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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.

View the full answer 1 ) Y = A. KE. LZ
4 = f ( K L ) -&gt; 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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