Problem 2: Two-period model with investmentConsider a two-period economy facing the following budget constraints:C1 + k +b< y,C2 < y2 + (1+r)b,where y, is an exogenous endowment and second-period output42 = Ak"with 0 < a < 1 and productivity A. Note that k is both first period investment andsecond period capital stock (implicitly assuming full depreciation, & = 1). Also note thatinitial bo = 0, and hence b is both first-period current account and second-period netforeign assets.1. Explain how this special environment maps into the general framework of NationalIncome Accounts, and in particular why:caį = Y1 – C1 – k = band= rb + y2 – C2 = -b.ca2Note that ca, + caz = 0 applies in this model as well.2. Explain how to derive the intertemporal budget constraint:C2AkaC1 += Y1 - k+1+r1+r*3. Given this budget constraint, characterize the optimal capital investment k of thecountry and interpret your results (how does optimal k depend on r and A, and why).4. Explain why it is possible to determine optimal investment without characterizingthe optimal consumption-savings decision. In other words, why investment andsavings decisions separate and when would they not?5. Explain why we expect a country with a high A relative to yi to run a currentaccount deficit? What may be real-world examples of such countries?

When the needs and wants of human beings are unlimited and the budget of one person is limited, it…

Consider a two-period economy facing the following budget constraints: Ci +k +b< yı, C2 S2 + (1+r)b, where y is an exogenous endowment and second-period output 2 = Ak" with 0 < a < 1 and productivity A. Note that k is both first period investment and second period capital stock (implicitly assuming full depreciation, o = 1). Also note that initial bo = 0, and hence b is both first-period current account and second-period net foreign assets. 1. Explain how this special environment maps into the general framework of National Income Accounts, and in particular why: ca = y1 – C1 – k = b and caz = rb+ y2 – c2 = -b. Note that ca + ca2 = 0 applies in this model as well. 2. Explain how to derive the intertemporal budget constraint: Ak Y1-k+ C2 Ci + 1+r 1+r 3. Given this budget constraint, characterize the optimal capital investment k of the country and interpret your results (how does optimal k depend on r and A, and why).

Consider a two-period economy facing the following budget constraints: Ci +k +b< yı, C2 S2 + (1+r)b, where y is an exogenous endowment and second-period output 2 = Ak" with 0 < a < 1 and productivity A. Note that k is both first period investment and second period capital stock (implicitly assuming full depreciation, o = 1). Also note that initial bo = 0, and hence b is both first-period current account and second-period net foreign assets. 1. Explain how this special environment maps into the general framework of National Income Accounts, and in particular why: ca = y1 – C1 – k = b and caz = rb+ y2 – c2 = -b. Note that ca + ca2 = 0 applies in this model as well. 2. Explain how to derive the intertemporal budget constraint: Ak Y1-k+ C2 Ci + 1+r 1+r 3. Given this budget constraint, characterize the optimal capital investment k of the country and interpret your results (how does optimal k depend on r and A, and why).

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

Problem 2: Two-period model with investment
Consider a two-period economy facing the following budget constraints:
C1 + k +b< y,
C2 < y2 + (1+r)b,
where y, is an exogenous endowment and second-period output
42 = Ak"
with 0 < a < 1 and productivity A. Note that k is both first period investment and
second period capital stock (implicitly assuming full depreciation, & = 1). Also note that
initial bo = 0, and hence b is both first-period current account and second-period net
foreign assets.
1. Explain how this special environment maps into the general framework of National
Income Accounts, and in particular why:
caį = Y1 – C1 – k = b
and
= rb + y2 – C2 = -b.
ca2
Note that ca, + caz = 0 applies in this model as well.
2. Explain how to derive the intertemporal budget constraint:
C2
Aka
C1 +
= Y1 - k+
1+r
1+r*
3. Given this budget constraint, characterize the optimal capital investment k of the
country and interpret your results (how does optimal k depend on r and A, and why).
4. Explain why it is possible to determine optimal investment without characterizing
the optimal consumption-savings decision. In other words, why investment and
savings decisions separate and when would they not?
5. Explain why we expect a country with a high A relative to yi to run a current
account deficit? What may be real-world examples of such countries?

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