.

Productivity of each worker = Output produced/input = $100/1 = $100

Total Output = 100 * 100 = $10000

1% growth in labor = 1/100 * 100 = 1 (So if we consider a growth of 1% labor for a year, labor number rises to 101 the next year.)

New Total Output for the next year given productivity is unchanged = 101*100 = 10100

Growth rate of output is percentage change in output when labor grew by 1%

= (10100-10000)/10000 * 100 = 1%

Hence if labor grows by 1 percent and productivity is unchanged then output is likely to grow by 1%

Hence option a - 1% is correct.

Based on our calculations we easily infer that the other options must be incorrect.

Note we dont really need to find productivity here as I have. We can keep it as a constant C and then observe the change is output with change in labor by 1%. The result will regardlessly be same.