The following graph shows the isoquant representing the combinations of capital and labor needed to produce 100 left-handed can openers. Assume that diminishing marginal returns characterize the production function. (Hint: Select a point on the graph to see its coordinates.) ? 500 450 400 350 300 LABOR (Number of workers) 250 * 4 200 150 XB 100 D 50 0 0 3 6 24 27 30 9 12 15 18 21 CAPITAL (Machines) Using the information provided on the graph, complete the following table with the changes in capital and labor moving from point D to C and B to A, respectively. Capital Change (Machines) Labor Change (Workers) Moving from Point... D to C Decreases by Increases by B to A Decreases by Increases by Notice that moving from point D to point A the marginal product of labor (MPL) and the marginal product of capital (MPK). This means that, as a firm moves along an isoquant in this way, it will become to replace machines with workers and keep output at the same level. This trade-off between labor and capital is called the , and it is represented by the slope of an isoquant. Now that you have found what the slope of an isoquant at different points means intuitively, it is time to derive its mathematical formula. Recall that output remains constant for each combination of labor and capital along an isoquant. When a firm moves down along an isoquant, you know that capital increases and labor decreases. In general, an increase in capital should output, while a decrease in labor should output. Since output remains constant at all points along an isoquant, the following must be true (in absolute value): Change in Output from Increasing Capital = Change in Output from Decreasing Labor The change in output resulting from an increase in capital and a decrease in labor respectively is as follows: Change in Output from Changing the Amount of Capital = Change in Output from Changing the Amount of Labor Plugging this into your original equation comparing the change in output from increasing capital to the change in output from decreasing labor results AL in the following (in absolute value): Ak = =