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- i) Derive the output elasticity of labour for the following further alternative production function: InY = c + aK +BL ii) Suppose ß = 0.5 and other factors are fixed, explain the percentage change in output due to a unit change in labour.i) Derive the output elasticity of labour in the following alternative production function: Y = c + alnk + ßlnL ii) Suppose B = 0.5 and other factors are fixed, explain the unit change in output due to a percentage change in labour.Calculate the elasticity of substitution for the production function
- b) Given the following Constant Elasticity of Substitution production function, show whether or not it is homogeneous, and the scale it exhibits. Q=[L² + K³]73Given the following Constant Elasticity of Substitution production function, show whether or not it is homogeneous, and the scale it exhibits. Q= [L^2 + K^3]^2/3What is the marginal Physical Productivty (MPP) of the inputs given the function Q= 18x21+2x1x2+2x22 ?
- b) Given the following Constant Elasticity of Substitution production function, show whether or not it is homogeneous, and the scale it exhibits. Q= [L² + K³]3Q = 4L + 8K Q = 50K04L0.6 Q = [K0510.5]3 i) Calculate the marginal products of labor and capitalConsider 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.
- Consider the following production function: x = f0.K) = A e°k where xis the output e is the labour input, kis the capital input, and A, bare positive constants. (a) Set up the cost minimization problem and solve for the first order conditions using the Lagrange Method. Let wbe the wage rate and rthe rental rate of capital. (b) Using your answer in (a), find how much labour and capital would the firm use to produce x outputs, given wage rate wand rental rate of capital ? what are these functions called? (e) Using your answer in (b), find the minimum cost it takes to produce xoutputs, What is this function called?Consider the following production function: q = 9LK + 6L² – Assuming capital is measured on the vertical axis and labor is measured on the horizontal axis, determine the value of the marginal rate of technical substitution when K= 30 and L= 10. MRTS = -. (Enter a numeric response using a real number rounded to two decimal places.) 20 tv MacBook Air F6 FB 10 F3 23 2$ & з 4 6 7 8 { [ E Y U P D F G J K > C V N M command option - .. .- BTake a Cobb-Douglas production function, find its Elasticities w.r.t output and Elasticity of Substitution with the help of partial derivatives.