MP vs MC curve
If the MPL (Marginal Product of Labor) is low , then the firm needs to hire many extra workers to produce 1 additional unit of output so the MC (Marginal cost) is high .
Proof:
Assume that the price of an additional labour is $100 (PL) and he can produce extra 5 units of output (MP). Thus the additional cost of producing extra one unit of output (MC) is $20 (PL/MP).
AP vs AVC curve
If the APL (Average Product of Labor) is low, then the firm needs to hire many workers to produce each unit of output so the AVC is high.
Proof:
Assume that 200 units of output are produced by 40 workers. This means each worker produces 5 units of output (Q/L). If the price of labor is $100 per worker, the average cost of producing one unit of output is $100 / 5 (PL/AP), which equals $20.
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