This study material provides advanced macroeconomics content including solved assignments, essays, and dissertations. It covers topics such as optimization issues faced by representative agents, population growth equations, Solow Model of Development, and the dynamics of capital stock per capita.
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Advanced Macroeconomics
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3. Increased need for rehabilitation and restoration services is accompanied by cost increases in all global disasters. Our model presupposes normal post-disaster rate inflationsassumptions, although demand-driven inflation becomes highly non-linear, andcost acceleration could make catastrophe much cheaper even under pessimistic conditions and dramatically improve recovery time, all of which will have a larger effect on financial stocks. Question 2 The optimization issue faced by representative-agent: Here, λt is Langrangian multipliers linked with resource’s constraint. There first orders condition is ct : 1 ct = λt
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Question 3 The number of people is rising increasingly g. Thus the,current (N) population and potential (N') population are related by means ofpopulation growth equation, hereN'= N(1+g). There is no change inpopulation growth equation. When the population now is 100 andpopulation growth- rate is 2 percent, the population forfuture is 102. Both customers save their wages, "s" and spend the majority in the market, a steady proportion.consumption formula C = (1+s)Y is thus intertwined betweenconsumption (expressed by C) and production (expressed by Y). When a consumer receives 100 units of outputsas profits, andsavings rates of 40 percent,consumer consumes sixty units as well assaves forty. All enterprises ineconomy generate production that usesame production technologies as supplies in capital fundsas well as labour. There are also the output scale (expressed by Y). Here,production function expression Y = aF islevel of capital (expressed by K), andwork level (expressed by L). Solow Model of Development suggests the output function is continuously restored (CRS). In this respect, when we double that of our supplies of capital fundand double that of our labour, we double that of our production. The statistical study ofSolow model thus
emphasizes on production per employee and resources per employee rather than on combined production and capital stocks. Existing stocks of capital (expressed by K), potential stocks of capital (expressed by K,') including capital depreciation levels (expressed by d) are related to equity accruals K'=K(1-d) + I. In thisanalysis, we presume the following type of output function: Y = aKbL1-b whereby 0 < b < 1. The manufacturing pattern is defined as Cobb-Douglas Productions,neoclassical production function that is used more extensively. In accordance with the presumption that corporations are competitive, namely the pricing companies, the b-coffector isshare stock. Thus the, worker performance is provided infollowing equation: y = akb, whereby y = Y/L (workersoutput and k = K/L) (capital stock per worker) (capital stock per worker) We have the below under the presumption ofcompetitive balance: Identity of income-expenditure asstate of balance: Y = C + I Budget restraint of the consumer: Y = C + S So at balance: I = S = sY. So at balance. The expression of capital accumulation has become: The equation for capital accumulation throughout the time of the workersis given as follows: (1 + g)k' = (1 – d)k + sy = (1 – d)k + saf(k) = (1 – d)k + sakb The definition of solutions used is a lasting one. The constant condition is a state in whichcapital level per employee does not alter. Take the following diagram:
In the lengthy period, there's also no development. If nations havesame g (population has increased), s (save rate) as well as d (capital depletion rate), so these countries havesame stable level so that they can converge. A developing nation is rising faster in this route of convergence. Country with strong saving rates also have constant states and would not convergence, that is, zero absolute convergence is expected bySolow Model. Innation withlower/reducedinitial capital stock, expansion is not necessarily greater when savings rates are distinct. Question 4 Under this model, Economy has following characteristics: For all timesyoung (age 1) and the old two generations are alive (age 2). (age 2). Nt = N0 divide the scale of the latest generation in time t.Families only function in first lifespan and gain money Y1,t. IncomesInsecond life-time (Y2,t+1 = 0), they obtain no money. They eat portion
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from their first cycle earnings and savebalance until they are old to fund their consumptions. The resources ofyoung atend of time t are the origins of the resources used throughoutperiod t+1, Kt+1=Nta1,t for overall output while a1,t areassets per young householdsafter consumption in cycle 1. (We conclude that depreciation also isn't available for convenience).Olderin period t holds the whole share and (as they have zero inheritance motive) absorbs all, thus, the olderin period t becomes Nt‐1a1,t‐1 = Kt. The olderwould be dissolved by the older(The old people get interest oncapital and thus spending would be Kt including interest income, however saving wouldnotimpacttherKtportionsinceitisanintegratedcomponentofincomesand consumptions). Capital and labour economies remain perfectly competitive as well as the aggregate new technologies is CRS, Y = F(K, L) (note that F(K, L) = F(K, L). FLL + FKK). Let young populations Nt normalise all, write normalised variables in lowered case. Thus the overall output feature per young person is translated into: f(kt) ≡ F(Kt ,Nt)/Nt = F(Kt/Nt , 1) The presumption of perfectly competitive means that wages as well as net interestsrates contribute respectively tomargins of labour and capital: Wt = f(kt) − kt f 0 (kt), rt = f0 (kt) We have to make clear decisions regardingutility function as well as the overall output functionsto make more progress. Assuming the utility to be CRRA, u(•) = • 1−р/(1 − − ̈ ) and assuming the net output of Cobb-Douglas F[K, L] = CL 1−р − for the production feature f[ k] Throughout this case it is possible to solve the following:
The modell dynamics ofcapital stock per capitalin time t + 1 could be evaluated by a single statistic referring to time frame t A diagram ofequation issolid locus (5). (5). (5). We display the 45-° line as the collection of "state" objects demonstrates where kt+1 = kt as well astherefore any 45° line interaction withkt+1(kt) function showsmodel's steady-state. This is the experimentsmentioned in the diagram. In cycle t = 0 we launch the economy mostly withper capita of k0 that indicates from (5) some capital k1 that time t. + 1 = 1. Then think of period 1 as t and period 2 as t + 1. In order to evaluatecorrect capital amount indicated bymodel in time t + 2, we must find45 degree line position, equal to k1, therefore vertically move up there just to seek kt +1 = k2. The consequence is thatdegree of capital corresponds to the norm ofstate as the same series of turning points are replicated.