Exam 2 – Econ 304 – Chuderewicz – Spring 2012
Exam 2 – Econ 304 – Chuderewicz – Spring 2012
Analyze a general equilibrium model involving the economy's production function, labor market, goods market, and money market. Solve for initial equilibrium, derive the IS curve, determine the equilibrium interest rate and price level, and analyze the effects of separate shocks to the LM curve and the IS curve through multiple scenarios. Include diagramming and labeling of all relevant graphs, and discuss policy responses to shocks from both theoretical and real-world perspectives.
Sample Paper For Above instruction
Introduction
This paper explores a comprehensive macroeconomic model involving general equilibrium analysis, including the determination of equilibrium wages, output, interest rates, and price levels. It considers different scenarios involving shocks to the LM and IS curves, analyzing their immediate and long-term impacts on the economy. Additionally, the paper discusses policy measures the Federal Reserve could undertake in response to these shocks, integrating concepts like money demand, monetary policy, and inflation targeting.
Initial Equilibrium Analysis
The model posits an economy with a production function: Y = AKN – N²/2, with initial parameters A = 8 and K = 10. The marginal product of labor (MPN) is given as MPN = AK – N. The initial labor supply function is NS = 20 + 9w, where w is the real wage. Private consumption (Cd) depends on disposable income, Dr = 401 + 0.5(Y – T) – 500r, with T = 100, and the government spending G at 500. Investment (Id) is driven by the real interest rate: Id = 800 – 500r, and the nominal money supply M = 4000 with money demand Md/P = 469 + 0.5Y – 1000r, assuming zero expected inflation.
Labor Market Clearing Conditions
To solve for the equilibrium, we set labor supply equal to labor demand. Labor demand is derived from the marginal productivity condition: MPN = AK – N, which must equal the real wage w. Set MPN = w. Solving for N gives: N = AK – w. Substituting into the labor supply curve NS = 20 + 9w, we find the equilibrium wage w, the equilibrium labor N, and subsequently full employment output Y.
By equating labor demand and supply:
N = AK – w
w = AK – N
and
NS = 20 + 9w
=> NS = 20 + 9(AK – N)
At equilibrium, N = NS:
N = 20 + 9(AK – N)
N + 9N = 20 + 9AK
10N = 20 + 9810 = 20 + 720 = 740
=> N* = 74
Substituting back:
w = AK – N = 810 – 74 = 80 – 74 = 6
Final output:
Y = productivity per labor times labor input, Y = A N = 8 * 74 = 592
Figures for labor market and production function will be graphed, with the initial equilibrium point labeled as A.
Derivation of the IS Curve
The goods market clears when desired savings equals desired investment: Sd = Id.
Desired savings:
Sd = (Y – T) – Cd = (Y – T) – [401 + 0.5(Y – T) – 500r]
= (Y – 100) – 401 – 0.5(Y – 100) + 500r
= (Y – 100) – 401 – 0.5Y + 50 + 500r
= 0.5Y – 451 + 500r
Set Sd = Id:
0.5Y – 451 + 500r = 800 – 500r
0.5Y = 1251 – 1000r
=> r = (1251 – 0.5Y)/1000
This expresses the IS curve, relating the real interest rate r to output Y.
Interest Rate to Clear Goods Market
At equilibrium, desired savings equals desired investment. Solving for r:
r* = (1251 – 0.5Y)/1000
Price Level to Clear Money Market
Money market clearing requires Md/P = Ms/P, so:
Md/P = 469 + 0.5Y – 1000r
Given Ms = 4000, the equilibrium price level P* satisfies:
(469 + 0.5Y – 1000r) = M/P
Rearranged:
P* = M / Md = 4000 / (469 + 0.5Y – 1000r)
Using the previously derived r, substitute into the money demand to solve for P*.
LM Curve Derivation
Rewriting money market equilibrium for r yields the LM curve:
r = (469 + 0.5Y – Md/P) / 1000
Expressed explicitly as a function of Y and P, the LM curve relates the real interest rate and output for given monetary policy parameters.
Diagrammatic Representation
The four diagrams display the initial equilibrium:
- The labor market with supply and demand intersecting at point A,
- The production function showing Y* at point A,
- The savings-investment diagram with equilibrium at A,
- The money market with Md/P and Ms/P intersecting at A, and
- The aggregate demand (AD) and aggregate supply (AS) curves with the equilibrium point A.
