Recall the Cobb-Douglas production function we worked with in class, f (21, 2) = z} z} . What is the marginal rate of technical substitution (MRT S) based on this production func- tion?
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- Explain the properties of production function? Given a production function of this nature AX1a X2b=Y, determine the Marginal Rate of Technical Substitution.Given a production function of this nature; AX1aX2b determine the Marginal Rate of Technical Substitution.If the production function is F(K,L)=A∗K0.4L0.6 then what is the marginal rate of technical substitution
- Suppose a firm is planning to replace a labor intensive production process with an automated robot production line. Calculate the marginal rate of technical substitution (MRTS) using the following information. Labor Intensive Production: 27 workers / 2 machines Automated Robot Production: 70 workers / 14 machines Assume both production process can produce the same level of output.Gıven two inputs X1 and X2 with Prices W1 and W2, and a production function Y=F(X1X2) show that the marginal rate of substitution between the two inputs is equal to the ratio of their prices.Joe owns a small coffee shop. His production function is q = 2K0.5 L where q is the number of cups of coffee produces, K is the number of coffee machines, and L is the number of employees. a) If K=1 and L=2, the marginal rate of technical substitution is _________. b) If, starting from 1 machine and 2 employees, Joe hires one more employee, then he can produce the same quantity of cups of coffee with _________ less machines.
- Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?What is the marginal rate of substitution at point A? Interpret this value.
- The production function is Q = K.6 L.4. The marginal rate of technical substitution is: 2/3 K-1 L. K-1 L-1. 2/3 K L-1. K.4 L-.6.Distinguish between the Marginal Rate of Technical Substitution and Elasticity of Substitution in productionCalculate your marginal rate of substitution as a function of B and C. U(B,C)=B^(1/4)C^(3/4)
