Economics • Economic BasicsHard
Analyze the structural properties of the Cobb Douglas production function represented as Y equals A multiplied by L to the power of alpha multiplied by K to the power of beta. What does the sum of exponents alpha plus beta signify regarding returns to scale?
A. A sum greater than one indicates decreasing returns to scale across all factor inputs
B. A sum equal to one denotes constant returns to scale where proportionate input changes match output changes✓ Correct Answer
C. A sum less than one implies increasing returns to scale due to technological spillovers
D. The sum of exponents determines the marginal rate of technical substitution exclusively
💡 Solution & Explanation
When the sum of output elasticities alpha and beta equals one in a Cobb Douglas production function, doubling all inputs doubles total output, representing constant returns to scale. If the sum exceeds one, increasing returns to scale prevail due to specialization advantages. Factor shares of national income correspond to these exponents under conditions of perfect competition. Solow growth models utilize similar aggregate production frameworks to analyze long term output paths.
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