Part I: Effects of Corona and Social Policy (35)In this problem, you will analyze the short-run and long-run effects of the Corona crisis and of the epidemiological and social policies implemented against it on labor supply, consumption, and welfare. We work, unless otherwise stated, in the consumption-leisure choice model from lecture under standard assumptions. In particular, we study Hannah, who, before the advent of the crisis, worked an 8-hour day for $15/hour. She paid no taxes (for simplicity) and received a profit income from shares in her mom’s company of $20 per day. We assume that she has 16 hours of waking time.1) Illustrate her consumption-leisure choice in the appropriate diagram and make sure to illustrate the graphs and label the axes. Also, indicate Hannah’s wage in the graph XXXXXXXXXXRedraw the situation in 1) and now assume that she faces a lockdown which amounts to allowing her to work (say, in her home office) at most 1 hour per day. Assume that her hourly wage stays at $15/hour. How does her budget set change, and what will her new optimal choice point be? How do you know that this must be her choice? Compare her consumption and leisure choice as well as her welfare with and without the lockdown XXXXXXXXXXRedraw the lockdown situation from 2). Now assume that, in addition to the lockdown, Corona also leads to a closure of her mom’s business so that her profit income declines to $0. How does her budget set change, and what will her new optimal choice point be? Compare her consumption and leisure choice as well as her welfare before and after the profit decline (assuming the lockdown in place for both cases XXXXXXXXXXRedraw the situations from before Corona (see 1)) and the end situation from 3), that is, lockdown plus zero profit income from her mom. Is there a transfer policy from the government that would give Hannah the same welfare as in the situation before the Corona crisis? How does her consumption and leisure choice under that social policy compare with the situation before Corona? In light of your results, comment on the welfare implications of the current CARES Act, which provides most Americans with a check from the government XXXXXXXXXXNow let us assume that, after the pandemic is fully over, Hannah really hates staying at home and has a preference shift away from leisure towards market consumption. Redraw the initial situation before the Corona crisis from 1), then illustrate this preference shift in the consumption-leisure diagram, and analyze the resulting choices of consumption, leisure and labor supply XXXXXXXXXXAgain redraw the pre-Corona situation from 1) and assume that consumption-leisure preferences are now such that the income effect dominates the wage effect (differently from our standard assumption in lecture). Illustrate the effects of a hypothetical wage cut on the consumption-leisure choice as well as labor supply and do not forget to illustrate the substitution and the income effect in the graph XXXXXXXXXXDraw the labor supply curve together with a standard labor demand curve in the labor market diagram. Assume that there is a sticky nominal wage such that there is unemployment in the labor market. Is the resulting real wage higher or lower than the market-clearing real wage? Distinguish two cases XXXXXXXXXXAssuming that nominal wages tend to fall when there is unemployment what will happen in both of the cases in 7)? Is there a case for which you would recommend the introduction of the minimum wage as a good social policy? A verbal answer is sufficient here. (4)Part II: Corona in the Real Intertemporal Model with Money (36)In this problem, we will, step-by-step, investigate the various macroeconomic aspects of the Corona crisis in the real intertemporal model with money (recall: in this model, wages and prices are fully flexible and hence all markets clear; so there cannot be any unemployment, just lower employment, which is clearly counterfactual but in this analysis we will not focus on the labor market). 