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whether the statement is true1 false, or uncertain3 and give a complete and convincing explanation of your answer. Note: Such explanations typically appeal to specic macroeco nomic models. 1. 2. A tax on consumption is equivalent to a tax on labor income. An increase in government spending without a commensurate increase in taxes will increase national income. . In the past few months: the Federal Reserve has dramatically increased the money supply3 but output, employment and prices have all increased very slowly. Such an outcome is evidence in favor of the quantity theory. An increase in government spending without a commensurate increase in taxes will increase welfare. . A permanent increase in productivity should cause permanent increases in both con sumption and employment. . The lowering of a country's sovereign debt rating is equivalent to an increase in every one's income tax rate and having the revenues thrown into the ocean. Households save by purchasing riskfree bonds. Let Bi denote the quantityr of bonds bought at time t1 measured in terms of output. 1 unit of bonds delivers {l + rt} units of output at time t + 1. Households face the usual initial1 nonnegativity and NoPonziGame conditions. (a) Solve the consumer's and the producer's problems. (b) Note that there is no capital in this economy, so that bonds represent trades between consumers. Imposing equilibrium, nd the resource constraint and the labor allocation condition. Use this result to express output and consumption in terms of the aftertax rate 3:, and then solve for the equilibrium value of (l + rt). (c) Do higher labor tax rates (lower values of 5}) increase or decrease output? Briey explain in terms of income and substitution effects. {(1} Let lowercase letters with carats \" A \" denote deviations of logged variables around their steady state values. Show that the loglinearized expressions for labor hours and output are: E; = s a = as, the. Find the log of average labor productivity, cpl: = } t- e \"Till labor roductivity to be I'D or countercyclical in this model? Briey ex P P plain. Is the cyclicality of labor productivity found in the model consistent with that in the data? If not, how might the model be modied? 10. Diamond Coconut Economy with uniform idiosyncratic preferences Time: Discrete= innite horizon Geography: A trading island and a production island. Demography: A mass of 1 of ex ante identical individuals with innite lives. Preferences: The common discount rate is 7', consumption of own produce yields CI utils. consumption of someone whose good you like yields 2;. utils. The share of individuals whose goods I like is (I)- Whether an individual likes my good or not is independent of whether I like hers. (So she likes my good with probability (D too.) Productive Technology: On the production island individuals come across a tree with a coconut with probability a- each period. The cost of obtaining the coconut is c which is uniformly distributed over {0) E] where E > u (so some trees will get rejected). Matching Technology: On the trading island people with coconuts meet each with probability qr, a constant. Navigation: Travel between islands is instantaneous. Endowments: Everyone has a boat and starts oIT with one of their own coconuts {a} write down the asset value (Bellman) equations for this economy. Dene the terms you introduce. {b} Dene a search equilibrium