The unemployment rate is a primary economic indicator calculated by dividing the number of unemployed persons by the total labor force and multiplying by 100. It serves as a vital metric for assessing the health of the labor market and the broader economy, reflecting the proportion of the workforce that is willing and able to work but cannot find employment.

Keynesian economics, named after John Maynard Keynes, emphasizes that aggregate demand is the primary driving force in an economy. It advocates for active government intervention, specifically through fiscal and monetary policies, to mitigate the adverse effects of economic recessions and depressions.

John Maynard Keynes introduced the concept of 'priming the pump' during the Great Depression. He argued that during periods of economic stagnation, government intervention through increased public spending could stimulate aggregate demand, thereby 'priming' the economy to return to a state of self-sustaining growth and full employment.

Keynesian economics argues that aggregate demand—the total spending in the economy—is the primary driving force of economic activity. Keynes posited that during recessions, private sector demand might be insufficient to maintain full employment. Therefore, he advocated for active government intervention through fiscal policy, such as increased public spending or tax cuts, to stimulate demand, reduce unemployment, and stabilize the economy during periods of volatility or market failure.

Keynesian economics gained prominence during the 1930s because classical economic theory failed to explain or resolve the persistent, high levels of unemployment seen during the Great Depression. John Maynard Keynes argued that aggregate demand was the primary driver of an economy and that government intervention through fiscal policy was necessary to restore full employment when private demand was insufficient.

Sticky prices, or nominal rigidity, occur when prices do not adjust instantly to changes in economic conditions. This can be due to menu costs, long-term contracts, or imperfect information. Because prices are 'sticky,' markets do not always clear immediately, which can lead to short-run fluctuations in output and employment, a key concept in New Keynesian economics.

In basic macroeconomic models, if savings exceed investment, it implies a leakage from the circular flow that is not offset by injections. This typically leads to a contraction in aggregate demand and a subsequent decrease in national income, rather than it remaining unchanged. The source answer is flagged as it contradicts standard Keynesian multiplier theory.

The equilibrium rate of unemployment represents the gap between the total number of individuals willing and able to work at the prevailing real wage and the actual number of people currently employed. It reflects structural and frictional factors that prevent the labor market from achieving full employment.

Discouraged workers are individuals who are not currently looking for work because they believe no jobs are available for them; thus, they are excluded from the labor force. If these individuals were reclassified as part of the labor force and counted as unemployed, both the numerator (number of unemployed) and the denominator (total labor force) would increase, resulting in a higher overall unemployment rate.

Abolishing income tax increases the net take-home pay for workers, which incentivizes labor supply and increases the number of people in employment. By reducing the tax wedge, the equilibrium rate of unemployment is expected to fall as the labor market clears more efficiently at higher participation levels.