SOSC1449 Understanding Our Economy
Assignment 2
Due date: 6th of May 11:59 pm
1. (5 points) Derive the IS curve, where using the following five equations:
2. (5 points) Draw the IS curve on a diagram with the real interest rate on the y-axis and short-run output on the x-axis. Using the diagram, illustrate and explain the effect on the IS curve if the government increases the investment tax credit to promote investment.
3. (5 points) Draw the IS curve on a diagram with the real interest rate on the y-axis and short-run output on the x-axis. Using the diagram, illustrate and explain the effect on the IS curve if the central bank lowers the nominal interest rate.
4. (5 points) Suppose consumption and short-run output have a relationship
where is between 0 and 1. Mathematically derive the new IS curve shown below based on this consumption function. [Hint: Substitute and then rearrange the equation so that is only on one side of the equation.]
5. (5 points) On a single diagram with the real interest rate on the y-axis and short-run output on the x-axis, draw and label the IS curves derived in Questions 1 and 4. Clearly distinguish between the two curves.
6. (5 points) Using the IS curve and the monetary policy rule provided in the lecture slides, mathematically derive the Aggregate Demand (AD) curve. Draw the AD curve on a diagram with the inflation rate on the y-axis and short-run output on the x-axis.
7. (5 points) Using the Phillips curve, where the expected inflation rate is mathematically derive the Aggregate Supply (AS) curve. Draw the AS curve on a diagram with the inflation rate on the y-axis and short-run output on the x-axis.
8. (25 points) Draw the AS and AD curves on a diagram with the inflation rate on the y-axis and short-run output on the x-axis. Use the diagram to analyze the relationship between inflation and output when the central bank lowers its inflation target, Follow each step below. Provide a discussion and illustrate all relevant shifts and outcomes.
a. (5 points) Identify and explain which curve (AS or AD) shifts when the central bank lowers its inflation target. Use the diagram to support your explanation.
b. (5 points) After the central bank lowers the inflation target at time 1, what is the level of inflation? Explain your answer, referencing the AS-AD framework.
c. (5 points) At time 2, what is the equilibrium level of inflation? Using your answers from Questions a and b, provide the precise level and explain how it is determined.
d. (5 points) At time 3, what is the equilibrium level of inflation? Using your answers from Questions a and b, provide the precise level and explain how it is determined.
e. (5 points) As time progresses, to what level does the equilibrium inflation rate converge? Explain why, referencing the AS-AD framework.
9. (25 points) How would this analysis be different if the AS curve is based on expectation πt =
a. (5 points) Draw the AS and AD curves on a diagram and show which curve shifts when the central bank lowers the inflation target,
b. (5 points) After the central bank lowers the inflation target at time 1, what is the level of inflation? Explain your answer.
c. (5 points) At time 2, what is the equilibrium level of inflation? Provide the precise level, referencing your answers from Question a and b.
d. (5 points) As time progresses, to which level does the equilibrium inflation rate converge? Explain why.
e. (5 points) Compare the analyses in Questions 8 and 9. Describe the main difference in the inflation and output dynamics due to the different expectations assumptions.
10. (5 points) If the monetary policy rule is where γ > 0 that the central bank cares not only about inflation, but also about the short-run deviation. Compared to which policy rule incentivizes the central bank to raise the interest rate more aggressively, and why?
11. (5 points) Using the new policy rule, mathematically derive the revised version of the AD curve as shown below [Hint: Substitute and then rearrange the equation so that is only one side of the equation.]
12. (5 points) On a single diagram with the inflation rate on the y-axis and short-run output on the x-axis, draw and label the AD curves derived in Questions 6 and 11. Clearly distinguish between the two curves.