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Economics

Calculate the elasticity of substitution for the production function

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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 the production function Y=3x+2x2-0.1x3 Compute The APP and MPP
IV. Will can produce a higher grade, Gw, on an upcoming economic exam by studying. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, Gw = 2.5A0.36R 0.64. His roommate David's grade production function is G) = 2.5A0.25R0.75 a. What is Will's marginal productivity from studying supply and demand problems? What is David's? b. What is Will's marginal rate of technical substitution between studying the two types of problems? What is David's?
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.
What effect might a decrease in the demand for high definition televisions have on the short-run average total costcurve for this product?
Given the following data on input and output levels. Suppose the output price is $5 and input price is $10. Find the values of APP and MPP when X = 6: X 0 2 4 6 8 10 12 Y 0 100 250 450 600 700 750 50 and 150 6 and 200 100 and 75 75 and 100
If the average cost function of a good is 15 AC = +20 + 11 '이 find the fixed costs and an expression for the marginal cost function. The fixed costs are (Type a whole number.) The expression for the marginal cost function is (Simplify your answer. Type an expression using Q as the variable.)
Input either "increase" or "decrease" where relevant: An increase in the prices of inputs will cause the equilibrium price to ....... and the equilibrium quantity to .....
b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ Kß where Q represents total product, L represents labour units, K represents capital units, A is some fixed constant representing technology and a and B are fixed parameters. Show that if a + B> 1 there is increasing returns to scale. Also show that the output elasticities with respect to labour and capital are constants and equal to a and B, respectively.
BJO Ⓒ4 f(X₁, X₂) = (x₁² + X₂²) & 0
The Constant Elasticity of Substitution (CES) production function is a flexible way to de- scribe how a firm combines capital and labor to produce output, allowing for different levels of substitutability between the two inputs. The elasticity of substitution, denoted by σ, measures how easily the firm can substitute capital for labor (or vice versa) while maintaining the same output level. The parameter p is related to the elasticity of substi- tution by the formula σ = 1/(1 - p). Now, let's consider a firm that operates for two periods (t and t + 1) and produces output according to the CES production function: F(KN)=[αK² +(1−a]N₁°]¹/º, 0
Consider the "Cobb-Douglas" production function given by Y = AKº L¹-a where A> 0 and 0 < a < 1. Which of the following is FALSE? The marginal product of capital is positive The marginal product of labour is positive There is diminishing returns to capital O There is decreasing returns to scale