C is correct. The participation ratio (or activity ratio) is the ratio of the number of people in the labor force to the total population of working-age people, and the unemployment rate is the ratio of the number of unemployed to the number of people in the labor force. The labor force is the numerator in the participation ratio, and the denominator is the unemployment rate. Therefore, assuming all else remains unchanged, an increase in the number of people included in the labor force would cause the participation ratio to increase and unemployment rate to decrease. 

A is incorrect. Although a decrease in the total number of unemployed people would decrease the unemployment rate, this would not have a direct effect on the participation rate. 

B is incorrect. Although a decrease in the total population of working age people would increase the participation rate if the size of the labor force remained unchanged, this would have no direct effect on the unemployment rate.

B is correct. The ratio of consumer installment debt to income is a lagging indicator. An increase in it, by itself, would be evidence that an upturn is already underway. This would confirm the implication of positive changes in coincident indicators that an expansion is in place. 

A is incorrect. Leading indicators indicate what is coming, but the ratio of consumer installment debt to income is a lagging indicator. The reason it is a lagging indicator is because consumers only borrow heavily when they are confident in the economy. 

C is incorrect. Although the ratio of consumer installment debt to income is a lagging indicator, it is more directly indicating that an upturn has been underway, not that the expansion is over because consumers only borrow heavily when they are confident in the economy.