Average and marginal productivities can be derived directly from the firm's production function. For each of the following cases, discuss how the values of these measures change as labor input expands. Explain why the cases differs.
Case 1. Apples harvested (q) depend on hours of labor employed (L) as $q=10+50 L$.

Case 2. Books dusted $(q)$ depend on minutes spent dusting $(L)$ as $q=-10+5 L$.

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 \(\boxed{MP2 = 5}\)