In the alternative non-linear cost model for the Beautiful Cars firm, which utilizes a quadratic cost function, the resulting marginal cost function is an upward-sloping straight line. This graphical representation signifies that the firm's marginal costs increase at a constant rate as the volume of car production grows. This linear characteristic of the marginal cost is a specific property of the quadratic total cost model.

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As an alternative to a linear model, the production costs for the Beautiful Cars firm can be represented by a non-linear, quadratic cost function. This function is given by the formula $C(Q) = 118,750 + 1,500Q + 190Q^2$. Because this function is quadratic, it possesses properties not found in more general cost functions.

Alternative Non-Linear Cost Function for Beautiful Cars

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To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

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Upward-Sloping Marginal Cost for Beautiful Cars (Non-Linear Model)

The slope of an isoprofit curve is determined by the relationship between price (P) and the firm's marginal cost (MC). Specifically, the curve slopes downward in areas where price is greater than marginal cost (P > MC) and slopes upward where price is less than marginal cost (P < MC). For a firm with a constant marginal cost, such as Beautiful Cars, the isoprofit curve is horizontal when price equals marginal cost (P = MC) and slopes downward when P > MC. [7] In contrast, for firms with non-constant marginal costs, the isoprofit curves can have both upward and downward sloping sections based on the relationship between price and marginal cost at different quantities.

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