Mid-term Exam(Version A)
Advanced Macroeconomics
Answer Key
(a)Why the accumulation of physical capital cannot account for either growth di¤erence or cross-country income di¤erence?
If returns of capital are a rough guide to its contributions to output,then variations in the accumulation of physical capital do not account for a signi…cant part of either di¤erences.For example,to account for a a factor of10in output per worker,we need a factor of1000in capital per worker.There is no evidence of such di¤erences in capital stocks.Or Required di¤erence in capital imply enormous di¤erence in the rate of return on capital,for example,a factor of 100.
(b)Why in the Ramsey model,the adjustment to shock is more rapid than in the Solow model?
Besides the kind of adjustment happen in the Solow model,that is,the di¤erence of marginal product and break-even investment,the change of saving rate also help the adjustment process.Here the saving rate is greater than s when k is less than k and less than s when k is greater than k .This is because
interest rate is high when k is less than k and it is low when k is greater than k .
(c)Explain why in the Diamond(OLG)Mode,there is possibility of dynamic ine¢ciency.Or how a planner is able to improve e¢ciency in some case.
Answer1
If the marginal product of capital is less than n,or k GR<k ,the planner can take1unit of labor income from each young person and transfer it to the old. This increases the consumption of each old person by1+n units.The planner then asks the next generation of young to do the same thing in the following period.....continuing.It is more e¢cient than saving.Ine¢ciency stems from the intertemporal structure of the economy,or the in…nity of generations.
Answer2
In BGP,if f0(k )<f0(k GR),then,in some period t0,a planner can allocate more resources to consumption and fewer to saving than usual,so that capital per worker the next period is k GR and thereafter also k GR<k .In period t0, f(k )+(k k GR) nk GR>f(k GR) nk GR,so more resource for consumption, In each subsequent period,f(k GR) nk GR>f(k ) nk ,we also have more consumption,which make every generation better o¤.
(d)Why we cannot use technology to explain cross-country income di¤er-ences?
Why poor countries do not have access to the same technology?The lags in the di¤usion of knowledge from rich to poor countries that are needed to account for observed di¤erences in incomes are extremely long–on the order of a century or more.Second,technology is nonrival.If the relevant knowledge is publicly available,poor countries can become rich by having their workers or managers read the appropriate literature.If the relevant knowledge is private,
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poor countries can become rich by inviting foreign…rms to open factories in poor countries.There are numerous examples of poor regions or countries, where foreign investors can establish plants and use their know-how with a high degree of con…dence:that the political environment will be relatively stable. We do not see incomes in those areas jumping to the levels of industrialized countries.
(e)Why human capital may help explain cross-country income di¤erences?
For example,after introducing human capital,output per worker is AG(E)y, where G(E)is human capital,which is a function of education.Then,to account for a a factor of10in output per worker,we only need a factor of about10in human capital per worker.Human capital is not like technolgoy,rich countries ’human capital is not easy to transfer to poor countries.
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