Show that the production function f (x1, x2) = a In x1 + B In x2 has elasticity of substitution equal to one. a) Find the marginal rate of technical substitution MRTS,2, express it in terms of a ratio of x2 to x1, call this r = X1 b) Take logs on both sides, c) Find the derivative of In MRTS12 with respect to In r. The inverse of this quantity is the elasticity of substitution.

Show that the production function f (x1, x2) = a In x1 + B In x2 has elasticity of substitution equal to one. a) Find the marginal rate of technical substitution MRTS,2, express it in terms of a ratio of x2 to x1, call this r = X1 b) Take logs on both sides, c) Find the derivative of In MRTS12 with respect to In r. The inverse of this quantity is the elasticity of substitution.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.9P

See similar textbooks

Similar questions

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 factors
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 production function Q = 2(KL)0.5 c) What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit?
Consider the production function Q = 2(KL)0.5 What is the marginal product of labour and capital What is the marginal rate of technical substitution of labor for capital What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit?
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 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 scale
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.
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
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.
Given a Cobb-Douglas Technology specified as follows:f(x1, x2) = x1α x21−α 1. Find the marginal rate of technical substitution (MRTS)2. Derive the expression for Elasticity of Substitution
The marginal rate of technical substitution of L=2K means that the firm can substitute 2 units of capital for an additional 1 unit of labor in the market. True or false.
Describe the concept of the marginal rate of technical substitution