(Solved): 4. Deriving the slope of an isoquant The following graph shows the isoquant representing the combin ...

4. Deriving the slope of an isoquant The following graph shows the isoquant representing the combinations of capital and labor needed to produce 20 left-handed can openers. Assume that diminishing marginal returns characterize the production function. (Hint: Click a point on the oraph to see its coordinates.) Notice that moving froen point I. to point I the marginal physical product of lator (MPL) and the marginal physical product of cagital (MPPK). This means that, as a firm moves along an isequant in this way, it will become to replace machines with woikers and keep output at the same level. TNis trade off between labor and capital is called the it is regresented by the slope of an isoquant. Now that you havn found what the slope of an isoquant at diflertent points means intuitholy, it is time to derive its mathematical formuda. Recall that butpit renains constant for each combination of labor and capat along an isoquant. When a firm mowos down along an lsoevant, you luee that. cagital increaces and labor decreases. In peneral, a decrease in labor should betput, while an increase in capital thould output. Since outpet remains constant at all points along an koguant, the following must be true fin absolute valuela Change in Output from Increaning Capetal = Change in Output from Decrearing Iabor The charse in outout resuiteng fram an increase in canifal and a devorease in tabov respectively is as followis! Changet in Dutput from Bhanging the Amount of Capital - Charge in Output frem Changing the Amount of I abor' Phopging this inte your criginal equation comparing the change in output from increasing cacital to the change in output from decreaving tabor reeilts in the folluing (in aboolute value): \( \frac{A R}{d K}= \)