Question 4. A rm's long-run cost curve is C(Q) = 40Q lOQ2 + Q3 and its long-run marginal cost curve is MC(Q) = 40 20Q + 3Q2. 1. Derive the long-run average cost curve AC. Answer: The long-run average cost curve is AC(Q) = 40 10Q + Q. 2. At what positive level of output the two curves AC and MC intersect? Answer: The two curves intersect when AC(Q) = 40 10Q + Q2 = 40 209 + 392 = MC(Q) Hence, 10Q = 2Q2 and Q = 5. 3. Over what range of output does the production function exhibit increasing returns to scale? Answer: AC attains its minimum at Q = 5 and, similarly to the generic form presented in class, it is decreasing when 0 5. Hence, the production function exhibits decreasing return to scale at this range