The Cobb-Douglas production function is a common representation of the relationship between inputs and outputs in economics. It is typically written as:

$ Q = A L^\alpha K^\beta $

Where:

• $Q$ is the total output
• $A$ is the total factor productivity
• $L$ is the labor input
• $K$ is the capital input
• $\alpha$ and $\beta$ are the exponents associated with labor and capital, respectively.

Cobb-Douglas Exponents Meaning

The exponents $\alpha$ and $\beta$ in the Cobb-Douglas function have specific economic interpretations:

• Output Elasticity: The exponent of a factor represents the output elasticity with respect to that factor. For example, $\alpha$ measures the percentage change in output (Q) resulting from a 1% change in labor (L), holding capital (K) constant. Similarly, $\beta$ measures the output elasticity of capital. This directly corresponds to Option 1.
• Factor Income Share: Under the assumption of competitive markets where factors are paid their marginal products, the exponents also represent the share of total income paid to each factor. If $\alpha + \beta = 1$ (constant returns to scale), then $\alpha$ is the share of income going to labor, and $\beta$ is the share of income going to capital. This aligns with Option 2.

Since the exponents represent both the output elasticity of the factors and, under standard assumptions, the share of factor income in total income, both interpretations are correct.

Conclusion

Therefore, the exponents of the Cobb-Douglas production function represent both output elasticity and the share of factor income.

The correct option is Both (1) and (2) of the above.