1. Suppose we are given a production function: q = 10.5 * k0.7. a. Does this production function exhibit constant, increasing, or decreasing returns to scale? b. Please derive the marginal rate of technical substitution RTS (1 for k or k for 1, either one is fine) c. Please derive the elasticity of substitution o.

1. Suppose we are given a production function: q = 10.5 * k0.7. a. Does this production function exhibit constant, increasing, or decreasing returns to scale? b. Please derive the marginal rate of technical substitution RTS (1 for k or k for 1, either one is fine) c. Please derive the elasticity of substitution o.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A firm has the production function f(x, y) = x®y0.3, where a>0.7. This firm has Select one: a. decreasing returns to scale and increasing marginal product for factor x and y. b. None of the above. c. increasing returns to scale and diminishing marginal product of factor x. d. constant returns to scale. e. decreasing returns to scale and diminishing marginal products for factor y.
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.
Suppose that a firm has a production function given by: q= 10 L² K. The firm has 10 units of capital in the short run. Which of the following will describe the marginal product of labor (MPL) for this production function? Select one: a. Constant Marginal Returns to Labor b. Increasing Marginal Returns to Labor O c. Decreasing Marginal Returns to Labor
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1. A firm’s production function is Q = L1/2 K1/2 They have 16 units of capital (which is fixed in the short-run). The unit cost of labour is 2 and the unit cost of capital is 4. They receive an order of 4. a) Is the cost of fulfilling the order lower in the short- or long-run? Why is this the case?
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The elasticity of substitution of a Cobb-Douglas production function is constant alongthe whole range of any isoquant, and is equal to 1. Can you show this property that the elasticityof substitution is equal to one everywhere? Is the elasticity of substitution for a CES (ConstantElasticity of Substitution) production function the same?Kindly explain the answer to me.
Consider a short run production function q = cL+K where the value for c=3, using L units of labour and K units of capital. a) Compute the marginal product of labour. b) Does the production function exhibit decreasing, increasing or constant returns to scale? Explain your answer.