# take home test hard grader professor

1 AS-AD

Consider the following AS-AD model. Please note that I have given you the AD curve explicitly and simpliï¬ed many of the expressions you saw in lecture and previous HW (i.e. no z, I already solved for the relationship between unemployment and output, etc.).

Aggregate demand:

Y = 200âˆ’10P

Wage setting relationship:

w = Pe(1âˆ’u)

Price setting relationship:

P = 1.1w

Output and the unemployment rate:

u = 1âˆ’

Y 110

1. Derive the AS curve.

2. Solve for the medium run equilibrium output and price level.

3. Suppose Pe = 30. Do you expect Pe to rise or fall? Solve for the equilibrium price and output level when Pe = 30.

4. Suppose Pe = 6. Do you expect Pe to rise or fall? Solve for the equilibrium price and output level when Pe = 6.

2 European Competition Law

When new European Union member countries join the EU they become subject to the European Union competition law â€“ a law that regulates anticompetitive behavior and keeps markets within Europe more competitive.

1. What eï¬€ect will this have on the new member countyâ€™s natural rate of unemployment? Provide a graph supporting your answer.

2. What eï¬€ects will joining the EU have on the new memberâ€™s prices and output? Provide a graph to support your answer.

3. Do you expect higher or lower inï¬‚ation after the country joins the EU? Explain your answer.

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3 IS-LM and Excess Reserves

Consider the following IS-LM model with a banking system:

Consumption:

C = 10 + 0.5YD

Investment:

I = 0.4Y âˆ’100i

Government expenditure:

G = 5

Taxes:

T = 10

Money demand:

Md P

=

Y i

In periods of ï¬nancial turmoil, banks often choose to hold excess reserves above and beyond what they are required to hold by law. We shall denote the proportion of deposits held as excess reserves as Ï and the required reserve ratio as Î¸. Suppose that consumers hold 37.5% of their money as currency (c = 0.375) and the required reserve ratio is 20% (Î¸ = 0.2). The banking system is then described by:

Demand for reserves:

Rd = 0.2Dd + ÏDd

Demand for deposits:

Dd = (1âˆ’0.375)Md

Demand for currency:

CUd = 0.375Md

Demand for central bank money (Hd) is the total amount of currency being demanded plus the total demand for reserves. Suppose the price level is P = 1.

1. Suppose that that banks do not wish to hold excess reserves (Ï = 0) and that the supply of central bank money is H = 500. Solve for the money multiplier and the overall money supply. Explain/show your work.

2. Solve for equilibrium output and the equilibrium interest rate when H = 500. 3. Suppose that banks start holding 8 15 of their deposits as excess reserves (Ï = 8 15). Solve for the new equilibrium output when H = 500. HINT: Overall money will be a whole number â€“ donâ€™t round when calculating the new money multiplier. Output and interest rates will not.

4. Provide an IS-LM graph that demonstrates what happens to the general equilibrium when banks increase their holdings of excess reserves. Label all curves, points, and shifts clearly.

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4 Investment Subsidies

This problem considers the mortgage interest deduction â€“ a U.S. tax incentive program to encourage residential home ownership (an investment subsidy). Provide an IS-LM graph that explains what might happen to the macroeconomy if the government eliminated this investment subsidy. Clearly label all curves, points and axes and explain any shifts that are occurring in your graph.

5 Greek Debt Crisis

As a member of the Eurozone, Greece was/is unable to conduct itâ€™s own monetary policy. Instead, Eurozone monetary policy is set by the European Central Bank in Frankfurt. Suppose that Greece is facing a recession and wants to boost output.

1. What type of government policy would you suggest to boost output? Provide an IS-LM graph with a clear explanation of what you are suggesting.

2. How would the government fund such a policy?

3. What are some of the longer term implications of Greece using this approach to stabilizing output?

6 Energy Prices in an AS-AD Model

Consider the following AS-AD model where Y is real output, N is the number of employed workers, E is the amount of energy resources used in the economy, pE is the price of energy, w is the nominal wage, Pe is the expected price level, P is the price level, u is the unemployment rate, U is the number of unemployed workers, L is the size of the labor force, and z is our catch-all variable for other labor market conditions. NOTE: be careful to distinguish energy prices pE from expected aggregate prices Pe

Production function:

Y = N

1 2 E

1 2

Wage Setting relationship:

w = Pe z u

Price setting relationship

P = (1 + m)w

1 2 p

1 2 E

Unemployment rate:

u =

U L

Unemployment level:

U = Lâˆ’N 1. Let x = pE/P be the real price of energy. Derive an expression for the real wage in the price setting relationship as a function of the markup and the real price of energy x.

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2. Will the natural rate of unemployment change if the real price of energy goes up? If so, how? If not, why not? Show your work.

3. Derive the AS curve as a function of m,x,Pe,z,Y,E, and L. Show your work. HINT: it will help to start with your real wage expression from part 1).

4. Suppose that the economy starts oï¬€ in medium run equilibrium. Provide an AS-AD graph that demonstrates the eï¬€ects of an increase in the real price of energy. Clearly label/explain all curves, points, shifts, etc.

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