Question

Workers are compensated by firms with “benefits” in addition to wages and salaries. The most prominent benefit offered by many firms is health insurance. Suppose that in 2000, workers at one steel plant were paid $30 per hour and in addition received health benefits at the rate of $6 per hour. Also suppose that by 2010 workers at that plant were paid $31.5 per hour but received $13.5 in health insurance benefits. 

a. By what percentage did total compensation (wages plus benefits) change at this plant from 2000 to 2010? Instructions: Round your answer to 2 decimal places. Total compensation by: What was the approximate average annual percentage change in total compensation? Instructions: Round your answer to 2 decimal places. 

b. By what percentage did wages change at this plant from 2000 to 2010? Instructions: Enter your answer as a whole number. Wages by: What was the approximate average annual percentage change in wages? Instructions: Round your answer to 1 decimal place. 

c. If workers value a dollar of health benefits as much as they value a dollar of wages, by what total percentage will they feel that their incomes have risen over this time period? Instructions: Round your answer to 2 decimal places. What if they only consider wages when calculating their incomes? Incomes by: 

d. Is it possible for workers to feel as though their wages are stagnating even if total compensation is rising?

Answer 1

Given that:

Workers are compented by firms with "benefits" in addition to wages and salaties.

(a)

Total compensation, 2000 = $(30 + 6) = $36

Total compensation, 2010 = $(31.5 + 13.5) = $45

% Change = ($45 / $36) - 1 = 1.25 - 1 = 0.25, or 25%

Average annual % change = 0.25 / 10 = 0.025, or 2.5%

(b)

% Change in wage = ($31.5 / $30) - 1 = 1.05 - 1 = 0.05, or 5%

Average annual % change = 0.05 / 10 = 0.005, or 0.5%

(c)

In this case, they would judge their increase in income as the increase in total compensation, as computed in part (a).

% change in income = 25%

If they only consider wages, % change in income = 5% (as computed in part (b)).

(d)

Yes, it is possible. If price level has increased by more than 5% over the period, purchasing power of their wages are lower. In this case they would feel that their wages are stagnant (or even lower), since health benefits are not a part of wages and is a contingent expense they can avail of only when they are sick.