1) The first aspect of the Corona crisis is a savings glut: an exogenous increase in aggregate private saving, unrelated to income and the real interest rate (because people no longer can or want to spend their income). Illustrate the saving glut jointly in the market for funds and the commodity market diagrams. Since both diagrams have the real interest on the y-axis, draw them next to each other and make sure that the first- and second-round effects of the savings glut are compatible between the two diagrams. Make sure to clearly mark which curve shifts are first-round effects and which are second-round effects (hint: use different colors). Make also sure to label the axes XXXXXXXXXXFrom 1): what happens to aggregate output, the real interest rate, national saving, aggregate investment and aggregate consumption in the new equilibrium relative to the old equilibrium? You can use simple arrows to summarize your results: for example, if a variable X increases, write X↑; if it does not change, write X↔, etc. If a change for a variable X is ambiguous, write X? (3)3) The second aspect of the Corona crisis is an investment collapse: an exogenous decrease in aggregate investment, unrelated to income and the real interest rate (think of the Corona crisis causing very negative animal spirits). Illustrate the investment collapse jointly in the market for funds and the commodity market diagrams. Since both diagrams have the real interest on the yaxis, draw them next to each other and make sure that the first- and second-round effects of the investment collapse are compatible between the two diagrams. Make sure to clearly mark which curve shifts are first-round effects and which are second-round effects (hint: use different colors). Make also sure to label the axes XXXXXXXXXXFrom 3): what happens to aggregate output, the real interest rate, national saving, aggregate investment and aggregate consumption in the new equilibrium relative to the old equilibrium? You can use simple arrows to summarize your results: for example, if a variable X increases, write X↑; if it does not change, write X↔, etc. If a change for a variable X is ambiguous, write X? (3)5) Now combine the savings glut and the investment collapse in a diagram group with the market for funds and the commodity market diagrams. Since both diagrams have the real interest on the yaxis, draw them next to each other and make sure that the first- and second-round effects are compatible between the two diagrams. Make sure to clearly mark which curve shifts are firstround effects and which are second-round effects (hint: use different colors). Make also sure to label the axes XXXXXXXXXXFrom 5): what happens to aggregate output, the real interest rate, national saving, aggregate investment and aggregate consumption in the new equilibrium relative to the old equilibrium? You can use simple arrows to summarize your results: for example, if a variable X increases, write X↑; if it does not change, write X↔, etc. If a change for a variable X is ambiguous, write X? (3)7) Focus on the commodity market now and draw the pre-Corona Yd-curve as well as the Coronaaffected Yd-curve from 5). Also, draw a pre-Corona Ys-curve. Add to it an adverse supply shock to the Ys-curve. What happens to aggregate output, the real interest rate, aggregate investment and aggregate consumption in the new equilibrium relative to the old pre-Corona equilibrium? You can use simple arrows to summarize your results: for example, if a variable X increases, write X↑; if it does not change, write X↔, etc. If a change for a variable X is ambiguous, write X? (5)8) Show with the help of an aggregate production function diagram the implications for aggregate employment, assuming that the aggregate supply shock is tantamount to a downward pivot of the aggregate production function XXXXXXXXXXAnalyze the effect of the Corona crisis on the price level in the appropriate money market, under the additional assumption that the demand side and supply side effects on the real interest rate just balance each other out. (3)Part III: Corona in the Keynesian Sticky Nominal Wage Model (18)In this part, we continue the analysis from Part II in the Keynesian sticky nominal wage model. 1) Draw an ISLM-ADAS diagram group and illustrate the combined savings glut and investment collapse in it. Recall that the Yd-curve in the real intertemporal model is identical to the IS-curve here. Since both diagrams have Y on the x-axis, draw them vertically stacked and make sure that the first- and second-round effects are compatible between the two diagrams. Make sure to clearly mark which curve shifts are first-round effects and which are second-round effects (hint: use different colors). Make also sure to label the axes. What happens to aggregate output, the real interest rate, and the aggregate price level in the new equilibrium relative to the old equilibrium? You can use simple arrows to summarize your results: for example, if a variable X increases, write X↑; if it does not change, write X↔, etc. If a change for a variable X is ambiguous, write X? (5)2) Redraw your analysis from 1) and add to it, in yet a different color, the adverse supply shock that the Corona virus brings. Focusing now on the adverse supply shock, make sure to clearly mark which curve shifts are first-round effects