mn

. Consider the following simplified version of a stochastic growth model. There are a fixed number of price-taking producers that solve (PRF) (GBC) (TS) Mostly cloudy where: II, is profit; L, is labor; and W, is the real wage. There is no population growth, and the population and number of firms are normalized to 1, so that upper case letters denote intensive as well as aggregate quantities. G=(1-S?)We Les where: G is the government's purchases of goods and services and S, 1-r is the after-tax rate on labor income. Government spending is driven by the after-tax rate. which follows an AR(1) process around the log of its steady state value: 3 In (S?/S) = 05?-1+? 0?6

(c) Do higher labor tax rates (lower values of S?) increase or decrease output? Briefly explain in terms of income and substitution effects. (d) Let lower-case letters with carats "denote deviations of logged variables around their steady state values. Show that the log-linearized expressions for labor hours and output are: 94 = 08? 0 0. Find the log of average labor productivity, (e) Will labor productivity to be pro- or counter-cyclical in this model? Briefly ex plain. Is the cyclicality of labor productivity found in the model consistent with that in the data? If not, how might the model be modified?

We were all pretty relieved that Ali from our first prelim got such a simple consumption problem. Yet, we also realized that putting him into the ICobbDouglas straightjacket missed some features of the story. Since the overall theme of the second prelim should be \"We can do betterl\d. You would expect that the more almonds Ali eats1 the more they get stuck in his teeth and the more toothpicks he purchases. In light of such considerationsJ does it make sense to assume Ali has the utility function above? [Consider changes in the demand for almonds and toothpicks caused by changes in the price of almonds and changes in the parameters ha and or? respectively} e. Consider now a utility function given by {bf-Ta: Iii-Ty) : (In _ balfrt _ brief-Tc _ bellEl: with or? EU]:- 3} D? or + 6'