Labor-Capital Tradeoffs

Business Calculus · Axiom Academy

EXAMPLE Labor-Capital Tradeoffs Understanding input substitution in production In production, companies can often substitute between labor (workers) and capital (machines/equipment) to produce the same output. The Marginal Rate of Technical Substitution (MRTS) measures this tradeoff. How much capital can be replaced by one unit of labor while maintaining the same output Labor is highly productive relative to capital. One worker can replace several machines. Capital is more productive. You need many workers to replace one machine. An isoquant shows all combinations of L and K that produce the same output. The slope at any point equals -MRTS. Move along the isoquant to see how MRTS changes. The tangent line shows the substitution rate. A furniture company has production function . Currently they use L = 100 workers and K = 64 units of capital equipment. MRTS = 0.96 means: to keep output constant, the company can replace 1 unit of capital with approximately 0.96 units of labor. Or equivalently, 1 additional worker can replace about 1.04 units of capital. The optimal combination of labor and capital depends on their prices. The cost-minimizing condition is: where w = wage rate and r = rental rate of capital A company is considering automating part of its production line. Currently: 50 workers at 40,000/year each = 2M labor cost Production: 100,000 units/year The automation equipment costs 800,000 and would allow reducing staff to 20 workers. Capital cost: assume 200,000/year

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