By how much does n fall, Consider a planning economy with a

By how much does n fall

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Problem

Consider a planning economy with a continuum of workers of measure 1. Production of the good is given by y = zn where n is the abor input and z is labor productivity. The social planner tells the fraction n of all workers that they have to work, and tells the fraction 1 - n that they don't need to work. An agent who works can only work ¯h hours. There is one consumption level associated with each of these (types of) agents, c1 and c0 (c1 is consumption for someone who works, c0 is consumption for someone who doesn't work). Get the instant assignment help. The maximization problem of the social planner is maxn,c1,c0 nu(c1, ¯h) (1 - n)u(c0, 0) subject to the resource constraint nc1 (1 - n)c2 = zn Assume now that the utility function u is MaCurdy with a σ > 1, that is, u(c, h) = c1-σ - 1 1 - σ - ψ h1 1 θ 1 1 θ . Show that an increase in z leads n to fall. By how much does n fall?

Reference no: EM133917933

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