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z Medical Questions

Your Question
2nd year university level:

Suppose the output at time t can be written as
Y(t)=[s(t)L(t)]ᵝK(t)(1-β)

where 10<<&#946;, and
Y(t): is output at time t
L(t): is the population (and number of workers) at time t
K(t): is the amount of capital in the economy at time t
a(t): an indicator of the efficiency of labour at time t.
Further assume
(a) &#916;L(t)/L(t)= n > 0 for all t.
(b) &#916;a(t)/a(t)= g > 0 for all t
(c) &#916;K(t)=I(t)-&#948;K(t), where I(t) is investment at time t and &#948; > 0 is
the rate of depreciation.
(d) I(t)=sY(t) (savings equals investment where s is the MPS)
(i) [5 marks] Derive the labour share in income and the capital share in national income
(given factors are paid there marginal product)
(ii) [5 marks] Derive the production function that expresses output per effective worker
(y(t)=Y (t)/[a(t)L(t)]) as a function of capital per effective worker
(k(t)=K(t)/[a(t)L(t)])
(iii) [5 marks] Derive the balanced growth path and the steady-state of this model.
(iv) [5 marks] What are the steady-state levels of capital per head, output per head,
and capital/output ratio? Explain.
(v) [5 marks] Given empirical research determines that &#946; =0.3, &#948; =0.1, g =0.02,
n =0.005 and s =0.2, describe the implied steady-state.
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