## Math Problem Statement

In a country, output is produced with labor and physical capital. The production function in per-worker terms is y =š^(1/2). The depreciation rate is 2%. The investment rate (Ī³) is determined as follows:

Ī³ = 0.20 if y < 10

Ī³ = 0.40 if y > 10

Draw a diagram showing the steady state(s) of this model. Calculate the values of any steady state levels of k and y. Also, indicate on the diagram and describe briefly in words how the levels of y and k behave outside of the steady state. Comment briefly on the stability of the steady state(s). Draw a Solow growth graph with all the values afterwards.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Economic Growth Models

Solow Growth Model

Differential Equations

Stability Analysis

### Formulas

Production function: y = k^(1/2)

Depreciation function: Ī“k

Investment function: Ī³y

### Theorems

Solow Growth Model

Stability of Equilibrium

### Suitable Grade Level

Undergraduate Economics or Advanced High School Economics

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