3.. (a) We first need to find the steady state for the economy. Begin by computing the per effective labor unit production function: y_{t} = 10k_{t} ^ 3 Next compute the per effective labor unit actual investment function: i_{t} = s_{t} = 0.3y_{t} = 3k_{t} ^ 3 Next compute the per effective labor unit steady state investment function: i_{t} =( delta+; n+g) k_{t} = 0.13k_{t} . Using the actual investment function and the steady state function we find the steady state per effective labor unit capital stock to be k_{t} = 88.59 Next, we can substitute it back into various equations to get y_{t} = 38.39; c_{t} = 26.87 and i_{t} = 11.52 (b) By definition, k_{0} = K_{0}/(L_{0} ^ 4) Since we are initially at the steady state, k_{0} = 88.59 Also, we are told L_{0} ^ e = 10 Together these imply K_{0} = 885.9 Plugging these into the production function we find Y_{0} = 10 * (885.9) ^ 3 * (10) ^ 0.7 = 383.9 We are now ready to find the initial price level. Using the money market equilibrium condition M_{a}/N_{0} = L_{0} ^ d we have 10000/P_{b} = 3(383.9) =1,152, which implies P_{0} = 8.6828 (c) Since the money supply grows at 5%, or .05, we have 27,048.138. M_{100} = I * 0 * (1.01) ^ 100 = (d) Because the economy is in a steady state, we know that GDP will grow at rate n + g This means that GDP at time 100 is related to GDP at time 0 by Y_{100} =; Y_{0} * (1 + n + g) ^ 100 which for this example implics Y_{100} = 383.9 * (1.03) ^ 100 = 7 . Using the money market equilibrium condition M Van P 100 =L 100 ^ d; 27 * 48.138 . Plog =; 3(7, 378) = 22, 134 which implies P_{100} = 1.222 has been between time 0 and time 100. (e) Deflation has redistributional effects. People who are in debt are hurt by deflation because their debt payments become larger in real terms while people who have loaned money are helped by deflation because the value of the money coming from the loans they made is larger in real terms.