Part A – Short-run Keynesian macro models:

1. Consider a closed economy (NX = 0) with a government that spends, taxes, and makes transfer payments to households. Government spending is G = 200 and the tax function is T =
-62.5 + 0.25Y (note the - sign is not a mistake; the -62.5 term includes transfer payments which are like negative taxes—they flow to households and add to disposable income—so think of T as “taxes net of transfers”). The consumption function is C = 50 + 0.8YD and investment is fixed at I = 100.
a. Solve for the aggregate demand function Z and the equilibrium level of income Y. Illustrate your answer on a diagram.
b. Calculate the value of the multiplier. Discuss how the multiplier is affected by the tax rate, t1 = 0.25. Would a higher tax rate increase or decrease the multiplier? Why?
c. What is the government’s equilibrium budget balance (surplus) (T - G)? (Hint: Use the equilibrium value of Y*).
d. If the “animal spirits” of business firms improve (confidence increases), so that I rises to 150, what happens to Y ? What happens to the budget balance? Calculate and explain.
e. What happens if the government increases its spending G to 250 (with investment back at I = 100)? Compare the effects with part d. of this question and discuss how they are similar or different. (What is the policy significance of the difference?)

2. All assumptions of the model are the same as in the previous question (#A.1), but here you will analyze it using Krugman’s diagram (see class notes and handout on “Math for Krugman Diagram” posted on Blackboard) and focus on fiscal policy during a recession.
a. First, draw the equilibrium of the economy using Krugman’s diagram, where the govern- ment deficit (G - T ) and private sector surplus (S - I) are shown on the vertical axis and national income Y is on the horizontal axis. Solve for (G - T ) and (S - I ) as functions of Y . Draw these two lines on your diagram and carefully label/identify all lines, slopes, vertical intercepts, and equilibrium points. Be sure to solve for the equilibrium budget deficit (G - T)* as well as Y* (Hint: the latter should be the same as in #A.2!).
b. Now suppose there is a financial crisis resulting in a collapse of both housing and busi- ness investment, so I falls by 50 (i.e., from 100 to 50). Show the effects on your diagram from part a. and also calculate the effect on equilibrium income Y*.
c. What happens to the equilibrium budget deficit (G-T)* as a result of the fall in invest- ment? Is this a cause or effect of the recession? What would happen if the government tried to maintain a balanced budget after the fall in private investment, or responded with fiscal austerity? Show on the graph and discuss.
d. Compare the model’s predictions about the effects of the following stimulus policies on output (calculate Y), starting from the recession equilibrium in part b.:
i. The government increases spending G by 25.
ii. The government increases unemployment compensation by 25 (this is part of trans- fers, hence the negative constant term of the tax function becomes more negative).
iii. The government cuts taxes (the constant part of T is reduced) by 25.
Rank the effectiveness of these three alternative stimulus policies in terms of the size of the ΔY they generate, according to the model. Do you find this ranking realistic? Why or why not? Also, thinking outside the model: in reality, would it make a difference if taxes are cut more for the wealthy or the middle class? Why?
e. After any one of the stimulus policies in part d. is adopted, a cable TV pundit observes that the economy has not fully recovered and claims that the stimulus must have been ineffective. Comment.

3. Suppose that the economy is characterized by a simple Keynesian model of a purely private, closed economy, in which private domestic investment is fixed at I = 50. There is no govern- ment (G = T = 0) or foreign trade (X = IM = 0).
a. Assuming that the consumption function is C = 100 + 0.9Y, where 0.9 is the “marginal propensity to consume” (MPC, or c1 in our algebraic model), what is the equilibrium level of income (Y*)? the equilibrium level of saving (S*)? What is the value of the “multiplier”? Illustrate your answer on a graph showing the equilibrium condition Y = Z along with the Z (aggregate demand) function.
b. Now suppose that consumers desire to save more and reduce their MPC to 0.8. How does the saving function change? What is the new marginal propensity to save? What is the equilibrium level of national income Y? What happens to the value of the “multiplier”?
c. Does the equilibrium amount of saving actually increase? Why or why not? Illustrate your answer on a (separate) diagram showing the equilibrium condition as I = S, and discuss why this result is called the “paradox of thrift” or “paradox of saving.”
d. If I rises to 100 (i.e., ΔI = 50), how would this affect equilibrium income with the original MPC of 0.9? What would happen to equilibrium saving? Illustrate on a diagram showing the I = S equilibrium condition.
e. Explain the impact of the rise in I in part d. in terms of successive “rounds” of spending. How is this related to the stability of the new equilibrium point?

Part B – Money:

1. Suppose that all deposit accounts (D) are checking accounts paying zero interest and there is only one kind of money (M), which consists only of these deposits (credit and debit cards are used so universally that the public holds zero currency). The required reserve ratio is θ = .05, and banks hold no excess reserves. GDP is Y = 10,000. [The price level is P = 1, so there is no difference between real and nominal income ($Y = P*Y).] The public’s demand for money is determined by Md = 0.25Y - 250i. [Note that i is measured here in percentage points, e.g., 5 means 5%, so do not convert your result to a decimal here!]
a. First, assuming the “traditional view” of money, suppose that the central bank sets the money supply at M = 1,600. Solve for the equilibrium interest rate (i). How much “central bank money” (H, also known as monetary base or high-powered money) must

exist in this situation? What does H consist of here?
b. Subsequently, the central bank decides instead to target the monetary base at H = 100. What kind of open market operation would the central bank have to conduct, starting from the situation described in part a.? Use a balance sheet for the central bank (showing the changes only). What would happen to the money supply (M)? to the interest rate (i)?
c. Alternatively, suppose the central bank targets the interest rate at i = 5% (use “5” here, do not convert to a decimal), as in the new/alternative views. What does the central bank have to do to achieve this target (relative to the situation in part a.)? What are the implications for the money supply? Be specific—calculate M and H— and explain using a balance sheet.
d. Now the country’s economy grows and Y = 11,000. Compare the effects under a monetary target (either M or H) versus an interest rate target (i). HINT: for the monetary target, calculate the change in the interest rate Δi; for the interest rate target, just calculate ΔM and ΔH. Just find the changes; don’t worry about levels.

2. Answer the following questions about money and monetary policy, taking into account the “new” or “alternative” views we studied:
a. Before the financial crisis of 2008, how did the U.S. Federal Reserve (Fed) control the federal funds rate (its target interest rate) using open market operations? Explain, and be sure to define your terms.
b. Do banks need the Fed to create additional reserves (for example, through open market operations) in advance of making new loans? Why or why not? Does new investment (purchase of newly produced housing or capital goods) require a prior increase in saving? Why or why not? Hint: study the 3rd view of money in the class presentation, and read the articles by McLeay et al. and Kumhof & Jakab.
c. The traditional view of how the Fed (allegedly) controls the money supply was based on the idea of a “money multiplier.” Does this view of the money supply make sense today after the Fed’s policy responses to the financial crisis of 2008? Why or why not?
d. If the Fed wants to raise its target for the federal funds rate above its current range of 1.75 to 2.00 percentage points, can it use open market operations to accomplish this? Why or why not? Hint: use diagrams showing the supply and demand for reserves pre- and post- crisis, and discuss.
e. If your answer to d. is “no” (and it should be!), what are the two primary tools that the Fed is now using to control the federal funds rate? Briefly explain how each one works.

Part A – Short-run Keynesian macro models: 1. Consider a closed...