PLEASE HELP ME... MY ASSIGNMENT IS SO DIFFICULT... BLESS YOU... 2. Consider an infinite horizon model where time is indexed by t = 0, 1, 2,..., ∞. Each period, Lt numberof two-period-lived consumers are born, where Lt = 2Lt-1. Each worker is endowed with one unit oflabor in the first period of life, and zero unites in the second period. In period 0, there are some oldconsumers alive who life for one period and collectively endowed with Ko units of capital. Preferencesfor a consumer born in period t are given byu (c²,c²+1)log c + Blog +1.Young agents supply their labor to firms and old agents rent capital to firms in perfectly competitivemarkets. The representative firms operate via Cobb-Douglas production function Y = √KªL¹-a₂where y> 0 and a € (0, 1). The first-order conditions for a profit maximization areFK (K, L) = rt and FL (K, L) = wt.Since F(,) is homogeneous of degree one, we can rewrite these conditions as=f'(k)f(k) - kf' (k)== w.Capital will depreciate with 8 = 1.(a) Define and solve a life-time utility maximization problem of a young agent born in period t.(b) Does the optimal saving amount s* depend on rt+1? Explain.(c) Solve for the steady state capital-labor ratio of this economy (i.e., kt = kt+1 = kss where kt = K₂).(d) Denote the capital stock that maximizes the consumption amount in steady state as kgold. Is youranswer in part (c) equivalent to kgold?(e) Suppose the government raises runs a "fully-funded" social security program. Young workerscontribute de in period 1, and the funds are invested in capital stock and Rt+1dt amount of socialsecurity check is paid back when old. Solve for the inidividual's maximization problem under thefully-funded social security and compare your answer to part (a).

(a) Define and solve a life-time utility maximization problem of a young agent born in period t. (b) Does the optimal saving amount s* depend on rt+1? Explain. (c) Solve for the steady state capital-labor ratio of this economy (i.e., kt = kt+1 = kss where kt = Kt). (d) Denote the capital stock that maximizes the consumption amount in steady state as kgold. Is your answer in part (c) equivalent to kgold? (e) Suppose the government raises runs a "fully-funded" social security program. Young workers contribute de in period 1, and the funds are invested in capital stock and Rt+1d amount of social security check is paid back when old. Solve for the inidividual's maximization problem under the fully-funded social security and compare your answer to part (a).

(a) Define and solve a life-time utility maximization problem of a young agent born in period t. (b) Does the optimal saving amount s* depend on rt+1? Explain. (c) Solve for the steady state capital-labor ratio of this economy (i.e., kt = kt+1 = kss where kt = Kt). (d) Denote the capital stock that maximizes the consumption amount in steady state as kgold. Is your answer in part (c) equivalent to kgold? (e) Suppose the government raises runs a "fully-funded" social security program. Young workers contribute de in period 1, and the funds are invested in capital stock and Rt+1d amount of social security check is paid back when old. Solve for the inidividual's maximization problem under the fully-funded social security and compare your answer to part (a).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

PLEASE HELP ME... MY ASSIGNMENT IS SO DIFFICULT... BLESS YOU...

2. Consider an infinite horizon model where time is indexed by t = 0, 1, 2,..., ∞. Each period, Lt number
of two-period-lived consumers are born, where Lt = 2Lt-1. Each worker is endowed with one unit of
labor in the first period of life, and zero unites in the second period. In period 0, there are some old
consumers alive who life for one period and collectively endowed with Ko units of capital. Preferences
for a consumer born in period t are given by
u (c²,c²+1)
log c + Blog +1.
Young agents supply their labor to firms and old agents rent capital to firms in perfectly competitive
markets. The representative firms operate via Cobb-Douglas production function Y = √KªL¹-a₂
where y> 0 and a € (0, 1). The first-order conditions for a profit maximization are
FK (K, L) = rt and FL (K, L) = wt.
Since F(,) is homogeneous of degree one, we can rewrite these conditions as
=
f'(k)
f(k) - kf' (k)
=
= w.
Capital will depreciate with 8 = 1.
(a) Define and solve a life-time utility maximization problem of a young agent born in period t.
(b) Does the optimal saving amount s* depend on rt+1? Explain.
(c) Solve for the steady state capital-labor ratio of this economy (i.e., kt = kt+1 = kss where kt = K₂).
(d) Denote the capital stock that maximizes the consumption amount in steady state as kgold. Is your
answer in part (c) equivalent to kgold?
(e) Suppose the government raises runs a "fully-funded" social security program. Young workers
contribute de in period 1, and the funds are invested in capital stock and Rt+1dt amount of social
security check is paid back when old. Solve for the inidividual's maximization problem under the
fully-funded social security and compare your answer to part (a).

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