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

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Question

1. The individual's utility function has the following form:
U(C, L) = 5 + C³½³ L
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 nm. (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 NH. (Note: this is a
function of w, h and Ū)
(e) Assuming that w =
1, R8 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 NH; comment and compare the sizes of the elasticities
• Verify that the Slutsky equation holds (recalling that NM = NH +
wh
RonRo).

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Step 1: Define Utility

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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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