Principles of Microeconomics / Unit 6 MIC 0541 review, 2 to 3 minutes
From a Production Function to Every Cost Curve
The idea
Every short-run cost curve in this course descends from one production table and two prices, and building the family once shows why the curves have the shapes they do. Start with the production table: output at each number of workers. Take marginal product between the rows; it rises while workers specialize and falls once they crowd the fixed input. Attach the wage: variable cost is workers times the wage, and total cost adds the fixed cost. Now take marginal cost between the rows as the change in variable cost over the change in output, and notice it is the wage divided by marginal product, so it falls where marginal product rises and rises where marginal product falls. Its low point is marginal product's high point. Divide to get the averages. Average fixed cost falls forever, since a constant is spread thinner. Average variable cost falls while marginal cost is below it and rises once marginal cost is above it, so it bottoms where marginal cost crosses it. Average total cost is the two added, and bottoms further right, where marginal cost crosses it too, because the falling fixed average keeps pulling it down a while longer. One table, two prices, seven columns, and every relation among them is arithmetic: marginal below average pulls the average down, and diminishing marginal product is the single fact that makes marginal cost turn up and drag the averages up after it.
In practice
Worked example, the bakery in full. Workers zero to five; loaves zero, twenty, fifty, seventy, eighty, eighty-five. Marginal product twenty, thirty, twenty, ten, five. Wage sixty; fixed cost one hundred. Variable cost zero to three hundred in steps of sixty; total cost one hundred to four hundred. Marginal cost three, two, three, six, twelve, and each is sixty over the marginal product beside it. Average variable cost three, two forty, two fifty-seven, three, three fifty-three, lowest at fifty loaves, where marginal cost passes from two to three. Average fixed cost five, two, one forty-three, one twenty-five, one eighteen, falling every row. Average total cost eight, four forty, four, four twenty-five, four seventy-one, lowest at seventy loaves, where marginal cost passes from three to six. At every row the two smaller averages add to the larger, and the table is consistent from the first loaf to the last.
Where people slip
Three cautions. Marginal cost uses the change in variable cost, so the first loaves cost three dollars each and not eight; charging fixed cost to them is the anchor's own slip. The averages bottom at different outputs, variable first, because only one of them carries a fixed cost to spread. And the whole family is a short-run family: change the oven and every column changes, which is what the long-run curve of video five thirty-four collects.
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