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Given a production function of this nature; AX1aX2b determine the
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- Given a constant elasticity of substitution (CES) production function as follows:y = [a1x1ρ + a2x2ρ]1/ρ 1. Find the marginal rate of technical substitution (MRTS)2. Derive the expression for Elasticity of SubstitutionDistinguish between the Marginal Rate of Technical Substitution and Elasticity of Substitution in productionSuppose the two factors are perfect complements and the production function is given by y=min { 13x1,2x2} Where x1=300, X2=50 What will be level of production and draw corresponding iso quant?
- Explain the properties of production function? Given a production function of this nature AX1a X2b=Y, determine the Marginal Rate of Technical Substitution.What is the marginal rate of substitution at point A? Interpret this value.How does the curvature of an isoquant relate to the marginal rate of technical substitution along an isoquant?
- If the production function is F(K,L)=A∗K0.4L0.6 then what is the marginal rate of technical substitutionThe degree of convexity of an isoquant determines the degree of substitutability of factors of production. Do you agree? Explain.Answer the Constrained Optimization: Cobb-Douglas Production Function:3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the 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
- 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.Consider the following production functions, to be used in this week’s assignment:(A) F(L, K) = 20L^2 + 20K^2(B) F(L, K) = [L^1/2 + K^1/2]^2For each of production functions (A) and (B) given above, do the following steps.(i) Calculate the marginal product of labor MPL(L, K) = ∂F(L, K) / ∂L.(ii) Calculate the marginal product of capital MPK(L, K) = ∂F(L, K) / ∂K.(iii) Calculate the absolute value of the technical rate of substitution as the ratio of marginal products andsimplify as far as possible: |TRS(L, K)| = MPL(L, K) / MPK(L, K). PLEASE SHOW ALL WORKAnswer 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?