According to Chapter 7 "The Spending Allocation Model", a decrease in government spending results in, among other things, an increase in investment in the long run. Suppose the capital stock is $1 trillion and a fall in government spending causes a $50 billion rise in investment. Determine the effect of the change in government purchases on long-run per capita output growth, using the growth accounting formula. (Assume that the coefficient on capital in the growth accounting formula is one-third.)