04 Unemployment and the Labour Market

Lecture from: 07.10.2025 | Video: Video ETHZ

Administrative Updates

Exam Format Confirmation

• Format: 90-minute written paper exam (closed book).
• Date: Tuesday, 13.01.2026, 14:00-15:30.
• Registration: Mandatory on myStudies. Course enrollment is not exam registration.

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Finishing Lecture 3: Production and Growth

The exploration of the Solow growth model, the foundational framework for understanding long-run economic growth, continues. Productivity has been established as the key determinant of living standards, and productivity itself depends on the factors of production.

The Production Function

The relationship between inputs and output ($Y$) is represented by the production function:

$$Y=A\cdot F(L,K,H,N)$$

Symbol	Meaning
$Y$	Quantity of output
$A$	Available production technology (Technological Knowledge)
$L$	Quantity of labor
$K$	Quantity of physical capital
$H$	Quantity of human capital
$N$	Quantity of natural resources
$F(\cdot )$	Function describing how inputs are combined

A crucial assumption in many growth models is constant returns to scale. This means that if all inputs are doubled, output doubles. For any positive number $x$:

$$xY=A\cdot F(xL,xK,xH,xN)$$

The Power of Per-Worker Analysis

Constant returns to scale allows for analysis in per-worker terms. By setting $x=1/L$, the production function becomes:

$\frac{Y}{L}=A\cdot F\left(1,\frac{K}{L},\frac{H}{L},\frac{N}{L}\right)$

This equation states that output per worker ($Y/L$), which measures productivity, depends on capital per worker ($K/L$), human capital per worker ($H/L$), natural resources per worker ($N/L$), and the state of technology ($A$). This simplifies analysis by focusing on the resources available to the average worker.

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The Solow Growth Model: A Framework for Analysis

The Solow growth model is the cornerstone of modern growth theory. It provides a simple framework for understanding how saving, investment, and technological progress affect economic growth over time.

Core Assumptions

1. Two Factors: The production function is simplified to include only capital ($K$) and labor ($L$), alongside technology ($A$): $Y=A\cdot F(K,L)$.
2. Constant Returns to Scale: Allows for per-worker analysis.
3. Diminishing Marginal Returns: As the stock of capital rises, the extra output produced from an additional unit of capital falls. (The first computer boosts productivity immensely; the tenth adds very little).
4. Closed Economy, No Government: It is assumed $G=0$ and $NX=0$, so the national income identity simplifies to $Y=C+I$.

The Central Equation: Saving Equals Investment

All output is either consumed ($C$) or invested ($I$). Therefore, what is not consumed is saved ($S$). This yields the crucial identity:

$$S=Y-C⟹S=I$$

Saving must equal investment for the economy as a whole. This is the mechanism through which the capital stock is built.

Further assumptions:

• A constant fraction $s$ of income is saved: $S=sY$.
• A constant fraction $\delta$ of the capital stock depreciates (wears out) each year: Depreciation $D=\delta K$.

The Dynamics of Capital Accumulation

The change in the capital stock is the difference between investment and depreciation. Investment adds to the stock; depreciation subtracts from it.

Model Logic:

• Purple Curve (Production): Shows output ($Y$) for any level of capital ($K$). Curved due to diminishing marginal returns.
• Black Curve (Investment): Represents $I=sY$. Since investment is a constant fraction of output, it follows the shape of the production function but lies below it.
• Pink Line (Depreciation): Represents $D=\delta K$. A straight line through the origin as depreciation is proportional to capital stock.

Evolution:

• If Investment > Depreciation ($I>D$): Capital stock grows $\to$ Higher output.
• If Investment < Depreciation ($I<D$): Capital stock shrinks $\to$ Lower output.

The Steady-State Equilibrium

The economy implies convergence to a steady-state equilibrium (point g), where the investment curve intersects the depreciation line.

$$I=D\text{or}sY=\delta K$$

In the steady state, investment is just enough to cover depreciation. The capital stock per worker and output per worker remain constant. In the basic Solow model, there is no long-run per-capita growth.

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The Effect of a Higher Saving Rate

What happens if a country decides to save more (i.e., $s$ increases)?

1. Shift: An increase in the saving rate shifts the investment curve upward ($I_1\to I_2$).
2. Transition: The old steady state g is no longer stable because investment now exceeds depreciation. Capital begins to accumulate.
3. New Equilibrium: The economy moves towards a new, higher steady state at n ($K_2$).
4. Growth Effect: During the transition, the economy grows faster. However, once the new steady state is reached, per-capita growth stops.

Level Effect vs. Growth Effect

A higher saving rate leads to a higher level of capital and income in the long run, but it does not lead to a permanently higher growth rate.

The Golden Rule: Optimal Saving

A higher saving rate increases output but reduces current consumption. The Golden Rule level of capital is the steady state that maximizes consumption.

Consumption is the vertical distance between output ($Y$) and investment ($I$). This distance is maximized where the slope of the production function equals the slope of the depreciation line ($MPK=\delta$).

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The Engine of Long-Run Growth: Technological Progress

The basic Solow model predicts zero long-run growth, contradicting reality. The missing piece is technological progress.

Technological progress ($A$ grows) shifts the entire production function upward.

• This shifts the investment curve up.
• The economy moves to a new, higher steady state.
• With continuous technological improvement, the economy continuously moves to higher steady states, resulting in sustained long-run growth.

The Key Takeaway

In the long run, the rate of economic growth is determined not by the saving rate, but by the rate of technological progress.

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Public Policy and Economic Growth

Since productivity is key, policies should aim to increase the factors of production:

• Saving and Investment: Tax incentives to encourage saving increase the capital stock.
• Foreign Investment: Attracting Foreign Direct Investment (FDI) supplements domestic saving.
• Education: Investment in human capital ($H$) is crucial. It generates positive externalities (new ideas).
• Property Rights: Political stability and the rule of law are prerequisites for investment.
• Free Trade: Trade acts like a technology, transforming exports into imports.
• R&D: Policies like patent laws and research grants encourage the technological progress ($A$) that drives long-run growth.

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Unemployment and the Labour Market

The focus now shifts from long-run output levels to the labor market and unemployment.

The Costs of Unemployment

• Individual Costs: Loss of earnings, skill atrophy (“hysteresis”), health problems, loss of self-esteem.
• Societal Costs: Opportunity cost of lost output, lower tax revenue, higher welfare payments.

Economically, a clear inverse relationship exists between unemployment changes and real wage growth. When unemployment falls, real wages tend to rise.

Categories of Unemployment

1. Natural Rate of Unemployment (Long-run): The “normal” unemployment rate the economy experiences. It persists even in the long run and is not constant (changes with structural shifts).
2. Cyclical Unemployment (Short-run): Year-to-year fluctuations around the natural rate, associated with the business cycle.

How Is Unemployment Measured?

The population is divided into three groups:

1. Employed: Has a job.
2. Unemployed: Jobless, available for work, AND actively looking for work (in the last 4 weeks).
3. Not in the Labour Force: Everyone else (students, retirees, homemakers).

Strict Definition

Someone who wants a job but has given up looking is not counted as unemployed. They are “discouraged workers” and fall out of the labor force.

Key Statistics:

• Labour Force $=\text{Employed}+\text{Unemployed}$
• Unemployment Rate $=\frac{\text{Unemployed}}{\text{Labour Force}}\times 100$
• Participation Rate $=\frac{\text{Labour Force}}{\text{Adult Population}}\times 100$

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Continue here: 05 Saving, Investment, and the Financial System