Building a Cost Table from a Production Function

A production function tells you how many workers it takes to get each level of output. A cost table just prices that out. Pick a wage, say 100 dollars per worker. Variable cost at any output is just workers hired times 100. Add fixed cost, the money spent whether you produce zero units or a million, and you get total cost at each output level. Two firms can hire identical workers at an identical wage and still end up with different cost curves, because what matters is how productive each worker is. A firm whose workers have higher marginal product reaches the same output with fewer hires, so its costs rise more slowly.

Marginal cost comes from the same table read differently. Instead of dividing total cost by total output, you look at the extra cost of the next worker and divide by the extra output that worker adds, the marginal product. Early on, workers are highly productive, each one adds a lot of output for the same 100 dollars, so marginal cost is low. As diminishing returns set in, each added worker contributes less, so that same 100 dollars buys fewer extra units and marginal cost climbs. This is the core link in the unit: a production function with diminishing marginal product mechanically produces a cost curve with rising marginal cost, no extra assumptions needed.

This cost table is the raw material for everything after it. Average variable cost, average total cost, and the marginal cost curve all get read straight off these numbers, and the shape of marginal cost here is exactly what later drives the MR equals MC decision.