Solow model

Question 1

The Solow model asks:

Answer 1

How does an economy’s capital stock evolve over time?
Think of it this way:

An economy has machines, buildings, equipment (capital)
Each year, some capital wears out (depreciation)
Each year, people save part of their income, which becomes new capital (investment)
We want to know: where does this process eventually lead?

Question 2

Understanding the Per-Worker Terms
Why “per worker”?

Answer 2

Question 3

The Production Function

Answer 3

Question 4

What is alpha in the production function?

Answer 4

Question 5

what are teh three ways to understand alpha?

Answer 5

Three Ways to Understand α
1. α = How much capital contributes to production
Think of α as measuring how important capital is in producing output.

α = 0.3 means capital contributes 30% to production
α = 0.5 means capital and labor contribute equally
α = 0.7 means capital is very important (70%)

Since the **exponents must sum to 1 **in a Cobb-Douglas function (α + (1-α) = 1):

α = capital’s share
(1-α) = labor’s share

2. α = Capital’s share of income (in perfect competition)
   In a competitive economy, α tells us **what fraction of total income goes to capital owners **(profits, rents, interest) versus workers (wages).
   Example: If α = 1/3:

Capital owners receive 1/3 of total output as profits
Workers receive 2/3 of total output as wages

Empirically: In most developed economies, α ≈ 0.3 to 0.4

About 30-40% of income goes to capital
About 60-70% goes to labor in producing output.

α = 0.3 means capital contributes 30% to production
α = 0.5 means capital and labor contribute equally
α = 0.7 means capital is very important (70%)

Since the exponents must sum to 1 in a Cobb-Douglas function (α + (1-α) = 1):

α = capital’s share
(1-α) = labor’s share

Question 6

Important Properties of α

Answer 6

**α must be between 0 and 1
**0<α<10 < \alpha < 10<α<1
Why?

Diminishing returns to capital:

If α = 1, doubling capital doubles output (constant returns)
If α < 1, doubling capital less than doubles output (diminishing returns) ✓ realistic

Both factors matter:

If α = 0, only labor matters (no role for capital)
If α = 1, only capital matters (no role for labor)
We need 0 < α < 1 so both capital AND labor are productive

Question 7

difference between the Capital Accumulation Equation and the slow model

Answer 7