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 Substitution
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A: Given: MPK=42K-1/2=2K-1/2MPL=42L-1/2=2L-1/2MRTSLK=MPLMPKMRTSLK=2L-1/22K-1/2MRTSLK=KL Formula for…
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Q: Define and then derive the expression for the marginal rate of technical substitution.
A: Marginal rate of technical substitution (MRTS) measures the rate at which one factor must give up in…
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Q: Calculate the elasticity of substitution for the production function
A: elasticity of substitution refers to the ratio of the two inputs to a production function with…
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A: Given; Production function; f(L,K)=LK Formula to calculate:- MPK=df(L,K)dKMPL=df(L,K)dLMRTS=MPLMPK
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A: The answer is a. The isoquant is a straight line and the MRTS is constant Therefore, if two inputs…
Q: Consider the following production function q = F (L, K) = L²K What is the marginal rate of…
A: Marginal rate of technical substitution (MRTS): - it is the rate that shows the number of one input…
Given a constant elasticity of substitution (CES) production function as follows:
y = [a1x1ρ + a2x2ρ]1/ρ
1. Find the
2. Derive the expression for Elasticity of Substitution
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- Define Cobb-Douglas production. How does the elasticity of substitution (assume sigma = 1) between two inputs affect the shape of a single ISOQUANT? Use a diagram to support your answer.Consider the following equation Q = f(K, L) = K0.7 L0.3 Find (d) Equation representing an isoquant and show that it is convex to the origin (e) Elasticity of substitution (f) Output elasticities of factorsDescribe the concept of the marginal rate of technical substitution
- Suppose that a firm cannot give up one input in exchange for the other and still maintain the same level of output. Calculate the elasticity of substitution in this case and elaborate on your answer.Consider the following production functions F(L,K)=LK^3 F(L,K)=L+3K (a) Discuss if each marginal product is diminishing, constant or increasing (b) Calculate the marginal rate of technical substitution (c) Calculate if the function exhibits constant,increasing, or diminishing returns to scalea) For an output level of 40 units, calculate the marginal rate of technical substitution between points A and B. b) Also for an output level of 40 units, calculate the marginal rate of technical substitution between points D and E
- Given the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. Find the profit function π(K,L) and simplify Find the first order conditions to maximize the profitDistinguish between the Marginal Rate of Technical Substitution and Elasticity of Substitution in productionGiven the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. a) Find the profit function π(K,L) and simplify b) Find the first order conditions to maximize the profit c) Find the value function for L and K, i.e the functions L* = L*(p,r,w) and K* = K*(p,r,w) and simplify. What is the meaning of the value functions d) Find the best production quantity and the maximum profit, i.e Q*(P,r,w) and π*(P,r,w) simplify results
- Define and then derive the expression for the marginal rate of technical substitution.Consider the following production function: y = lnx1 + lnx2, where x1>0, x2>0. Is it homogenous? Is the input requirement set monotonic and convex? Find its elasticity of substitution.Suppose that a firm can not give up one input in an exchange for the other and still maintain the same level of output. Calculate the elasticity of substitution in this case and elaborate on your answer.
