## 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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