What is the relationship between Economics and Human Resource Management? How are these two subjects related to each other?

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It looks like you may be referring to labor or personnel economics in your question. Labor or personnel economics is related to human resources management in terms of wages, human capital investment, hiring practices, and employment changes.

Personnel economics approaches human resource management from an economic and mathematical standpoint. In terms of wages, there is a direct correlation between productivity and wage incentives. Higher wages are earned by employees who provide the highest productive value to employers. Specifically, incentives such as bonuses and promotions often motivate employees to work harder and to produce higher quality work for their employers. Personnel economics studies how market conditions (demand and supply) affect the material advancement of both employers and employees; in terms of human resources, it also explores how employers and employees navigate changes in employment levels.

These market conditions or movements in employment and unemployment are explained through shifts in labor demand, labor supply, and wages. Shifts in the employment rate depend on how quickly the market recovers from external shocks such as abrupt changes in raw material prices, interest rates, product demand, or regulatory oversight. For example, high regulatory costs often affect industry hiring levels. In light of increased government oversight, firms may opt to raise their investments in physical capital (tools and machinery), as opposed to human capital. Still other firms may look to combine offshore labor solutions with virtual talent. Exchange rate fluctuations and temporary oil price hikes may also lead to long-term effects on employment levels. Meanwhile, union participation rates affect the supply of labor to employers. 

Whatever the employment climate, personnel economics concerns itself with how human resource management can leverage pay and other wage incentives to produce optimal effort from employees. 

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These are two very different academic subjects. Economics is a social science that describes the production, consumption, and exchange of goods within a society. It is by its nature a science, meaning that it seeks understanding of a subject. Although people with degrees in economics are hired for a range of well-paying jobs in both government and industry, the subject itself is an academic rather than vocational one. 

Human resource management is a vocational subject intended to prepare students to work as human resource managers in industry. Its remit is far more limited than that of economics, as it focuses on specific corporate jobs. People in HR departments are normally involved in hiring, firing, promotions, staffing decisions, and issues of regulatory compliance. 

There really is no direct relationship between the subjects. People studying Human Resource Management or other business courses normally need to take a few economics modules to understand some underlying principles of how economic factors affect businesses; economics students would have no need to study Human Resources Management. 

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