Texts: 1. Answer the following questions:
a.
b.
What are the micro-foundations of the Real Business Cycles model? What are the stylized facts about Business Cycles/fluctuations?
Consider a Real Business Cycles model where the agent maximizes max cnkt+1 Et=0 Bt [Inct+ln(1-nt)] subject to kt+1 = Atkintact Vt; where a is the share of capital in output, n is employment, ct is consumption, kt is capital, and the productivity/technology shock At follows an AR process InA = plnAt-1 + Et; p is the persistence parameter, and εt is an independently and identically distributed (i.i.d) random variable with mean 0 and variance σ².
i.
ii.
iii. If p = 0, what will be the response of capital, output, employment, and consumption to a positive productivity shock? What is the nature of your impulse response functions?
iv.
Using your equilibrium trace, how will one standard deviation of a positive technology shock impact real variables such as output, consumption, capital accumulation, employment, etc.? Describe your impulse response functions using all possible iterations of the variables.
How does p = 0.99 and a = ? affect the performance of the model?
V.
Now consider the effect of a one-time (temporary) positive technology shock. Assume the share of capital, a = 3/4. Let yo be the output at time t - 1. Suppose that at time T, the technology shock is realized and let εT = 1. Suppose that the technology shock is entirely temporary, i.e. t = 0 Vt > T. What would be the response of output and capital?
Now assume p = 0 and consider the effect of a one-time (temporary) positive technology shock. Assume the share of capital, a = 3/4. Let yo be the output at time t - 1. Suppose that at time T, the technology shock is realized and let εT = 1. Suppose that the technology shock is entirely temporary, i.e. t = 0 Vt > T. What would be the response of output and capital?