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).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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