Why does the GDP produced in small metropolitan areas tend to grow faster than GDP produced in large metropolitan areas?

Growth rates measure the increase in GDP over a given time period as a ratio of GDP for the first year of the time period. Therefore, a modest increase in the GDP of a small MSA will indicate a fast growth rate because the denominator of the ratio is small. For example, assume two metropolitan areas experienced the same amount of growth in dollars and that one area is significantly smaller than the other. In the formula below to compute percent change, the numerator (the amount of growth) will be the same for both areas. The smaller area will have a smaller denominator, and therefore, a larger (faster) percent change.

where

GDP_t is the level of activity in year t; and

GDP_t+1 is the level of activity in year t +1.