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Abstracting from longrun growth by setting '31. = g = 0 and from persistent shocks by setting pA = pa = 0, with A; E lnAt [ml and G, E lnGt Inc, and...
1. Abstracting from long-run growth by setting ng 0 and from persistent shocks by setting pA-PO-0, with At ? InAt-InA and Gt ? InGt-InG, and normalizing the population to N 1, the following nine equations describe the "baseline" RBC model in Chapter 5 AtEA.t Ct+1 Ct Wt (a) Find the steady state for this economy under the following calibration: a 1/3, 0.05, ? = 0.025. ? = 1, and L = 0.5 and ? such that ?/Y = 0.2. In particular, find the remaining parameters values b and ? that are consistent with steady state and determine steady-state values for the endogenous variables, Y, C, I, G, K, and w (b) Now consider the special case of the model where ? = 1 instead of ? = 0.05 and = 0 for all t. Solve for Yt, Ct, It, Kt+1, Tt, and w as analytical expressions of exogenous and predetermined variables A, and K and constants. (Hint: with 100% depreciation, there is a constant saving rate s = ae-p and constant labour supply L,-L.) (c) Again, for the special case of the model, what is the percentage change in output and percentage point change in the interest rate if the economy is at steady state at time t-1, but there is a shock EAt 0.05 (i.e., 5%) at time t? Explain the economic intuition behind the responses of output and the interest rate. (Hint: note that the EA.t0.05 shock is to lnAt, but the model solution is for the level of At.)
