FINAL EXAM: 100 POINTS TOTAL L. Tesfatsion
Econ 502
Fall 2001
QUESTION 1: SHORT ANSWERS [20 Points Total, About 20 Minutes
Total Time]
PART A: [8 Points Total]
(1) [2 Points] Explain briefly (in words) the meaning of the
Lucas Critique.
(2) [6 Points] Why do many rational expectations theorists argue
that traditional dynamic IS-LM models (as studied at the beginning
of class) are "fatally flawed" for policy analysis purposes on the
grounds that these models are subject to Lucas Critique problems?
PART B: [12 Points Total]
(1) [2 Points] Define (in words) what is meant by a moral
hazard problem.
(2) [2 Points] What is the basic efficiency wage hypothesis?
(3) [2 Points] Why does this basic efficiency wage hypothesis
imply that labor markets are potentially subject to moral hazard
problems?
(4) [6 Points] How might setting a wage rate that is "too high"
relative to a competitive wage alleviate this moral hazard problem
from the viewpoint of a profit-maximizing firm?
QUESTION 2: [35 Points Total, About 35 Minutes Total Time]
Consider an economy E* existing over all past and future periods
that is described by the following equations in each period t,
with t ranging from minus to plus infinity.
Period-t Model Equations:
(1) y_t = a_0 + a_1[m_t - E_t_-_1m_t ] + a_2y_t_-_1 + u_t ;
(2) m_t = g_0 + g_1y_t_-_1 + v_t .
Period-t Classification of Variables:
Period-t Endogenous Variables:
y_t = log of real GDP ;
m_t = rate of growth of the real money supply .
NOTE: y_t and m_t are assumed to be observed by the modeller
at the end of each period t (i.e., at the beginning of each
period t+1)
Period-t Predetermined Variables:
y_t_-_1 ;
E_t_-_1m_t = expectation of m_t formed by the representative
agent at the end of period t-1 (i.e., at the beginning of
period t).
Exogenous Variables:
u_t = serially independent and identically distributed exogenous
random shock term with variance å^2_u and mean 0 in every
period t;
v_t = serially independent and identically distributed exogenous
random shock term with variance å^2_v and mean 0 in every
period t;
a_0, a_1, a_2 = exogenous positive constants ;
g_0, g_1 = exogenous monetary policy variables under the control
of the government.
PART A: [23 Points Total]
(i) [2 Points] Provide a brief general definition IN WORDS for
what it means to say that a representative agent in an economic
model has STRONG-form (Muthian) rational expectations.
(ii) [4 Points] Suppose the representative agent in the economy
E* described by model equations (1) and (2) above forms a
STRONG-form rational expectation E_t_-_1m_t for m_t at the end of
each period t-1. Explain carefully what specific information must
then be in this representative agent's information set I_t_-_1 at
the end of each period t-1.
(iii) [12 Points] Using your answer to part (ii) above, determine
an explicit analytical expression for E_t_-_1m_t in model equation
(1) assuming that this is a STRONG-form rational expectation. Be
sure to justify all the steps of your derivation and to show your
work.
(iv) [5 Points] Replace the expression E_t_-_1m_t in model
equation (1) for economy E* by the explicit analytic expression for
the strong-form rational expectation you derived in part (iii),
above. Call the resulting modified model equation (1)'. Now
consider the economy E' described by model equations (1)' and (2) in
each period t. To what extent is government able to systematically
control y_t in economy E' through the use of monetary policy (i.e.,
through changes in the values of the monetary policy variables g_0
and g_1 that it controls)? Explain carefully, and provide an
economic interpretation for your findings.
PART B: [12 Points Total]
(a) [2 Points] Provide a brief general definition IN WORDS for
what it means to say that a representative agent in an economic
model has WEAK-form rational expectations.
(b) [10 Points] Suppose the representative agent in economy E*
described by equations (1) and (2) above has a WEAK-form rational
expectation E_t_-_1m_t for m_t. Does this necessarily imply that
government CAN systematically control y_t through its monetary
policy (i.e., through changes in the values of the monetary policy
variables g_0 and g_1 that it controls)? That government CANNOT
systematically control y_t through its monetary policy? Explain
carefully, using simple analytical examples of weak-form rational
expectations for m_t to illustrate your assertions, and provide an
economic interpretation for your findings.
QUESTION 3: [45 Points Total, About 45 Minutes Total Time]
Consider an economy E in some period T that consists of 100
utility maximizing consumers, i = 1,...,100, and 2 profit-maximizing
firms FX and FY who produce consumption goods X and Y, respectively.
Each consumer has the same exogenously given endowment L* of
labor services for period T, measured in person-hours, and every
unit of labor is like every other unit. For each i=1,...,100, the
preferences of consumer i in period T are described by a utility
function U_i(x_i,y_i,le_i) defined over consumer i's consumption x_i
of good X, consumption y_i of good Y, and "consumption" le_i of
leisure given by le_i = [L* - LX_i - LY_i], where LX_i and LY_i
denote the amounts of labor that consumer i supplies to firm FX and
firm FY, respectively, in period T. This utility function modeling
implies that each consumer i directly cares only about its total
consumption of leisure, le_i, not about which firm it works for.
Firm FX produces good X in amount Q_x using labor as its only
input in accordance with the production relation Q_x = f(L_x), where
L_x denotes the total amount of labor used in production by firm FX
in period T. Similarly, firm FY produces good Y in amount Q_y using
labor as its only input in accordance with the production relation
Q_y = g(L_y), where L_y denotes the total amount of labor used in
production by firm FY in period T. Since every unit of labor is
like every other unit, firms FX and FY are indifferent regarding
which consumer's labor they hire.
Let P_x denote the period T dollar price of X, P_y denote the
period T dollar price of Y, and W denote the period T dollar wage
rate paid per hour of labor by either firm FX or firm FY. Then the
dollar profits PROFX and PROFY of firms FX and FY in period T are
given by
PROFX = P_xQ_x - WL_x
PROFY = P_yQ_y - WL_y
The firms are owned by the consumers, and all profits earned by
these firms are returned back to the consumers in the form of
dividend payments. Each of the 100 consumers owns an equal share
(1/100) of firm FX and an equal share (1/100) of firm FY.
Consequently, each consumer i in period T receives a dollar dividend
PROFX/100 from firm FX and a dollar dividend PROFY/100 from firm FY.
PART A: [10 Points Total]
(1) [5 Points] Provide a carefully labeled diagram that depicts
for economy E in period T the flow of goods and services together
with the flow of price, wage, and dividend payments under the
standard Walrasian economy assumptions.
(2) [5 Points] Using this diagram to illustrate your points,
describe in words the most important assumptions underlying the
conception of a Walrasian economy.
PART B: [21 Points Total]
(1) [16 Points] Using both verbal descriptions and corresponding
analytical expressions, provide a careful definition of a "Walrasian
equilibrium" FOR THE ECONOMY E PRESENTED IN QUESTION 3 -- NOT FOR AN
ARBITRARY ECONOMY. Try to make your definition as precise and clear
as possible in relation to economy E.
(2) [5 Points] In what sense does this Walrasian equilibrium
provide a "benchmark of coordination success" for the economy E?
PART C: [14 Points Total]
(1) [7 Points] Using the economy E for illustration, carefully
explain the critique by Robert Clower of the Walrasian conception of
equilibrium for a decentralized market economy.
(2) [7 Points] What are the potential implications of this Clower
critique for (a) the persistence of unemployment; and (b) the role
of government policy makers?