I Consider the following two~period OLG model. The economy is innitely lived and each individual lives for two periods. The population size is...
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Please help me solve the following macroeconomics problem below.

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  1. Provide the definition of a perfectly competitive (Walrasian) equilibrium.
  2. Find a set of equilibrium conditions that can be used to determine the steady state allocations of this economy.

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\. I Consider the following two~period OLG model. The economy is infinitely lived and each individual lives for two periods. The population size is constant over time with a measure N > 0 individuals being born each period. Period utility of a young individual in period t, u(c1't,llat), is defined on the amount of the consumption good consumed in youth, cm, and from effort exerted accumulating labour capital, I". Given an investment in labour capital, 31,, exerted in youth, an individual's labour productivity in old age is equal to he,t+1 2 651,3. Assume that uc[c, l) > D, 1110,:(8, I) < 0, u;{c, I} < O with limHg u(c) = 00 and linnno u;(c,l) = I]. Period utility of an old individual in period 13, New), is defined on the amount of consumption enjoyed in old age, 03;, with 1),:(c) > U and USCIIC) < O with limcno 115(6) 2 oo. Individuals discount utility across each successive period by a discount factor 18 E (O, 1]. Young individuals and old individuals each provide a single unit of labour effort inelastically. When young, a unit of labour effort yields one unit of labour services. When old, a unit of labour effort results in hit units of labour services which depends on the level of investment, I", chosen in an individual's youth. In period if, each unit of labour services is sold to firms in a perfectly competitive labour market at the wage rate, wt. Labour income of the young is used to finance consumption in youth or saved to contribute to consumption in old age. Savings from period t are rented to firms in the following period at the competitive price in the market for capital services, n+1. Old individuals finance their consumption out of labour income from selling labour services as well as the gross return from renting capital to firms. Capital does not depreciate and can be consumed after use in production. The representative firm in each period produces the consumption good in the amount y, using capital services, K3, and labour services, Ht, as inputs with y; = Kng'". Output is sold in a perfectly competitive final goods market. Here X, is aggregate capital services and H, is total labour services. Total labour services is the sum of labour services provided by both young and old individuals. The representative firm chooses inputs to maximize profits. Assume that all prices are defined in units of the consumption good, whose price is normalized to unity each period.

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