1. Show that for an economy where the growth rate of GDP is zero, to keep its debt-GDP ratio constant, the government must run a primary surplus equal to the interest payments on its outstanding debt.

2. Explain how an acceleration of the GDP growth rate could have contributed to the fall in the debt-GDP ratio during the 1990's.

3. Consider the money supply model that we discussed in class. (a) Show that we can express the money multiplier m =M/B as m =cr+1/cr+rr. (b) What is the value of m under 100% reserve banking? (c) What is the value of m if depositors keep all their cash in their bank accounts as deposits? Provide some intuition for your result. (d) Describe how bank failures during a financial crisis could adversely affect the money multiplier.

4. Consider the unemployment model. (a) Show that U/L =1/(1+f /s) . (b) Imagine that the government provides new funding for re-training programs to re-train former workers displaced by workplace automation. Explain how this might impact the unemployment rate, referring to the equation above.