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ECON 100C: Midterm exam #2

November 16, 2016, 5pm-6:20pm

Show all work to receive full credit

No material allowed

Problem 1 is worth 8 points Problem 2 is worth 3 points

Multiple choice questions are worth 10 points

Student�s name: _____________________________

Student�s ID number: _________________________

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Problem 1: Alternative Matching Function

Consider the Mortensen-Pissarides model of unemployment where the aggre- gate matching function is:

H(U;V ) = �A UV

U +V with �A > 0; (1)

where U denotes the number of unemployed workers and V denotes the number of vacant jobs.

(i) (1 point) Does this matching function exhibit constant returns to scale? (Give a proof).

(ii) (1 point) Derive the expressions for the job �nding probability (f) and the vacancy �lling probability (q) as a function of market tightness, � = V=U.

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(iii) (2 points) Give the expression for the equilibrium unemployment rate, u, as a function of market tightness and the separation rate, s. Give a graphical representation of the Beveridge curve.

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(iv) (2 points) Write down the vacancy supply condition where y denotes labor productivity, w the real wage, k the cost of opening a vacancy. Find the closed form solution for market tightness. Represent the vacancy supply condition graphically.

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(v) (2 points) Suppose that the new Congress votes policy measures to make it less costly to open jobs. Assume w = �w and use your answers to the questionsabovetoexplainhowsuchmeasureswoulda¤ect theunemployment rate and market tightness.

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Problem 2: The IS model

Consider the following IS model:

Y = C + I +G (2) C �Y

= �ac ��bc(R � �r) (3) I �Y

= �ai ��bi(R � �r) (4) G �Y

= �ag (5)

The notations are the same as in your textbook. The only novelty is the second term on the right side of (3) where �bc > 0. It says that private consumption decreases with the real interest rate, R. We interpret �r as a long-run real interest rate. (Also, relative to the lecture, the marginal propensity to consume out of transitory income is �x = 0.) (i) (2 points) Derive the equilibrium relationship between short-run output, ~Y = (Y � �Y )=�Y , and the real interest rate, R. Represent this relationship graphically.

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(ii) (1 point) Suppose the policymaker raises the interest rate R. What are the e¤ects on consumption, investment, and output? Explain.

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Multiple choice questions

1. If Pt is the price level in time t, the in�ation rate is calculated as:

(a) 1=Pt

(b) 1=(Pt+1� Pt) (c) (Pt+1=Pt)�1 (d) (Pt �Pt+1)=Pt+1

2. According to the quantity theory of money an increase in the velocity of money leads to:

(a) lower prices and higher output

(b) higher prices and higher output

(c) higher prices and unchanged output

(d) lower money supply and unchanged output

3. The Fisher equation is:

(a) 1+ i = (1+ r)(1+�)

(b) 1+ r = (1+ i)(1+�)

(c) 1+ i = (1+ r)(1��) (d) 1+ r = (1+ i)(1��)

4. The average annual in�ation rate in Zimbabwe in 2008 was:

(a) Less than 10%

(b) Between 10% and 100%

(c) Between 100% and 1000%

(d) More than 1000%

5. Suppose the money supply grows at an annual rate of 5% while real GDP grows at an annual rate of 2%. According to the Quantity Theory the in�ation should be:

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(a) 2%

(b) 3%

(c) 5%

(d) 7%

6. Suppose the velocity of money, V , is an increasing function of the in�ation rate, �. According to the Quantity Equation an increase in the in�ation rate _________ aggregate real balances (M=P) and _______ aggregate output.

(a) Reduces; Does not a¤ect

(b) Raises; Raises

(c) Raises; Reduces

(d) Does not a¤ect; Reduces

7. The IS curve is _______ sloping (in the space Y;R) and it shifts to the ______ as the marginal product of capital, �r, increases.

(a) Upward; Right

(b) Upward; Left

(c) Downward; Right

(d) Downward; Left

8. Consider the IS model and suppose that the marginal propensity to consume out of transitory income is �x = 0:25. A one-dollar increase in government purchases leads to a _____ dollar increase in GDP.

(a) 0.25

(b) 1

(c) 1.25

(d) 1.33

9. Consider the IS model and suppose that the marginal propensity to consume out of transitory income is �x = 0:25. A one-dollar cut in taxes leads to a _____ dollar increase in GDP.

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(a) 0

(b) 0.25

(c) 0.33

(d) 1.25

10. Consider the IS model and suppose that the marginal propensity to consume out of transitory income is �x = 0:25. A one-dollar increase in government purchases �nanced by a one-dollar increase in taxes leads to a _____ dollar increase in GDP.

(a) 0

(b) 0.33

(c) 1

(d) 1.25

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