Cost, Supply, and Farm Structure: A Pedagogical Note

Starting with an individual firm and its quadratic production function, this paper derives all related functions marginal and average cost, supply, profit, and input-demand. Since derivatives in other functions correspond to parameters of the quadratic, the results generalize. Explicit aggregation from firm to market shows that properly specified aggregate functions depend on firm numbers. To illustrate the results, marginal and average cost function for several dairy farms are drawn to scale, noting that large farms get more output per cow than small farms. Juxtaposing the cost curves with trends in dairy farms by size shows the link between firm-level profit and structural change.