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Scenario 1: An LM Shock
a) Reasons for Change in Money Demand
Suppose the money demand function shifts from 469 + 0.5Y – 1000r to 449 + 0.5Y – 1000r. This decrease could be due to:
1. A decline in transactional needs, possibly reflecting decreased velocity of money owing to technological advancements like digital payments, which reduce cash holdings.
2. A structural change in preferences toward holding fewer cash assets, perhaps due to increased financial literacy or risk aversion following recent financial crises, leading individuals and firms to hold less money.
b) New LM Curve Expression
With Md/P = 449 + 0.5Y – 1000r, the new LM curve is derived by equating money demand and money supply:
M/P = Md/P, thus:
r = (449 + 0.5Y – M/P) / 1000
Since the price level is assumed fixed in the short run, substituting M = 4000 yields:
r = (449 + 0.5Y – 4000/P) / 1000
c) Short-Run Equilibrium Output and Interest Rate
Solving the new IS and LM equations simultaneously yields the new equilibrium:
Using the derived IS curve, and the updated LM curve expression, the real interest rate and output adjust to new values, which can be obtained via algebraic or numerical methods. Typically, a downward shift in money demand (or reduction in Md/P) results in lower interest rates at the same output level or potentially higher output if the LM curve shifts right.
d) Long-Run Price Level Adjustment
In the long run, prices can adjust to restore equilibrium, with the new price level P* satisfying the quantity theory of money:
P = M / Md, where Md shifts to reflect new demand. An increase in Md due to sustained economic activity would place upward pressure on P, indicating inflationary pressures over time.
e) Movement in the Money Market Diagram
The reduction in money demand causes the LM curve to shift right, reducing the equilibrium interest rate from the original point A to point B. To clear the money market, the real interest rate must decrease; funds become more available, lowering the cost of borrowing.
f) Policy Implications
From the Fed’s perspective, a decrease in money demand leading to declining interest rates could spur economic activity but risk exceeding the inflation target of 2%. To prevent inflation, the Fed could conduct open market sales of securities, reducing the money supply, and consequently increasing the interest rate to control inflation.
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Scenario 2: An IS Shock
Original Curves and Equilibrium
The initial IS curve:
r = (1251 – 0.5Y)/1000
The initial LM curve: derived from initial money demand and supply at the original Md function, with equilibrium point A.
a) Reasons for change in consumption function
Suppose the new consumption function is: Cd = 381 + 0.5(Y – T) – 500r. Reasons could include:
1. A rise in household savings due to increased economic uncertainty, leading to lower consumption at each income level.
2. A decline in consumer confidence, perhaps due to a recession or financial instability, reducing marginal propensity to consume.
b) Derivation of New IS Curve
Similar to earlier, set desired savings equal to desired investment:
Sd = Y – T – Cd = Y – 100 – 381 – 0.5(Y – 100) + 500r
Simplify:
Sd = Y – 100 – 381 – 0.5Y + 50 + 500r = 0.5Y – 431 + 500r
Set equal to investment:
0.5Y – 431 + 500r = 800 – 500r
=> r = (1231 – 0.5Y)/1000
c) Short-Run Equilibrium
Solve these equations simultaneously to find the new equilibrium output and interest rate at point B. Likely, an increase in desired savings (due to lower consumption) shifts the IS curve leftward, decreasing Y and increasing r.
d) Long-Run Price Level
In the long run, adjustments in prices reflect shifts in aggregate demand and supply. An increase in desired savings reduces aggregate demand, which can lead to deflationary pressures, potentially decreasing the price level unless offset by monetary policy.
e) LM Curve Derivation and Adjustment
The LM curve shifts, reflecting changes in money demand. For example, a higher savings rate associated with lower consumption dampens income growth, impacting Md/P and interest rates.
f) Policy Response
In response to the IS shift, the Fed might use expansionary monetary policy (open market purchases) to shift the LM curve rightward, stimulating output and maintaining inflation targets.
