Math Problem Statement
- In a country the production function is y = 𝑘!/#. The fraction of output invested, γ, is 0.25. The
depreciation rate δ, is 0.05.
a. What are the steady-state levels of capital per worker, k, and output per worker, y?
b. In year 1, the level of capital per worker is 16. In a table such as the following one, show how
capital and output change over time (the beginning is filled in as a demonstration). Continue this
table up to year 8.
Year Capital
K
Output
Y=𝑘!/#
Investment
γ y
Depreciation
δk
Change in
Capital stock
γ y- δk
1 16 4 1 0.8 0.2
2 16.2
3
c. Calculate the growth rate of output between years 1 and 2.
d. Calculate the growth rate of output between years 7 and 8.
e. Comparing your answers from parts c and d, what can you conclude about the speed of output
growth as a country approaches its steady state?
Solution
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Math Problem Analysis
Mathematical Concepts
Production Functions
Solow Growth Model
Capital Accumulation
Steady-State Economics
Formulas
Production Function: y = k^(1/2)
Capital Accumulation: Δk = γy - δk
Steady-State Condition: γy = δk
Theorems
Solow Growth Model
Steady-State Theorem in Economic Growth
Suitable Grade Level
Undergraduate Economics or Graduate Level
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