The individual's utility function has the following form: U(C, L) = 5+ CL Here C indicates the consumption good and L the leisure. The individual has non-labour income R and Lo hours that can be used to work (h) or leisure. P = 1 is the numeraire. (a) Derive the Marshallian labour supply h*. (b) Derive the Marshallian elasticity of labour supply with respect to wages nм. (Note: this is a function of w, h and R) (c) Derive the Hicksian labour supply ĥ. (d) Derive the Hicksian elasticity of labour supply with respect to wages H. (Note: this is a function of w, h and Ū) (e) Assuming that w= 1, R 8 and Lo = 24: • Calculate the values of h* and ĥ (Hint: to do so, calculate before the optimal level of expenditure and of the utility.) What do you notice? • Calculate the values of NM and 7H; comment and compare the sizes of the elasticities • Verify that the Slutsky equation holds (recalling that NM = NH + whnRo) Ro

The individual's utility function has the following form: U(C, L) = 5+ CL Here C indicates the consumption good and L the leisure. The individual has non-labour income R and Lo hours that can be used to work (h) or leisure. P = 1 is the numeraire. (a) Derive the Marshallian labour supply h. (b) Derive the Marshallian elasticity of labour supply with respect to wages nм. (Note: this is a function of w, h and R) (c) Derive the Hicksian labour supply ĥ. (d) Derive the Hicksian elasticity of labour supply with respect to wages H. (Note: this is a function of w, h and Ū) (e) Assuming that w= 1, R 8 and Lo = 24: • Calculate the values of h and ĥ (Hint: to do so, calculate before the optimal level of expenditure and of the utility.) What do you notice? • Calculate the values of NM and 7H; comment and compare the sizes of the elasticities • Verify that the Slutsky equation holds (recalling that NM = NH + whnRo) Ro

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure. U(c,l) = lnC + 4lnl Queston: Show that the Slutsky equation holds for this worker
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d. Based on both the consumption-leisure optimality condition obtained in previous part (Based on both of the two first-order conditions, construct the consumption-leisure optimality condition) and on the budget constraint, qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relationship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes. in / affect the relationship (shift it outward, shift it inward, or impossible to deter mine). Briefly describe the economics of how you obtained your conclusions.
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assume the following labor supply curves: 1. N = C + .64 W -2.33 I + 0.08 K 2. N = C + 1.33 W - .59 I - .28 K 3. N = C - 1.11 W - .59I - .28K a. Determine whether leisure is inferior in the 2nd labor supply curve. b. which if any of the above three equations represent back-bending labor supply curves? justify your answer. c. which if any of the above three labor supply curves is inconsistent with theory? justify your answer.
Assume the following production function (photo aswell) q = [0.3k^(-1)+ 0.7l ^(-1)] ^(-1) a) Determine the rate of technical substitution, RTS. b) Determine the elasticity of substitution. c) What would happen to the capital intensity if the relative factor price w/v were to increase by 10%? d) If the elasticity of substitution were higher than what you calculated in (b), would the effect of a 10% increase in the relative factor price w/v on the capital intensity be higher or lower than what you calculated in (c)? Explain your reasoning.
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Cowles Foundationfor Research in Economicsat Yale UniversityCowles Foundation Discussion Paper No. 2021ARE WE APPROACHING AN ECONOMIC SINGULARITY?INFORMATION TECHNOLOGY AND THE FUTUREOF ECONOMIC GROWTHWilliam D. NordhausSeptember 2015An author index to the working papers in theCowles Foundation Discussion Paper Series is located at:http://cowles.yale.edu/This paper can be downloaded without charge from theSocial Science Research Network Electronic Paper Collection:http://ssrn.com/abstract=2658259Electronic copy available at: http://ssrn.com/abstract=2658259Are We Approaching an Economic Singularity?Information Technology and the Future of Economic GrowthWilliam D. Nordhaus1September 1, 2015AbstractWhat are the prospects for long-run economic growth? The presentstudy looks at a recently launched hypothesis, which I label Singularity.The idea here is that rapid growth in computation and artificialintelligence will cross some boundary or Singularity after whicheconomic growth will…
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