In country RBC, only labor is used in production. The production function is Y = zN, where z is labor productivity. In country RBC, economic booms and recessions are due to cyclical movements of zs. For simplicity suppose that z takes two values: either z = 195 or z = 205. The chance that z = 205 is 0.7 and the chance that z = 195 is 0.3. Roughly, country RBC is in economic boom 70% of time and recession 30% of the time. The representative household in country RBC has utility u(c, l) = √ c + 20√ l
. (4 points) The above stabilization policy leads to a waste of resources, hence may not be favorable to households. Instead, government stabilizes production through wage subsidies financed by a lump-sum tax (tax cut financed with debt). The representative household’s budget constraint becomes the following. c = w(1 + s)(1 − l) − T. Show that s = 6.5375% and T = 4.5412 during recession will achieve the goal of stable output as well.
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