Isoquants and returns to scale
An isoquant joins the labour–capital mixes for one output. Slide along it to see the substitution rate fall, and scale everything up to see returns to scale.
A teaching model — a Cobb-Douglas form is assumed; these are not real generation technology values.
Decreasing returns to scale — output grows slower than inputs: inputs ×2 → output ×1.866
An isoquant joins the labour–capital mixes that give the same output. As labour rises, the capital you can drop while holding output keeps shrinking — diminishing MRTS, which is why the curve bulges toward the origin. Scale every input up together: more than in proportion is increasing returns, equal is constant, less is decreasing.
Base isoquant 0.5× · 1.5× Tangent (slope = MRTS) All inputs ×2
Model assumption: Cobb-Douglas Q = A·L^a·K^b (elasticity of substitution 1). Convexity, diminishing MRTS and returns to scale are in the study guide; the functional form is a learning supplement. Curves never touching the axes is a property of this form only. Returns to scale is about all inputs together, not diminishing marginal product of one.
Not in this calculation
- Perfect substitutes (straight) and complements (L-shaped), and forms in between — only Cobb-Douglas is drawn
- Cost minimisation (tangency with an isocost) and the expansion path
- Input prices
- Real values for generation technology
- Changing one input in the short run — see the product curves tool
Using the example values
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