Consider the evolution of public debt: B+1=(1+r) B + D (1) Where Be is the real level of one period government debt in period t, is the real interest rate, and De is the primary deficit (G-T), where D. > 0 under a primary deficit and D, 0 (we have a primary deficit). Furthermore, let real GDP grow at a constant rate, g, with 1+1 = (1+9) a. Re-write the evolution of debt. (1) as a fraction of GDP. by defining the debt to GDP ratio as be=B/1. (5 points) b. i. Find a condition under which a steady-state value *> 0 exists and is unique and solve for b*. (7.5 points) ii. illustrate the law of motion of b under the condition above and discuss the dynamical properties of the steady-state. In your answer you need to show analytically the behavior of be outside the steady-state and explain the results. (13 points) c. Suppose a < 0; i.e. the government incurs a primary surplus instead. i. Find a condition under which a steady-state value *> 0 exists and is unique and solve for b. (7.5 points) ii. illustrate the law of motion of b under the condition above and discuss the dynamical properties of the steady-state. In your answer you need to show analytically the behavior of be outside the steady-state and explain the results. (15 points)