In the short-run, marginal costs are equal to the change in variable costs as output changes. ( mc = change in variable cost / change in quantity) assume that capital is fixed in the short-run. (a) start with the equation for marginal cost and derive an equation that relates marginal cost of production to the cost and productivity of labor. (b) draw a standard looking short-run marginal cost curve and use the equation you derived to explain its shape.