For all questions, if necessary, make appropriate assumptions. 1. A unit price of consumption is normalized to one. Suppose the price of one-period risk-free bor period t and t + 1 is ¾, and the price of two-period risk-free bond in period t and t + 2 is 3/ . (a) Solve for the interest rate between t and t + 1 of this economy. (b) Solve for the price of one-period risk-free bond in period t+1 (that delivers one unit of consum] in period t + 2).
For all questions, if necessary, make appropriate assumptions. 1. A unit price of consumption is normalized to one. Suppose the price of one-period risk-free bor period t and t + 1 is ¾, and the price of two-period risk-free bond in period t and t + 2 is 3/ . (a) Solve for the interest rate between t and t + 1 of this economy. (b) Solve for the price of one-period risk-free bond in period t+1 (that delivers one unit of consum] in period t + 2).
Chapter1: Making Economics Decisions
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![For all questions, if necessary, make appropriate assumptions.
1. A unit price of consumption is normalized to one. Suppose the price of one-period risk-free bond in
period t and t + 1 is, and the price of two-period risk-free bond in period t and t + 2 is.
(a) Solve for the interest rate between t and t + 1 of this economy.
(b) Solve for the price of one-period risk-free bond in period t+1 (that delivers one unit of consumption
in period t + 2).
2. Consider an economy consists of two types of agents, Capitalists and Workers. Capitalists save in
risk-free asset and receive rental rates rt. Workers have no access to capital accumulation but endow
with labor lt € [0, 1] and earn wt per hour. Firms hire workers and borrow risk-free assets to purchase
capital for production. Both factor prices rt and we are competitively determined in factor markets so
that FK (kt, lt) = rt and FL (kt, lt) = wt. Utility maximization problems for each type are given by
1
Capitalist:
Worker:
max
{Ct,kt+1}=0
∞
Σβα
max
{Ct}t=0 t=0
t=0
1-o
Capitalist:
Worker:
s.t. at+1+Ct = (1 + rt) at
s.t. Ct = Welt
with o = 1.
(a) Solve for the optimal consumption and savings for Capitalists. What is the level of capital in
steady-state?
(b) Suppose the government imposes capital taxes Tt and use the revenue to make a lump-sum transfer
Tt. Given Tt, the objective functions are identical, but the budget constraint of each type changes
such that
at+1+Ct = (1 - Tt) (1 + rt) at
Ct + Tt = Wt.
Compute the steady-state equilibrium under capital taxes. Compare the results with your answer
in part (a). How does capital tax affect the level of capital in steady-state?
(c) Suppose the government values the welfare of Workers only. Define the Ramsey taxation problem
and find the optimal capital taxes in the limit.
(d) Suppose o> 1 instead. Does your answer change? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff90bd7ae-d615-47ec-8bd0-e27869109b1e%2Fd679a0ed-1306-47b0-ae39-a827b19a22d5%2Fnac0zao_processed.png&w=3840&q=75)
Transcribed Image Text:For all questions, if necessary, make appropriate assumptions.
1. A unit price of consumption is normalized to one. Suppose the price of one-period risk-free bond in
period t and t + 1 is, and the price of two-period risk-free bond in period t and t + 2 is.
(a) Solve for the interest rate between t and t + 1 of this economy.
(b) Solve for the price of one-period risk-free bond in period t+1 (that delivers one unit of consumption
in period t + 2).
2. Consider an economy consists of two types of agents, Capitalists and Workers. Capitalists save in
risk-free asset and receive rental rates rt. Workers have no access to capital accumulation but endow
with labor lt € [0, 1] and earn wt per hour. Firms hire workers and borrow risk-free assets to purchase
capital for production. Both factor prices rt and we are competitively determined in factor markets so
that FK (kt, lt) = rt and FL (kt, lt) = wt. Utility maximization problems for each type are given by
1
Capitalist:
Worker:
max
{Ct,kt+1}=0
∞
Σβα
max
{Ct}t=0 t=0
t=0
1-o
Capitalist:
Worker:
s.t. at+1+Ct = (1 + rt) at
s.t. Ct = Welt
with o = 1.
(a) Solve for the optimal consumption and savings for Capitalists. What is the level of capital in
steady-state?
(b) Suppose the government imposes capital taxes Tt and use the revenue to make a lump-sum transfer
Tt. Given Tt, the objective functions are identical, but the budget constraint of each type changes
such that
at+1+Ct = (1 - Tt) (1 + rt) at
Ct + Tt = Wt.
Compute the steady-state equilibrium under capital taxes. Compare the results with your answer
in part (a). How does capital tax affect the level of capital in steady-state?
(c) Suppose the government values the welfare of Workers only. Define the Ramsey taxation problem
and find the optimal capital taxes in the limit.
(d) Suppose o> 1 instead. Does your answer change? Explain.
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