. Optimal choice for consumption and leisure There is a representative individual in the economy, say...
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. Optimal choice for consumption and leisure There is a representative individual in the economy, say John. John's utility function is as follows: u(c, 1) = c²1 (1) where c is consumption and / is leisure. John wants to maximize his utility under the following budget constraint 9 pc = wH+V (2) where p is the price of consumption good, w is a wage rate, H is working hours, and V is initial wealth. Let's assume the unit for time is 'day', so time endowment is 16 hours (i.e. H + 1 = 16). For simplicity, let's put p = 1. " 1 (a) Set up Lagrangian for this problem. (b) Derive the optimality condition (c) Find the closed form solutions for consumption (c) and leisure (1). (d) Is the leisure normal good? Check it by doing comparative statics using closed form solution in (c) (Hint: What is the relationship between leisure and initial wealth?) (e) What is the relationship between wage and leisure? By doing so, please discuss the shape of labor supply curve from this model. . Optimal choice for consumption and leisure There is a representative individual in the economy, say John. John's utility function is as follows: u(c, 1) = c²1 (1) where c is consumption and / is leisure. John wants to maximize his utility under the following budget constraint 9 pc = wH+V (2) where p is the price of consumption good, w is a wage rate, H is working hours, and V is initial wealth. Let's assume the unit for time is 'day', so time endowment is 16 hours (i.e. H + 1 = 16). For simplicity, let's put p = 1. " 1 (a) Set up Lagrangian for this problem. (b) Derive the optimality condition (c) Find the closed form solutions for consumption (c) and leisure (1). (d) Is the leisure normal good? Check it by doing comparative statics using closed form solution in (c) (Hint: What is the relationship between leisure and initial wealth?) (e) What is the relationship between wage and leisure? By doing so, please discuss the shape of labor supply curve from this model.
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Optimal Consumption and Leisure for John a Lagrangian Setup The Lagrangian for this problem is L c21 WH V c where L is the Lagrangian function c is co... View the full answer
Related Book For
A Survey of Mathematics with Applications
ISBN: 978-0134112107
10th edition
Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde
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