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answer me quickly please 5) In an economy with constant population (normalised to one), a representative one-period- lived agent decides on consumption (c) and labor

answer me quickly please

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5) In an economy with constant population (normalised to one), a representative one-period- lived agent decides on consumption (c) and labor supply (1) according to: maximse V = u(c) + v(T - 1) Subject to c = wit s- r where (T - I) is leisure, w denotes wages, s denotes a share of firms' profits and r is a lump sum tax. The terms u(. ) and v(. ) are utility functions associated with consumption and leisure. There is a fixed number of firms (normalised to one) and the decision problem for each of them is given as follows: maximize n = /(n) - wn where n denotes labor demand and f(. ) is a production function. a) Express the agent's optimality condition in terms of c, I, and w. b) Express the firm's optimality condition in terms of n and w. Express the firm's profit in terms of n. c) At the aggregate level, I = n and s = IT. In addition, g = T, where g denotes government expenditures. Given these relationships, together with your previous results, show that the general equilibrium of the economy may be expressed as: u'(c)f'(n) = v'(T -n)

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