Abstract
Bank crises and social problem came into being because of non-performing loans in Japan and Korea and US. Economist and specialist have noticed Bank non-performing loans. The paper applied a social utility function model for bank loans & non-performing loans and simulated the model in Beijing based on low carbon economy from 2003 to 2050, bank non-performing loans will cause high carbon economy. Bank non-performing loans will be harmful to economic growth and social welfare utility. The following result is obvious that from the above scatter simulation result:(1) The social utility increases from about -29042 to -65.63 units in Beijing when the non-performing loans growth rate decrease from 0.07 to 0.01 at 2050 year. (2) The social utility decrease in Beijing from 2003 to 2050 when the non-performing loans growth rate is 0.07, the social utility decrease from about -233.6 to -29042 units in Beijing when the time span is between 2040 and 2050.