課程名稱︰總體經濟學
課程性質︰必修
課程教師︰陳旭昇
開課學院：管理學院
開課系所︰財金系
考試日期（年月日）︰103/4/23
考試時限（分鐘）：150
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Problem 1 (40%) Choose the best answer for the following questions.
1. In the steady state of the Solow growth model
(A) consumption equals deprecation
(B) per capita variables grow at the rate of population growth
(C) aggregate consumption grows at a constant rate
(D) aggregate output is constant
2. In Solow's growth model, the steady-state growth rate of capital can
be increased by
(A) higher population growth
(B) higher deprecation rate
(C) higher saving rate
(D) higher interest rate
3. In Solow's growth model, the Golden Rule of capital accumultaion
maximizes the steady-state level of
(A) output per worker
(B) capital per worker
(C) comsumption per worker
(D) investment per worker
4. In the steady state of Solow's exogenous growth model, an increase in
the growth rate of labor force
(A) increase output per worker and increases capital per worker
(B) increase output per worker and decreases capital per worker
(C) decrease output per worker and increases capital per worker
(D) decrease output per worker and decreases capital per worker
5. The endownment point is the consumption bundle in which
(A) households maximize utility
(B) households are indifferent to interest rate changes
(C) permanent income is maximized
(D) savings are zero
6. For a borrower in a (c_t, c_t+1) graph, the optimal consumption bundle is
(A) to the left of the endownment point
(B) to the right of the endownment point
(C) on the endownment point
(D) dependent on other factors
7. An increase in first-period income results in
(A) an increase in first-period consumption, an increase in second-period
consumption, and an increase in saving.
(B) an increase in first-period consumption, a decrease in second-period
consumption, and an increase in saving.
(C) a decrease in first-period consumption, an increase in second-period
consumption, and an increase in saving.
(D) an increase in first-period consumption, an increase in second-period
consumption, and a decrease in saving.
8. An increase in the real interest rate is an example of a
(A) pure substitution effect
(B) substitution effect and a positive income effect
(C) substitution effect and a negative income effect
(C) substitution effect and in income effect whose sign dependes on whether
the consumer is initailly a borrower or a lender
9. In our two-perios model with exogenous endownment. At the endownment
point, we have the property that
(A) c_t = c_t+1
(B) c_t = y_t - tau_t
(C) y_t - tau_t = y_t+1 - tau_t+1
(D) y_t = y_t+1
10. In the endogenous growth model with human capital presented in my lecture,
spending more time on education
(A) decreases the growth rate and increases output in the short term
(B) increases the growth rate and decreases output in the short term
(C) decreases the growth rate and decreases output in the short term
(D) increases the growth rate and increases output in the short term
Problem 2 (35%) Consider a two-period model where a consumer has preferences
over consumption in the two periods given by:
U(c_t, c_t+1) = log c_t + beta * log c_t+1
The consumer has no initial assets and has income y_t in the first period,
y_t+1 in th second, pays lump-sum taxes tau_t in the first and tau_t+1 in
the second, and can borrow and lend at real interest rate r_t, thus giving
the budget constraints at each period:
c_t + s_t = y_t - tau_t
c_t+1 = y_t+1 - tau_t+1 + ( 1 + r_t ) s_t
The government finances spending through taxes and borrowing:
G_t = tau_t + B_t(G)
G_t+1 + ( 1 + r_t(G) ) B_t(G) = tau_t+1
where the government borrows at a lower rate than households: r_t(G) < r_t
1. Write down the lifetime budget constraint for the consumer
2. Write down the lifetime wealth we_t
3. Solve for the consumer's optimal consumption choices c_t* and c_t+1*
4. Now suppose that the government cuts taxes in the current perios, so tau_t
falls by some amount delt(tau_t) > 0, but government spending is unchanged.
Thus future taxes must rise to pay back the principal and interest on the
deficit this policy creates.
(a) Show that given such tax cut policy, the consumer's lifetime wealth will
change to a new level, ~we_t, where
~we_t = we_t + ( r_t - r_t(G) ) / ( 1 + r_t ) * delta(tau)
(b) How does this affect the consumer's optimal choices? Denote the new
optimal choices as c_t** and c_t+1**, and compare them with c_t** and
c_t+1**
(c) Does the Ricardian equivalence hold?
(d) Does the Ricardian equivalence hold if r_t = r_t(G) ?
Problem 3 (15%) Consider a variation on teh Solow model where each household
has a minimal consumption level. In particular suppose that as usual output
is produced competitively via a Cobb-Douglas production function:
Y_t = K_t ^ a * N_t ^ (1-a),
the population grows at the constant rate n,
N_t+1 = ( 1 + n ) N_t
Capital accumulation is
K_t+1 = ( 1 - delta ) K_t + I_t
Suppose that all households require a constant amount ~c > 0 consumption per
capita, and consume a fraction ( 1 - s ) of income as well. That is,
C_t = ~c * N_t + ( 1 - s ) Y_t
Market equilibrium requires
C_t + I_t = Y_t
Define per capita variables as
y_t = Y_t / N_t, c_t = C_t / N_t, k_t = K_t / N_t
1. Find the key dynamic equation of captial per capita, i.e. k_t+1 - k_t
2. Use graphs to answer the following questions:
(a) How many steady states does the model have?
(b) For various values of inital capital, characterize which steady states
the economy may converges to.
Problem 4 (10%) Consider a two-period model of consumption and savings where
consumers have "habits", meaning that they care about consumption relative to
their own past consumption. Thus preferences are given by:
u(c_t) + beta * u(c_t+1 - c_t)
Suppose the consumers face a constant interest rate and so face the contraints:
c_t + s_t = y_t
c_t+1 = y_t+1 + ( 1 + r_t ) s_t
where y_t and y_t+1 are exogenous endownments at time t and t+1, respectively.
1. Write down the Lagrangian for the consumer's optimization problem, and find
the Euler equation.
2. Provide an interpretation of the Euler equation.