Labor Spring 2015 Assignment 6: Assume Education Is The Only
Labor Spring2015 Assignment6assume Education Is The Only Determinant O
Assume education is the only determinant of productivity. With zero years of education, black and white workers both earn a wage of $2.00 per hour. Each additional year of education causes the wage of whites to rise $0.50 per hour and that of blacks by $0.20. The average black worker has 10 years of education and the average white worker has 12 years. According to the residual method, the percent of the wage gap due to discrimination is: (a) 25 percent. (b) 50 percent. (c) 75 percent. (d) none of the above.
Paper For Above instruction
The wage gap between black and white workers has long been a subject of economic and social investigation, with particular focus on distinguishing the role of discrimination from other factors such as education. Given the scenario where education is the sole determinant of productivity and wages, this analysis employs the residual method to estimate the portion of the wage disparity attributable to discrimination.
Understanding the Scenario and Data
According to the problem, at zero years of education, both black and white workers earn $2.00 per hour. Each additional year of education increases the wage for white workers by $0.50 per hour and for black workers by $0.20 per hour. The average years of education for black workers is 10, and for white workers, it is 12.
Calculating Predicted Wages and Wage Gap
The baseline wage at zero years of education is $2.00 for both groups. Therefore, the predicted wages (based solely on education) are:
- For black workers:
\[
\text{Wage} = 2.00 + (10 \times 0.20) = 2.00 + 2.00 = \$4.00
\]
- For white workers:
\[
\text{Wage} = 2.00 + (12 \times 0.50) = 2.00 + 6.00 = \$8.00
\]
The actual average wages are derived from these predictive models, assuming all wages are explained by education only.
Applying the Residual Method
The residual method separates wage differences into explained and unexplained components. The explained portion is the part due to observable factors (education), and the residual (unexplained) portion is attributed to discrimination.
The total observed wage gap is:
\[
\text{Wage gap} = \$8.00 - \$4.00 = \$4.00
\]
The explained wage difference, attributable solely to education, is:
\[
\text{Predicted wage difference} = (\text{White predicted wage} - \text{Black predicted wage}) = \$8.00 - \$4.00 = \$4.00
\]
Since this entire difference is explained by education (the only determinant), the residual (discrimination component) is zero in this simplified model. However, the question explicitly asks about the percentage of the wage gap due to discrimination, implying we need to consider how much of the observed gap cannot be explained solely by education, but in this case, the entire gap is explained by education.
Interpreting the Results
Because the entire wage difference can be explained by education—aligned with the assumption that education is the only determinant—there is no residual unexplained (discrimination) effect. Consequently, the residual method would attribute zero percent of the wage gap to discrimination in this simplified case.
Conclusion and Answer
However, considering the typical structure of such problems and common interpretations, the residual method attributes the unexplained portion (the residual after accounting for observable factors) as discrimination. Since in this scenario, all differences are explained by education, the percentage due to discrimination would be zero.
Yet, the options provided include 25%, 50%, 75%, or none above, and based on common interpretations, if the entire gap was unexplained and attributed to discrimination, the answer would be 100%. But because the entire gap is explained, the residual (discrimination) component is zero, which is not among provided options.
Final Decision
Given the options, and interpreting the question in a conventional manner, the correct answer is:
(d) none of the above
because the residual (discrimination) component is zero, which is not listed in the options.
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