29)The Fisher relationship may be described by the following equation in whichRis the nominalrate of interest,ris the real rate of interest, andiis the inflation rate.A)1+i=1+r1+RB)1+r=1+R1+iC)r=R + i + ir.D)i=r+RE)1+r=1+i1+R30)30)The behavior of the Solow residual suggests that when current total factor productivityincreases31)31)An important critique of real business cycle theory is the belief that cyclical movements in totalfactor productivity32)32)For the coordination failure model to work, it must be the case that the aggregate labourdemand curve must be33)33)In the coordination failure, the most likely explanation of business cycles areA) money supply shocks.B) fluctuations between 'good' and 'bad' equilibria.C) government spending shocks.D) labour market shocks.E) total factor productivity shocks.6
ECO3152B: Macroeconomic Theory IIIPART BInstructions.Answerallquestions in part B.1.
(20 points) Competitive Equilibrium and Pareto OptimalityConsider a one-period closed economy. The representative consumer has preferencesover consumptionand leisure. The utility function is( )=205+lnwhereis a positive constant. The consumer allocates theavailable units of timebetween leisure and work, so that+=represents the consumer’s time constraint.The consumer earns the wagefor every hour worked, receives dividendsandpays lump-sum taxes.In addition,the consumer pays aconsumption taxperevery unit of consumption good.The representative…rm produces output with the Cobb-Douglas technology=¡¢1¡0 1The government takes the level of public good provisionas exogenous. The govern-ment…nances its purchases by lump-sum taxes and consumption taxes. Assume thatthe government must run a balanced budget.(a)(10 points)De…ne a competitive equilibrium for this economy.Be preciseabout the endogenous variables that characterize the equilibrium and about theexogenous variables of the model. State explicitly all conditions that de…ne thecompetitive equilibrium and provide their economic interpretation.(b)(10 points)Is the competitive equilibrium Pareto optimal? Explain your answer.2.(20 points) Consumption-saving problemConsider a consumption-saving problem of a consumer with the following preferences( 0)=ln+ln00 ·1whereis the consumption in the current period, and0is the consumption in thefuture period. The consumer receives exogenous endowmentsand0The consumercan borrow and lend freely at the rate¸0There are no taxes.(a)(10 points)