Along Ivor’s Engines long-run expansion path, the firm can change its level of capital. Along Ivor’s short-run expansion path, capital is fixed at 6, and the expansion path is horizontal at . Ivor’s Engines can change its output quantity only by changing the quantity of labor used. At points X′, Y, and Z′, Ivor’s Engines minimizes cost in the short run by using 5, 9, and 14 laborers to produce 10, 20, and 30 engines at a cost of $120, $180, and $360, respectively. At Q = 20, the cost-minimizing capital and labor combination, Y, is the same in the long run and short run, and production cost is the same ($180). At Q = 10 and Q = 30, production is more expensive in the short run than in the long run.