Final answer:
A declining crime rate improves the broad standard of living in ways not captured by GDP, so if GDP rises during this time, it understates the true improvement in standard of living.
Step-by-step explanation:
If the crime rate declines in a given economy, it affects the relationship between GDP and the broad standard of living. While GDP measures the total economic output of a country, it does not directly account for social factors such as crime rates. Therefore, a decline in crime rate would improve the broad standard of living by making citizens feel safer and potentially lowering costs associated with crime prevention and losses due to crimes. However, this improvement in standard of living would not be reflected directly in the GDP figures. As a result, if the GDP were to rise while the crime rate is declining, the GDP would understate the true improvement in the broad standard of living since it does not incorporate the additional well-being derived from the lower crime rate.