and which are second-round effects. Make also sure to label the axes. What happens to aggregate output, the real interest rate, and the aggregate price level in the new Corona equilibrium relative to the old pre-Corona equilibrium? You can use simple arrows to summarize your results: for example, if a variable X increases, write X↑; if it does not change, write X↔, etc. If a change for a variable X is ambiguous, write X? (5)3) Illustrate now the effects from 2) in the appropriate labor market. You can assume that the labor happened to clear in the pre-Corona era (not a bad assumption given the low unemployment rate the US had in February XXXXXXXXXXYou can also assume that the adverse aggregate supply shock in 2) is tantamount to a downward pivot of the aggregate production function. Explain how and why unemployment arises in the Corona crisis XXXXXXXXXXDiscuss verbally (no need to draw graphs) what policy options stabilization policy usually has at its disposal to counteract such adverse shocks. What are their pitfalls and relative advantages in normal recessions, what problems are specific to a pandemic? (4)Part IV: The Tradeoff between Output Variability and Inflation Variability in the DAD/DAS Model (13)Recall the three central equations of the DAD/DAS model: XXXXXXXXXXYt is the level of output at time t. Y without any subscript is simply the (constant) level of natural output. it is the nominal interest rate. ρ denotes the natural real interest rate, a constant; π t the rate of inflation at time t, i.e., the rate of change between the price level in t and t-1, and ε t and ν t are demand and supply shocks, respectively. π * is the inflation target of the monetary authority, assumed to be a constant. The rest are parameters.1) Assume that the economy is in its long-run equilibrium. Illustrate the DAS curve and the DAD curve in (Y, π )–space and show what happens if there is an adverse aggregate supply shock in period t, just for one period (temporary shock), i.e., ν t>0. Also assume θY>0 and θ π >0. Draw carefully the short-run equilibria for t-1, t, t+1. Indicate the progression of time in the graph with different colors. Hint: (Y, π )–space means Y on the x-axis and π on the y-axis XXXXXXXXXXDraw the impulse response function of the inflation rate for the same shock as in XXXXXXXXXXNow consider the case of the European Central Bank (ECB). In contrast to the FED in the U.S., which you essentially drew in 1) and which is supposed to stabilize both the real economy and prices – the so-called dual mandate –, the primary mandate of the ECB is to maintain price stability only, defined as inflation rates “of below, but close to, 2%”. In other words and for the purpose of this analysis, assume that the ECB only reacts to deviations of inflation from its target level, but not to deviations of output from its natural level. What does that mean for the θY of the ECB? (1)How does the DAD curve change with this policy rule, if you assume the same θ π for the ECB and the FED? Draw the new (the ECB’s) DAD curve in the diagram in 1) using a different color XXXXXXXXXXIn order to minimize deviations of inflation from its target level after a temporary adverse supply shock, which approach to monetary policy would you recommend, the FED’s dual mandate or the ECB’s single mandate? Explain briefly why. (2)Part V: The Destruction of Capital in the Solow Model (Death Star Attack) (18)In a galaxy far, far away, the death star destroys half of the capital stock of a planet. Fortunately, through a miracle wrought by the Jedi no life was lost. You are the chief economist to the government of this planet and are asked to predict its economic development. You choose the standard Solow model as your analytical tool.1) Illustrate the Solow diagram with actual and required per capita investment for this planet before the disaster. Show where steady state per capita consumption, saving, investment, capital and output lie XXXXXXXXXXShow graphically in the same diagram as in 1), where the new steady state per capita consumption, capital and output lie (after the disaster). How does this new steady state compare to the old one? (1)3) Show graphically in the same diagram as in 1) with arrows, how the economy transitions into the new steady state XXXXXXXXXXIllustrate the behavior of per capita output in a time series graph. Mark the point in time, where the disaster occurs XXXXXXXXXXIllustrate the behavior of the natural logarithm of aggregate output in a time series graph. Mark the point in time, where the disaster occurs XXXXXXXXXXIllustrate the destruction of the aggregate capital stock also in the (k,k’) diagram, the fixpoint diagram. (4)