What do the long run marginal cost and the average cost curves look like?
Both the Long Run Marginal Cost (LRMC) and Long Run Average Cost (LRAC) curves are 'U'-shaped. The LRMC curve cuts the LRAC curve from below at the minimum point of the LRAC curve.
For the first unit of output, both LRMC and LRAC are the same. As output increases, LRAC initially falls, and then after a certain point, it rises. As long as the average cost is falling, the marginal cost must be less than the average cost. When the average cost is rising, the marginal cost must be greater than the average cost.
To the left of the minimum point of LRAC, LRAC is falling and LRMC is less than LRAC. To the right of the minimum point, LRAC is rising and LRMC is higher than LRAC.
Explanation
The answer draws directly from the textbook explanation of the shapes of long run cost curves. Both curves are U-shaped due to returns to scale - initially IRS (Increasing Returns to Scale) causes costs to fall, then eventually DRS (Decreasing Returns to Scale) causes costs to rise. The key relationship is that LRMC always cuts LRAC at its minimum point, staying below LRAC when LRAC is falling and above LRAC when LRAC is rising.