If a city's unemployment rate is at 8% and the natural rate is 3% with the current GDP at $100 million what is the full employment equilibrium?

To determine the full employment equilibrium, we need to understand a few concepts: unemployment rate, natural rate of unemployment, and the relationship between GDP and employment.

1. Unemployment rate: It represents the percentage of the labor force that is actively seeking employment but unable to find it.

2. Natural rate of unemployment: Also known as the non-accelerating inflation rate of unemployment (NAIRU), it refers to the level of unemployment that exists when the economy is operating at its potential or full employment. It includes frictional and structural unemployment but excludes cyclical unemployment.

3. GDP and employment: There is a relationship between the Gross Domestic Product (GDP) of an economy and the level of employment. As the GDP increases, it generally leads to higher employment levels.

Now, let's calculate the full employment equilibrium using the given information.

Step 1: Calculate the total number of unemployed individuals.
Unemployment Rate = (Number of Unemployed / Labor Force) x 100%
Given the Unemployment Rate = 8% and the Labor Force not provided, we cannot determine the number of unemployed individuals.

Step 2: Determine the full employment equilibrium.
The full employment equilibrium occurs when the actual unemployment rate equals the natural rate of unemployment. So, in this case, we need the natural rate of unemployment to proceed. You mentioned it is 3%, which indicates the desired unemployment level at full employment.

Therefore, without the labor force data or the number of unemployed individuals, it is not possible to calculate the full employment equilibrium.