This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) Prepare a table showing Total Output (TP), Average Product (AP) and Marginal Product (MP) of labour. Step 1: Calculate Average Product (AP) using the formula AP = (TP)/(L). Step 2: Calculate Marginal Product (MP) using the formula MP = ( TP)/( L). For L=0, MP is usually considered the MP of the first unit of labor. | Unit of Labour (L) | Total Product (TP) | Average Product (AP) | Marginal Product (MP) | | :------------------ | :----------------- | :------------------- | :-------------------- | | 0 | 0 | - | - | | 1 | 10 | (10)/(1) = 10 | (10-0)/(1-0) = 10 | | 2 | 25 | (25)/(2) = 12.5 | (25-10)/(2-1) = 15 | | 3 | 45 | (45)/(3) = 15 | (45-25)/(3-2) = 20 | | 4 | 60 | (60)/(4) = 15 | (60-45)/(4-3) = 15 | | 5 | 70 | (70)/(5) = 14 | (70-60)/(5-4) = 10 | | 6 | 75 | (75)/(6) = 12.5 | (75-70)/(6-5) = 5 | | 7 | 75 | (75)/(7) ≈ 10.71 | (75-75)/(7-6) = 0 | The completed table is: |c|c|c|c| Unit of Labour (L) & Total Product (TP) & Average Product (AP) & Marginal Product (MP) \\ 0 & 0 & - & - \\ 1 & 10 & 10 & 10 \\ 2 & 25 & 12.5 & 15 \\ 3 & 45 & 15 & 20 \\ 4 & 60 & 15 & 15 \\ 5 & 70 & 14 & 10 \\ 6 & 75 & 12.5 & 5 \\ 7 & 75 & 10.71 & 0 \\ b) Show (a) above in a combined diagram. To show the data in a combined diagram: • Draw a graph with the Units of Labour (L) on the horizontal (x) axis. • Use the vertical (y) axis to represent Output for the Total Product (TP) curve and Product for the Average Product (AP) and Marginal Product (MP) curves. Typically, TP is plotted on the upper part of the graph, and AP/MP are plotted on the lower part, sharing the same x-axis. • Plot the Total Product (TP) curve by connecting the (L, TP) points. This curve will initially increase at an increasing rate, then increase at a decreasing rate, reach a maximum, and then may decline. • Plot the Average Product (AP) curve by connecting the (L, AP) points. This curve will typically rise, reach a maximum, and then fall. • Plot the Marginal Product (MP) curve by connecting the (L, MP) points. This curve will typically rise, reach a maximum, then fall, intersect the AP curve at its maximum point, and can become zero or negative. Key relationships to observe in the diagram: • The MP curve intersects the AP curve at the maximum point of the AP curve (between L=3 and L=4, where AP is 15). • When MP is greater than AP, AP is rising. • When MP is less than AP, AP is falling. • When MP is zero, TP is at its maximum (at L=7, TP is 75).