Consider the production functions of three different Firms utilizing inputs labor (L) and capital (K) in producing goods X, Y, and Z given below. The three firms face the same fixed price for labor and capital at 5 per unit and 10 per unit, respectively. X = KL2 – L3; Y = 10K1.5L0.5; Z = K0.5L0.5 a. Show and discuss which Firm(s) exhibit(s) diminishing marginal productivity of capital b. Solve for the returns to scale of each Firm and interpret your results c. Solve for Firm Y’s MRTSLK and interpret your computed value. Comment on what happens to the MRTSLK if Firm Y decides to hire more labor
Consider the production functions of three different Firms utilizing inputs labor (L) and capital (K) in producing goods X, Y, and Z given below. The three firms face the same fixed price for labor and capital at 5 per unit and 10 per unit, respectively.
X = KL2 – L3; Y = 10K1.5L0.5; Z = K0.5L0.5
a. Show and discuss which Firm(s) exhibit(s) diminishing marginal productivity of capital
b. Solve for the returns to scale of each Firm and interpret your results
c. Solve for Firm Y’s MRTSLK and interpret your computed value. Comment on what happens to the MRTSLK if Firm Y decides to hire more labor
d. Mathematically show at what stage of production Firm X will experience the law of diminishing marginal productivity/ returns if it chooses to employ 30 units of capital. Graphically illustrate your results
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