MC_SR,10, MC_SR,20, and MC_SR,30 are derived from ATC_SR,10, ATC_SR,20, and ATC_SR,30, respectively. The long-run marginal cost curve must intersect MC_SR,10, MC_SR,20, and MC_SR,30 at A, Y, and B, the points at which labor is cost-minimizing for Q = 10, Q = 20, and Q = 30 given , , and . Therefore, A, Y, and B are the long-run marginal costs for Q = 10, Q = 20, and Q = 30, respectively, and the long-run marginal cost curve MC_LR connects A, Y, and B.