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Question 1 Production is given by: ? 1−? ?≡?(?,?)=?? ? where ??+1 = (1 + ?)??...

Question 1

Production is given by:

? 1−? ?≡?(?,?)=?? ?

where ??+1 = (1 + ?)?? and ??(0,1)

  1. Show that F exhibits a constant return to scale technology.

  2. Express output as a function of the capital labor ratio ?? = ?? ∕ ??.

  3. Find the dynamical system (describing the evolution of ?? over time) under the assumption

    that the saving rate is ? ?(0,1) and the depreciation rate is ? ∈ (0,1].

  4. What is the growth rate of ??, ???≡(??+1 − ??) ∕ ???

  5. Find the steady state level of the stock of capital per worker k, income per worker y and

    consumption per capita c.

  6. What is the Golden Rule value of k? (k in steady state s.th. the consumption in steady state is

    maximized?)

  7. What saving rate is needed to yield the Golden Rule?

  8. Find the dynamical system describing the evolution of ?? under the assumption of full

    depreciation ? =1.

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