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foundations of international macroeconomics phần 2

các khóa học cũng như các khóa học sau đại học về kinh tế vĩ mô và tài chính quốc tế. Mỗi chương kết hợp một mảng rộng lớn và bằng chứng thực nghiệm chiết trung của. Đối với các sinh viên bắt đầu, những ví dụ cung cấp động cơ thúc đẩy và hỗ trợ trong việc tìm hiểu giá trị thực tế của các mô hình kinh tế phát triển. | 65 2.1 A Small Economy with Many Periods Why is eq. 13 the condition we seek Think about how eq. 4 behaves as T gets very large. If limr-i-ooU r T Bf r 1 0 the present value of what the economy is consuming and investing exceeds the present value of its output by an amount that nexer converges to zero. The economy is continually borrowing to meet the interest pax ments on Its foreign debt rather than transferring real resources to its creditors by reducing c 1 below Y G. As a result its debt grows at the rate of interest at least which is why limr- -oo l r T Bt T i is strictly negative. But foreigners will never allow such a Ponzi scheme at their expense that would amount to providing another economy with free resources and they would prefer to consume those resources themselves.3 For this reason the requirement limr oofl r rBt r i 0 is called the no-Ponzi-game condition. In the opposite case ỉimr ocỢ 4- r T B T 1 0 a strict inequality the present value of the resources the home economy uses never converges up to the present value of its output. In that case domestic residents are making an unrequited gift to foreigners. Plainly they could raise their lifetime utility by consuming a little more. Only when lim r TBt r ỉ Ois the economy asymptotically using up exactly the resources its budget constraint allows no more and no less. Thus for the present problem conditions 13 2 5 and 6 are necessary and sufficient for optimality. Implicitly we are still assuming nonbinding nonnegativity constraints on c and K. The nonnegativity constraints imply that a country s foreign debt must be bounded from above by the market value of a claim to its entire future net output that is by f I r _ _ IG Gs Is . 4 Before going on we mention an existence problem analogous to the one caused by positing as in eq. 11 that utility accrues over infinitely many time periods. Because of the lack of a definite end to time the budget constraint 14 may not be well defined. For example one can .