Math Problem Statement

Consider a production function given by 𝑄 = 5𝐾^0.3*𝐿^0.7 , where 𝑄 represents output, 𝐾 represents capital, and 𝐿 represents labor. Determine the marginal rate of technical substitution (MRTS) between capital and labor for this production function for 𝐾 = 6 and 𝐿 = 7. Briefly interpret the MRTS value you found

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Partial Derivatives
Production Functions
Marginal Rate of Technical Substitution (MRTS)

Formulas

Production function: Q = 5 * K^0.3 * L^0.7
Marginal Product of Capital: MP_K = ∂Q/∂K
Marginal Product of Labor: MP_L = ∂Q/∂L
MRTS formula: MRTS_KL = MP_L / MP_K

Theorems

MRTS and Marginal Product Theory

Suitable Grade Level

Undergraduate Economics or Business Calculus