3. (8 Points) Derive the optimal rule of investment. Question 4 (15 Points) Consider the consumption-saving decision that we studied in Chapter 9. Explain how does a decrease in the current income y affect the consumer a consumption-saving decision. In particular, explain: 1) How will current consumption e, future consumption of, and savings s change; 2) Are there any substitution effect or income effect. Make sure you draw two figures, one for the borrowers and one for the lenders. Question 5 (25 Points) The COVID-19 pandemic has substantially affected the Canadian economy in several dimensions. As the Canadian governments, both federal and provincial, have issued various forms of "stay home" instructions, workers have to work from home. Working from home has two effects: firms are now less productive and hence the current TFP z declines; labor supply Na(r) declines. In addition, consumers can only go grocery once a week and hence consumption demand Cd(r) declines for any level of interest rate and income. Answer the following questions. 1. (15 Points) Use a real business cycle model that we studied in Chapter 13 to analyze the impact of Covid-19 in terms of output, employment, consumption, investment, wage, interest rate, money demand, and price. Make sure you show three figures: A figure illustrating the goods market, a figure illustrating the labor market, and a figure illustrating the money market. (In this question we assume that the change in output supply dominates the change in output demand, and the change in labor demand dominates the change in labor supply.) 2. (5 Points) According to the real business cycle model, are there anything that the central bank can do to help the economy recover from the recession? Why? You do not need to draw figures in this question. 3. (5 Points) If we use instead the coordination failure model to analyze this recession, then what should the central bank do in this scenario? Explain. You do not need to draw figures in this