In 2011, the Congressional Budget Office predicted that the US economy would grow by 2.8% per year on average over the decade from 2011 to 2021. At this rate, in 2021, the ratio of national debt to GDP (gross domestic product) is predicted to be 76% and the federal deficit is predicted to be $861 billion. Both predictions depend heavily on the growth rate. If the growth rate is 3.3% over the same decade, for example, the predicted 2021 debt-to-GDP ratio is 66% and the predicted 2021 deficit is $521 billion. If the growth rate is even stronger, at 3.9%, the predicted 2021 debt-to-GDP ratio is 55% and the predicted 2021 deficit is $113 billion.

(a) There are only three individual cases given (for three different economic scenarios), and for each we are given values of three variables. What are the variables?

(b) Use technology and the three cases given to find the regression line for predicting 2021 debt-to- GDP ratio from the average growth rate over the decade 2011 to 2021.

(c) Interpret the slope and intercept of the line from part (b) in context.

(d) What 2021 debt-to-GDP ratio does the model in part (b) predict if growth is 2%? If it is 4%?

(e) Studies indicate that a country’s economic growth slows if the debt-to-GDP ratio hits 90%. Using the model from part (b), at what growth rate would we expect the ratio in the US to hit 90% in 2021?

(f) Use technology and the three cases given to find the regression line for predicting the deficit (in billions of dollars) in 2021 from the average growth rate over the decade 2011 to 2021.

(g) Interpret the slope and intercept of the line from part (f) in context.

(h) What 2021 deficit does the model in part (f) predict if growth is 2%? If it is 4%?

(i) The deficit in 2011 was $1.4 trillion. What growth rate would leave the deficit at this level in 2021?