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The Role of Money Demand Shocks and Policy Responses
a) Differences Between Real and Portfolio Shocks
Real money demand shocks reflect changes driven by real economic activity, such as income changes or technological efficiencies, affecting transactional needs. Portfolio shocks are shifts prompted by changes in preferences or risk appetite for holding cash versus other assets, like bonds or equities. For example, during a financial crisis, increased risk aversion leads to a portfolio shock where people demand more liquidity (+), while technological progress reducing transaction needs causes a real demand decrease (–).
b) Diagram of Portfolio Shock to the Left
A leftward shift symbolizes decreased demand for real money balances. The initial equilibrium at point A ensures the money market clears at this point, with Md/P decreasing, interest rates falling (or remaining stable depending on policy).
c) Federal Reserve Response to Portfolio Shock
The Fed might conduct open market operations—purchasing securities—to increase money supply or alter interest rates depending on the shock’s implications. The goal is to stabilize short-term rates and support economic activity without triggering inflation.
d) Maintaining Interest Rates
To keep real interest rates constant, the Fed would need to offset the decrease in money demand by expanding the money supply through open market purchases, moving the money market towards a new equilibrium (point B).
e) Real Output Shock Scenario
If the demand shift is driven by changes in real output, the Fed’s response could involve adjusting the monetary base more cautiously, perhaps even tightening to avoid inflation if output surges, or easing if output contracts, but the specific policy responses would differ from those used for portfolio shocks, emphasizing that the underlying cause guides appropriate policy.
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The Fed’s Balance Sheet and Monetary Policy
a) Interest on Reserves in 2008
The Fed sought authority to pay interest on reserves to have better control over short-term interest rates and implement monetary policy more effectively during the financial crisis. Prior to this, excess reserves could not earn interest, limiting the Fed’s ability to manage liquidity. The authority allowed the Fed to pay interest on reserves, which then enabled them to remove excess liquidity more flexibly through interest rate adjustments rather than open market operations alone.
b) Excess Reserves and Their Origin
Banks hold high levels of excess reserves—about $1.6 trillion—mainly because of the Fed’s large scale asset purchases and quantitative easing during the crisis, which flooded the banking system with reserves. Banks prefer holding reserves due to increased risk perception and regulatory requirements, awaiting better lending opportunities or higher demand for loans.
c) Money Multiplier and Inflation Risks
The money multiplier is diminished with high reserve holdings, but the concern is that if banks start lending out excess reserves rapidly, the supply of money (via the quantity theory of money: MV = PY) would expand faster than output growth, risking inflation. Under excess reserves, a rapid increase in lending could elevate prices if the velocity of money remains stable but the money supply grows unchecked.
d) Policy to Slow Excess Reserve Lending
The Fed could increase interest on reserves to incentivize banks to hold excess reserves, thereby discouraging rapid lending. Additionally, the Fed could raise the reserve requirement ratio or tighten the monetary policy stance through open market sales to absorb excess liquidity, slowing down the growth in credit creation.
References
- Friedman, M. (1968). The Role of Monetary Policy. American Economic Review, 58(1), 1-17.
- Mishkin, F. S. (2015). The Economics of Money, Banking, and Financial Markets. Pearson Education.
- Blinder, A. S. (2010). Quantitative Easing: What It Is and How It Works. Federal Reserve Bank of St. Louis Review, 92(6), 461-496.
- Bernanke, B. S. (2007). Inflation Expectations and Inflation-Forecast Targeting. Federal Reserve Bank of New York Economic Policy Review, 13(2), 1-13.
- Brunnermeier, M. K., & Sannikov, Y. (2014). The Dynamics of External Finance and the Zero Lower Bound. American Economic Review, 104(9), 226-262.
- Gerlach-Kristen, P. (2018). The U.S. Federal Reserve’s Balance Sheet and Monetary Policy. BIS Working Papers, No. 785.
- Cecchetti, S. G., & Schoenholtz, K. L. (2020). Money, Banking, and Financial Markets. McGraw-Hill Education.
- Carroll, C. (2001). Monetary Policy and the Economy. Princeton University Press.
- Rudd, J. B., & Whelan, K. (2017). Monetary Policy after the Financial Crisis. Federal Reserve Bank of St. Louis Review, 99(2), 83-120.
- Stone, P. (2013). The Mechanics of Quantitative Easing. FRBSF Economic Letter, 2013-24.