This question requires you to understand the relationship between total product, average product, and marginal product. Each of the diagrams below shows how total product (TP) changes as the quantity of the variable input (which we call L) changes. These reflect four different production functions.
a. In each case, describe in words how total output depends on the amount of variable input.
b. For each production function, draw a diagram showing the average product (AP) curve. (Recall that AP is given by total output divided by total variable input. The value of AP is also equal to the slope of a straight line from the origin to the TP curve.)
c. On the same diagram, draw the marginal product (MP) curve. (Recall that MP is given by the change in total output divided by the change in the variable input. The value of MP is also equal to the slope of a tangent line to the TP curve.)
d. Is the relationship between AP and MP discussed in the text satisfied by each of the production functions?

TP TP Slope 10 0 Case (i) Case (ii) TP TP 30 Slope 3 10 Case (iii) Case (iv)