Macroeconomic Theory Problems As Stated On The Attached Sample (Coursework Sample)

Title: MACROECONOMIC THEORIES
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MACROECONOMIC THEORIES
Read pp. 211-213 (8th Edition) or pp. 217-219 (9th Edition) and answer the following questions.
1. Suppose production function is given by
Y=𝐾1/3𝐿2/3
* Derive the per-worker production function. (Show mathematical steps, in detail to receive full credits)
Per-worker production function is derived by dividing both sides of the production function by the labor force, L.
In this function,
Y=K1/3L2/3,
The per-worker production function therefore becomes,
Y/L = K1/3L2/3 / L
When rearranged,
Y/L = (K/L)1/3
Since Ï’ = Y/L and k = K/L
γ = k1/3
γ = 3√k
b. Suppose 40% of output is saved, and 10% of the capital stock depreciates every year. And the economy starts off with 27 units of capital per worker. Given these numbers, calculate the followings in year 1-year 500, and construct a table like table 8-2 in p.213 of your textbook. (p.219 of the ninth edition). Attached the excel file.
- 𝑘 (capital per worker)
- y (output per worker)
- c (consumption)
- i (investment)
- δk (capital depreciation)
- Δk (change in capital)
Summary
40% is saved (s=0.4)
Depreciation per year = 10% ( ᵟ = 0.1)
27 units of Capital-per worker = (k = 27)
Since γ = 3√k
γ = 3√27
27 units of capital per-worker produce 3 units of output per-worker.
Output per worker, y= 3 units
Since 40% is saved and 60% is consumed,
I = 1.2 and c = 1.8
Investment, I = 1.2
Consumption, c= 1.8
10% of the capital stock depreciates,
1 x 27 units = 2.7
( ᵟ k = 2.7)
Capital depreciation = 2.7
Change in capital stock, ∆k = I - ᵟ k
= 1.2-2.7
∆k = -1.5
Change in capital = -1.5
The economy begins its second year with (2.7+(-1.5)
= 1.2 units of capital per worker.
* Consider year 45. Should new capital be added or not? Justify your answer using specific numbers and equation Δk=sf(k)−δk
At year 45, there is 0.25298 unit capital per-worker, the output per worker is 0.63246, the consumption is 0.37947 and the investment is 0.25298 while capital depreciation is 0.0253 and finally the change in capital is -0.2277. These factors remain constant till the 500th year.
The economy has therefore stabilized in such a way that adding or reducing the new capital will of less or no substantial effect on the following years. The change in capital, Δk=sf(k)−δk , is therefore constant.
d. Calculate the steady-state level of capital, and interpret the result. Show mathematical steps in detail to receive full credits. (Refer t...