Marginal Cost Integration and Fixed Cost Sensitivity in an Illustrative Farming Model

Abstract

This study examines the reconstruction of total farming costs from an assumed marginal cost function and distinguishes minimum average cost from profit maximization. A deterministic analytical model uses MC(Q) = 5Q + 100 and integrates this expression to obtain TC(Q) = 2.5Q² + 100Q + F, where F is fixed cost. Two fixed-cost scenarios from the source manuscript, IDR 1,000,000 and IDR 7,750,000, are evaluated without treating them as validated farm observations. The corresponding minimum-average-cost outputs are approximately 632.46 and 1,760.68 units. The previously stated output of 20 units would require F = IDR 1,000 under the same monetary scale. A profit-maximizing output of 991.2 units implies a constant selling price of IDR 5,056 per unit. At that price, modeled profit is IDR 1,456,193.60 in the lower-cost scenario and a loss of IDR 5,293,806.40 in the higher-cost scenario. Fixed cost changes average-cost minima and profit levels but not the interior output choice when marginal cost and price are held constant. The results clarify the model's internal relationships; they do not establish an optimal production recommendation for a particular farm. Empirical application requires defined output units, consistent accounting periods, documented cost and price data, and production constraints.