Step 1 :Calculate the Average Product (AP) and Marginal Product (MP) for each case:
Step 2 :Case 1: \(AP = \frac{q}{L} = \frac{50L + 10}{L}\) and \(MP = \frac{dq}{dL} = 50\)
Step 3 :Case 2: \(AP = \frac{q}{L} = \frac{5L - 10}{L}\) and \(MP = \frac{dq}{dL} = 5\)
Step 4 :Analyze how the average and marginal productivities change as labor input (L) expands:
Step 5 :Case 1: The average product (AP1) increases as L increases, and the marginal product (MP1) remains constant at 50.
Step 6 :Case 2: The average product (AP2) increases as L increases, and the marginal product (MP2) remains constant at 5.
Step 7 :\(\boxed{\text{Final Answer:}}\)
Step 8 :\(\boxed{\text{Case 1:}}\) \(\boxed{AP1 = \frac{50L + 10}{L}}\) and \(\boxed{MP1 = 50}\)
Step 9 :\(\boxed{\text{Case 2:}}\) \(\boxed{AP2 = \frac{5L - 10}{L}}\) and \(\boxed{MP2 = 5}\)