3. George's utility function for earning $W teaching classes and spending R hours on his research is u(W, R) = W3/4 R¹/4. George is underpaid ($16 per hour) and overworked (80 hours total per week). How should he divide his time in order to maximise his utility?
3. George's utility function for earning $W teaching classes and spending R hours on his research is u(W, R) = W3/4 R¹/4. George is underpaid ($16 per hour) and overworked (80 hours total per week). How should he divide his time in order to maximise his utility?
Economics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter20: Consumer Choice And Elasticity
Section: Chapter Questions
Problem 2CQ
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Step 1: Introduce the Concept of Utility Maximization
VIEWStep 2: Understand the Question
VIEWStep 3: Define the Variables and Constraints
VIEWStep 4: Express Earnings in Terms of Research Hours
VIEWStep 5: Substitute and Simplify the Utility Function
VIEWStep 6: Calculate the Derivative of the Utility Function
VIEWStep 7: Solve for the Optimal Research Hours
VIEWStep 8: Interpret the Result and Conclude
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