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Hi I am trying to answer the following questions:


#1) Consider the following production

functions:

1. Y = AK1/2L1/2

2. Y =AK+BL

3. Y = (AK)2/3L2/3

4. Y = AH1/3


For each of the production functions listed above: 

  • Determine whether the function exhibits CRS, diminishing returns to physical capital (or human capital, when applicable), and diminishing returns to labor 
  • Check whether it satisfies the Inada conditions.
  • Compute the per capita production function. 


and

#2) Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKαL1−α

1. Use the production function to compute output per capita, y = Y /L, as a function of capital per person, k = K/L.


2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps.

Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.2, δ = 0.1 and n = 0.01. You do not know the value of A.


3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k.


4. In the steady-state, the growth rate of capital is zero. Using the parameters assumed above, find the steady-state level of the capital stock, k∗.


5.Imagine that this country is in its steady state so its capital stock is k∗. Imagine that the country receives a gift of one unit of capital from the world bank (so, suddenly, the capital stock is k∗+1). Can you say what is going to happen to the growth rate immediately after the donation? Why? What will the capital stock be in the long run? Explain. 

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1 ) Y = A. KE. LZ
4 = f ( K L ) -> a. y = f ( ak, aL )
a . 4 = A . ( a k( ) 2 . ( al ) 2
ay = A. Ki . LE. X
( constant ) CRS
1 ] Y = f lak, al ) - ay = A. a.k + B. al
9 Y = 9 ( AK + BL )
an )...

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