You are an efficiency expert hired by a manufacturing firm that uses K and E as inputs. The production function for a competitive firm is Q = K1/2 E1/2. The firm can hire labor at a wage of $15 per hour and rent capital at a rate of $60 per unit.
a. Compute the Marginal Rate of Technical Substitution (MRTS) between capital and labor
b. Find and interpret the slope of the Isocost function?
c. Find the level of labor (E) and capital (K) that the firm should use to produce 120 units of output (Q) at the lowest possible cost.
d. Graph the result labeling as many points as you can.