Company Z has the following data corresponding to the production function. Where (L) is the amount of the labor factor and (K) capital. Q=K0.4 L0.6 a) Calculate the amount of production, applying the production function for each of the respective values of K and L. K Q 10 80 30 160 50 320 70 640 90 1200 a) Graph the amount of production obtained on the Y axis, and with the labor input on the Х аxis b) Draw isoquant lines for each level of production, placing capital on the Y axis and labor on the X axis, to better appreciate the displacement.

Suppose that a firm's production function is given by the following relationship: Q = 2.5√/LK (i.e., Q = 2.5L0.5 K0.5) where is output, L is labor input, and K is capital input. What is the percentage increase in output if labor input is increased by 10%? (Assume that capital input is held constant.) What is the percentage increase in output if capital input is increased by 25%? (Assume that labor input is held constant.) What is the the percentage increase in output if both labor and capital are increased by 10%? 11

A firm's production function is given by Q = 20L0.8 K0.2. At that moment, the firm sets = 1,000 and K = 1,000. Which of the following combinations of L and Klies on the same isoquant? L = 1,063.9; K = 698.7 L= 1,063.9; K = 698.7 L=698.7; K = 1,063.9 L = 1,302.3; K = 936.1 L 936.1; K 1,302.3

The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = c₂LC1C²2 C2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co 5, C₁ = 0.25, and c2₂ 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. = = where co, C₁, and Max s.t. L, C ≥ 0 A ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L ≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when…