Over the past year, total factor productivity grew 4%, capital grew 3%, and the labor supply grew 2%. If the elasticities of output with respect to capital and labor are 0.4 and 0.6, respectively, how much did labor productivity grow? 6.6% 6.4% 4.4% 4.6%
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- Over the past year, output grew 9%, capital grew 3%, and labor grew 7%. If the elasticities of output with respect to capital and labor are 0.4 and 0.6, respectively, how much did productivity change in percent terms (approximately)? (Submit your answer with up to two decimals, i.e., -10.22 for -10.22% and 11.44 for 11.442%.)?3) Over the past year, total factor productivity (TFP) grew 0.025, capital grew 1.5%, and labor grew 0.015. If the elasticities of output with respect to capital and labor add to 1, how much did output grow? (The growth rate of output is the sum of i) the growth rate of TFP, ii) the product of capital's share of output and capital growth, and iii) the product of labor's share of output times labor growth.) A) 1% B) 2% C) 3% D) 4% E) 5%Find the elasticity of scale and the elasticity of substitution for the CES production function (x1; x2) = (x1rho + x2tho 1/P, where 0 * p > !!!
- Find the elasticity of scale and the elasticity of substitution for the CES production function: 1 1 f(x₁, x₂) = (x³ + x2)³. Solution: We first calculate the marginal products: 2 fx₁ = 3 + = x1fx1 -+ 2 2 10 - ² ( x² + x ) ( + x^²) = ( + + + + ² ) 15 ²0 x² -2/3 x₂ + x2fxz Elasticity of scale = _1₁_+_*__*(+)´<°¸«d«)*;»_ f(x1, f(x1, ‹2)² = -2/3 r2/3 = TRS = t (where TRS = =t). ⇒ r = t³/² ⇒ ln(r) = ln (t) and o = -2/3 dln (r) dln (t) To get elasticity of substitution, we first need TRS and denote r = 1 x3 X1 TMS - F (+4+2)0 = fx₁ fx₂ 2 1 + x²) x₂² MIN x2 3 -2/3 (x² -2/3 2 2/3 2/3 x1 -2/3 = r²/3 x¹/3 + 1/3 = 1.For a specific production function, the associated Average Product function is (AP=) 12 L -0.2 L2 and the associated Marginal Product function is (MP=) 24 L-0.6 L². Calculate the "point" version of the elasticity of Output with respect. to labor (Eq,L) when labor is (L=) 35 units. Use the template provided to classify the value calculated.Imagine you own a business firm with a friend of yours. During the first quarter you come up with the following information that: • Output elasticity of Capital is 0.2 • Output elasticity of Labour is 0.8 • Rate of Technological advancement is 12 a) What kind of business firm is the one that you own? Mention 2 of its characteristics. b) Derive the marginal productivity of capital and labour, by means of Cobb- Douglas production function. c) If Y = F (K, L) where K= 1000 and L= 400, determine the values of MPx and %3D MPL.
- *Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.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.(b) Identify the wage-rental ratio in a diagram with k on the horizontal axis and y and W(k) on the vertical axis. (c) The elasticity of substitution in production is defined as: FLFK OKL = F(K,L)FLK dk w Show that the elasticity of the (w) function, defined as is equal to oKL: dw k
- 1. If the estimated Cobb-Douglas production function is Q = 10K0408 a. What are the output elasticities of capital and labor? If the firm increases only the quantity of capital or only the quantity of labor used by 10%, by how much would output increase? ( b. What type of returns to scale does this production function indicate? If the firm increases at the same time both the quantity of labor and the quantity of capital used by 10%, by how much would output increase? (Assume that tighter immigration laws cause a reduction in the supply of agriculturalworkers and this leads to higher wages in the sector. Dean’s Fruity Produce Ltd, afarm in Leicestershire, uses two inputs to harvest its output – machines (capital) andagricultural workers. Dean, the managing director of the company, has employedKarishma (a brilliant statistician) and she has estimated that the business’s long-runwage elasticity of labour demand is -1.7. Using isoquant/isocost analysis, explain the possible impact of the higher wages on the output level, total cost of production and input-factor mix of this business in boththe short and long-run and how would your answer change if Karishma had estimated that the long-run wageelasticity of labour demand was -0.4? (1000 words)Calculate the elasticity of substitution for the production function