MGEA02H3 Chap.5 Production and Diminishing Marginal Returns
Production and Diminishing Marginal Returns
Productivity with a fixed plant
In the short run capital is fixed, so output changes only with labour. Marginal product is dQ/dL and average product is Q/L.
The law of diminishing marginal product says that, beyond some point, each additional worker adds less output, and marginal product crosses average product at the peak of the average.
The bridge to costs
Marginal cost equals the wage divided by marginal product, and average variable cost equals the wage divided by average product.
Rising marginal cost is therefore diminishing marginal product seen from the cost side.
Some questions state labour as a function of output, and the course method inverts dL/dq to find marginal product.
What the answer keys reward
The keys differentiate the production function at the stated labour input, compute average product as output over labour, and then convert both into costs with MC = w/MPL and AVC = w/APL.
When the question supplies labour as a function of output, they invert the derivative rather than solving for labour directly.
Statement sets are judged by testing each claim against those inverse relationships, so practise stating them in both directions.
How this topic connects to later chapters
The productivity curves here are the hidden half of the cost curves in chapter 6: marginal cost mirrors marginal product and average variable cost mirrors average product.
Through them, diminishing returns explains why a competitive firm’s supply curve slopes upward in chapter 7. The hiring rule, marginal product times price equals the wage, is the labour-side version of the output rule P = MC.
What this chapter covers
- 01
Total, marginal and average product
- 02
The law of diminishing marginal product
- 03
Marginal product crossing average product
- 04
Marginal cost as wage over marginal product
- 05
Average variable cost as wage over average product
- 06
Labour requirement functions
Worked example · free
Marginal product, average product and their peak
- 2MP = 12L − 0.6L², which peaks where 12 − 1.2L = 0, at L = 10.
- 2AP = 6L − 0.2L², which peaks where 6 − 0.4L = 0, at L = 15.
- 2At L = 15, MP = 180 − 135 = 45 and AP = 90 − 45 = 45.
Key terms
- Marginal Product of Labour
- The marginal product of labour is the extra output from one more worker, dQ/dL.
- Average Product of Labour
- The average product of labour is output per worker, Q/L.
- Diminishing Marginal Product
- Diminishing marginal product is the fall in extra output from each additional worker once a fixed input is shared.
- Short Run
- The short run is the period in which at least one input, usually capital, cannot be changed.
- Law of Variable Proportions
- The law of variable proportions is another name for diminishing marginal product: varying one input against a fixed one eventually lowers its extra output.
Production and Diminishing Marginal Returns FAQ
Why must one input be fixed for diminishing returns?
Diminishing marginal product describes adding more of one input to a fixed amount of another. If every input could grow together, workers would not have to share equipment, so the law is a short-run idea.
How does marginal product determine marginal cost?
Marginal cost is the wage divided by marginal product. When each extra worker adds less output, each extra unit of output needs more labour, so marginal cost rises.
How do I find marginal product from a labour requirement?
Differentiate labour with respect to output to get dL/dq, then take the reciprocal. Marginal product dq/dL is one over the extra labour needed for one more unit.
Why does average variable cost bottom out where average product peaks?
Average variable cost is the wage divided by average product. With a constant wage, the largest average product gives the smallest cost per unit, so the two turning points occur at the same output.
Exam move
Pick a production function, tabulate marginal and average product for several labour levels, and mark where each peaks. Then convert both into marginal cost and average variable cost with a stated wage. Keep one worked case where capital is given as a number and substitute it before differentiating, since that is where symbol errors creep in.
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