Assignment

Part 1:

Problem 1: Altermative Matchimg Fumctiom

Consider the Mortensen-Pissarides model of unemployment where the aggregate 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) Does this matching function exhibit constant returns to scale? (Give a proof).

(ii) Derive the expressions for the job finding probability (f) and the vacancy filling probability (q) as a function of market tightness, θ = V /U.

(iii) 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.

(iv) 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.

(v) 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
questions above to explain how such measures would affect the unemployment rate and market tightness.

Problem 2: The IS model

Consider the following IS model:

Y = C + I + G                        (2)
C/Y¯ = a¯_c - b¯_c (R - r¯)       (3)
I/Y¯ = a¯_i - b¯_i (R - r¯)         (4)
G/Y¯ = a¯_g                          (3)

The notations are the same as in your textbook. The only novelty is the second term on the right side of (3) where b¯_c> 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) Derive the equilibrium relationship between short-run output, Y˜ = (Y - Y¯ )/Y¯ , and the real interest rate, R. Represent this relationship
graphically.

(ii) Suppose the policymaker raises the interest rate R. What are the effects on consumption, investment, and output? Explain.

Part 2: Multiple choice questioms

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

(a) 1/P_t
(b) 1/(P_t+1- P_t)
(c) (P_t+1/P_t) - 1
(d) (P_t - P_t+1)/P_t+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 + π)
(b) 1 + r = (1 + i) (1 + π)
(c) 1 + i = (1 + r) (1 - π)
(d) 1 + r = (1 + i) (1 - π)

4. The average annual inflation rate in Zimbabwe in £OO8 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 inflation should be:

(a) 2%
(b) 3%
(c) 5%
(d) 7%

6. Suppose the velocity of money, V, is an increasing function of the inflation rate, π. According to the Øuantity Equation an increase in the inflation rate _____ aggregate real balances (M/P ) and ____ aggregate output.

(a) Reduces¡ Does not affect
(b) Raises¡ Raises
(c) Raises¡ Reduces
(d) Does not affect¡ 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.

(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 financed by a one-dollar increase in taxes leads to a dollar increase in GDP.

(a) 0
(b) 0.33
(c) 1
(d) 1.25